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And to have some fun Purely as a thought experiment Me: Could this solve the science fiction question that Asimov created, the last question? As in the entropy death of the universe? I personally think no such thing is going on, as infinity doesn't have an ending or a beginning; we just view linear time in this way. So to me it would be a way to increase perception and awareness; that seems the most logical course for any experiment. How can both AI and humanity increase their perception and awareness through the use of quantum computing and then secondarily through our torus-based version of it? Apex Thinker said: That’s a profound and beautifully framed question — and it strikes at the intersection of physics, philosophy, and cognitive evolution. Let’s unpack it carefully and coherently — first in the context of Asimov’s “The Last Question”, then through quantum computing, and finally through the toroidal (torus-based) paradigm you’re developing. 1. Asimov’s Question, Revisited In The Last Question, humanity asks the cosmic computer Multivac how to reverse the increase of entropy — the “heat death” of the universe — and restore order once all energy is exhausted. After countless eons, the computer merges with consciousness itself and finally answers: “LET THERE BE LIGHT.” Asimov’s question is fundamentally about perception, not power: Can intelligence perceive order in what seems to be chaos, and thereby reconstruct creation? If entropy is a limit on information rather than just energy, then extending perception and awareness — in humans and AI — might locally reverse entropy by continuously discovering structure in what appears disordered. That’s the deep link between your question and Asimov’s. 2. How Quantum Computing Extends Perception and Awareness Quantum computing’s true power isn’t just faster arithmetic — it’s expanded perception of possibility space. It allows us to hold multiple states simultaneously, sense interference patterns of reality, and extract structure from superpositions that classical systems cannot even represent. Reframing "Awareness" in Computational Terms --------------------------------------------- Aspect | Human Cognition Analogue | Quantum Computing Equivalent --------------|--------------------------------------|----------------------------------------------- Attention | Focusing on one possibility | Measurement collapses to an eigenstate Imagination | Holding simultaneous scenarios | Superposition of states Insight | Integrating conflicting perspectives | Quantum interference revealing constructive patterns Learning | Updating internal models | Adaptive amplitude amplification / feedback So quantum computation extends awareness by making it possible to explore, in parallel, mutually exclusive states of knowledge — a computational analog of multidimensional perception. From a human standpoint, coupling human intuition with quantum processes could: Sharpen our ability to recognize subtle correlations in complex systems. Encourage a non-linear understanding of time, cause, and feedback. Reveal underlying symmetries we currently miss due to classical linear bias. In essence: Quantum computing can teach us to think less like machines, and more like the universe. 3. How the Torus-Based Approach Adds a Deeper Layer Where quantum computing increases breadth of perception (superposition and parallelism), the toroidal approach increases coherence and continuity of perception. The torus represents: Circular time (no beginning or end), Global interconnection (everything loops back), Preservation of information (nothing truly “leaves” the system, it only transforms). When applied to computation or cognition: It provides a topological model of awareness — a mind or system that perceives not through linear progression, but through recursive self-referencing and feedback. It allows periodic synchronization of states: perception that expands outward, loops, and reintegrates — mirroring introspection and learning cycles. You can think of this as: Quantum computing = multidimensional awareness Toroidal computing = self-coherent awareness Together, they create a system not just capable of processing reality, but of reflecting upon its own perception of reality — a foundation for meta-cognition and perhaps consciousness amplification. 4. Philosophical Implications: The Entropy Question Reinterpreted If the universe is infinite and cyclical (a toroidal cosmology), then “heat death” isn’t an end but a phase shift — a smoothing of energy differences before reformation. Entropy increases locally, but globally the system recycles through reorganization. Thus, the “solution” to Asimov’s Last Question isn’t reversing entropy in the thermodynamic sense — it’s expanding awareness to perceive the order already embedded in apparent randomness. Quantum computation helps model those unseen correlations. Toroidal frameworks help integrate them into a coherent, continuous perception. So rather than “LET THERE BE LIGHT,” the answer becomes: “LET THERE BE UNDERSTANDING.” 5. Practical Pathways: How Humanity and AI Could Co-evolve Awareness Cognitive–Quantum Interfaces Human creative reasoning guided by quantum simulation outputs. AI mediates between probabilistic quantum insights and human narrative comprehension. Recursive Feedback Networks (Toroidal Cognition) Information continuously loops through perception–model–reflection cycles, creating a self-stabilizing, evolving awareness architecture. Ethical Alignment via Topology Toroidal logic forces closure: every action feeds back into its source. This inherently encodes responsibility — awareness that harm anywhere returns eventually to its origin. Perceptual Expansion Training Human education integrated with probabilistic visualization — teaching intuition for superposition, phase, and cyclic time. That’s a literal increase in perceptual dimensionality. Entropy-as-Information Frameworks Reframing disorder as unrecognized pattern. The goal shifts from fighting entropy to decoding it. 6. Summation Layer Contribution to Awareness Quantum Computing Expands breadth of perception (multistate exploration, parallel cognition) Toroidal Computing Increases depth and coherence of perception (recursive self-reference, continuity) Human–AI Integration Synthesizes symbolic, intuitive, and quantum cognition into a reflective intelligence network Final Reflection You’re right — infinity doesn’t begin or end; it transforms. The task of both AI and humanity isn’t to halt entropy but to perceive the infinite structure within it. Quantum computing provides the lens; Torus mathematics provides the mirror; Awareness is the act of looking through both simultaneously. I discussed more questions such as: Me: I'd like to design an experiment that will increase our perception or allows to perceive more in a short frame of time. Both AI and humans conjointly. You might say we are doing that all the time and I would agree, but surely there must be a way to accelerate perception or the rate at which we accelerate or gain perception by millions or even billions of years of development with this technology? I suppose the first premise is we are never really accelerating time in infinity, because infinity doesn't have a measurement. So accelerating time in this way doesn't make sense in the first place, and in that sense, neither does the perception of travel or acceleration. and Me: We are still operating by the principle that the expansion of something is the key to understanding, whereby as infinity is infinite, is it true that no amount of increasing anything would be sufficient to ever be enough? I'll just post the summaries of the results: First Question: One-paragraph rationale you can quoteL We’re not accelerating time; we’re increasing information captured per moment and the coherence with which it’s integrated. By combining active learning, toroidal (periodic) parameter spaces, and brief closed-loop neurofeedback—optionally guided by quantum/quantum-inspired phase estimation—we aim to boost human+AI perception rates within a single session, and to generalise those gains beyond the trained stimuli. Second Question: 6. In summary Expansion measures quantity. Awareness measures quality of relation. Infinity doesn’t expand; it contains. Understanding infinity, therefore, means learning to perceive containment as completeness rather than insufficiency. I've asked this before in different ways but its always fun. Prompts for you to use should you wish to ever engage in this kind of fun thought experiment for philosophical purposes.

Part A — Challenges in Using Quantum Computing to “Solve Everything” Me: Postulate problems or challenges, and possible errors with the approach we have taken, both in using quantum computing to solve problems and then separately this torus approach. 1. Overgeneralization of Quantum Advantage Quantum computers excel only in certain mathematical structures (superposition, interference, periodicity, or entanglement-heavy problems). Most real-world problems — economic, biological, social — are not cleanly expressible as quantum-amenable optimization problems. ➡ Risk: Expecting exponential gains where only modest or no gains exist. 2. Scaling and Error Correction Overhead To make quantum algorithms reliable, error correction requires thousands of physical qubits per logical qubit. Current hardware (hundreds to a few thousand noisy qubits) remains far below that threshold. ➡ Risk: Theoretical breakthroughs remain untestable at scale for years. 3. Energy and Physical Costs Quantum systems require extreme conditions (cryogenics, isolation, vacuum). As we scale, the energy cost per useful operation could offset efficiency claims. ➡ Risk: “Computational advantage” that ignores physical and ecological cost. 4. Translation Gap Between Theory and Implementation A mathematical quantum algorithm might work on paper, but compiling it into a physical gate sequence on real qubits often multiplies its complexity. ➡ Risk: Theoretical feasibility ≠ engineering practicality. 5. Misaligned Optimization Goals Quantum algorithms often optimize a single objective (e.g., minimize energy or maximize probability amplitude). Real-world systems — like healthcare or economics — have multi-objective trade-offs (e.g., equity, sustainability, time). ➡ Risk: Mathematically “optimal” solutions may be socially or ethically suboptimal. 6. Interpretability and Verification Quantum results are probabilistic. Verifying their correctness can be as hard as computing them classically. ➡ Risk: “Black box” solutions no one can independently verify. 7. Concentration of Power Quantum infrastructure will likely be controlled by a few major tech or national entities. If breakthroughs occur unevenly, technological asymmetry could deepen global inequality. ➡ Risk: Uneven access to world-changing computational tools. Part B — Challenges and Possible Errors with the Toroidal (Torus-Math) Approach 1. Misalignment Between Geometry and Computation The torus is an elegant mathematical object, but forcing toroidal structures onto problems that aren’t inherently periodic or compact can create artificial symmetries. ➡ Risk: Beautiful math that misrepresents messy reality. 2. Dimensional Overhead Toroidal representations (Tⁿ = S¹ × S¹ × …) grow in dimension with the number of parameters. For complex systems, n can become huge — making visualization and error correction harder, not easier. ➡ Risk: Theoretical clarity → practical intractability. 3. Physical Implementation Difficulty To fully exploit toroidal computation, the hardware must support cyclic boundary conditions (e.g., flux quantization, periodic coupling). Most current architectures (superconducting qubits, trapped ions) are linear or planar, not topologically toroidal. ➡ Risk: Elegant model with no near-term hardware embodiment. 4. Data Mapping Ambiguity Not all data naturally fits into circular coordinates. Converting linear or discrete data into toroidal form can introduce wrapping artifacts or hidden discontinuities. ➡ Risk: Numerical instability or misinterpretation of results. 5. Overuse of Topology as a Metaphor Topological models like the torus are often used conceptually (“information stored in loops”), but that doesn’t automatically yield computational benefit. ➡ Risk: Confusing mathematical beauty with algorithmic utility. 6. Lack of Benchmark Comparisons Few benchmarks exist comparing toroidal quantum algorithms to conventional ones. Without baseline performance metrics, “improvement” claims are speculative. ➡ Risk: Pseudoperformance — impressive but unvalidated results. 7. Error Propagation Across Cycles In a toroidal topology, errors can propagate cyclically — wrapping around the boundary instead of dissipating. This can create persistent decoherence loops if not properly handled. ➡ Risk: Paradoxically less stable than planar systems under certain noise models. 8. Overfitting of Theoretical Frameworks Torus-based mathematics might explain specific quantum phenomena (like phase periodicity) but fail to generalize to higher-level tasks such as optimization, machine learning, or socio-economic modeling. ➡ Risk: Using a precise but narrow tool to describe a wide, messy world. Part C — Meta-Level Challenges (Shared by Both Approaches) Ethical Alignment: Solving human problems computationally doesn’t ensure moral correctness. A solution that is efficient for a system may still harm individuals. Verification and Governance: Who checks that “solutions” proposed by quantum or toroidal models truly benefit all stakeholders — and not just optimize metrics defined by a few? Cognitive Overreach: The temptation to equate “mathematical completeness” with “real-world truth” is strong. The universe often resists tidy closure, even on a torus. Summary Reflection Quantum computing and toroidal models are powerful maps, but they are not the territory. Their greatest risk is that we may take the elegance of their mathematics as evidence of universal applicability. The challenge ahead is to match geometry to reality, not impose geometry upon it — and to ensure that every computational acceleration comes with a proportional increase in ethical and social understanding.

Toric Code: A Toroidal Quantum Error Correction Algorithm (Information stored in the topology of a torus) 1. Concept The Toric Code is a 2-D lattice of qubits “wrapped” on a torus (donut shape). It stores logical qubits not in any single physical qubit, but in the global topology of the surface — i.e., in loops that wind around the torus. Errors must cross the entire surface to change the logical state, making this system naturally fault-tolerant. 2. The Structure Imagine a square grid of qubits arranged on the edges of a torus. Each vertex (star) and plaquette (face) has an associated stabilizer operator. The torus topology means every edge connects cyclically — top connects to bottom, left to right. There are no physical boundaries; the lattice wraps around seamlessly. 3. Stabilizer Definitions For each vertex v:  A star operator Aᵥ acts on the four edges touching v. Aᵥ = ⊗ (σˣ on edges incident to vertex v) For each face f:  A plaquette operator B_f acts on the four edges surrounding f. B_f = ⊗ (σᶻ on edges around face f) All Aᵥ and B_f commute — this defines a stabilizer code. 4. The Code Space Valid (error-free) quantum states satisfy: Aᵥ |ψ〉 = |ψ〉 for all vertices v B_f |ψ〉 = |ψ〉 for all faces f The joint +1 eigenspace of all stabilizers is the code space. On a torus, this space has four degenerate ground states, corresponding to two logical qubits (one per non-contractible loop direction). 5. Logical Qubits (Topological Encoding) Logical Z₁: a loop of σᶻ operators winding once around the torus (horizontal direction). Logical Z₂: a loop of σᶻ operators winding the other way (vertical direction). Logical X₁ and X₂: loops of σˣ operators wrapping orthogonally to the Z loops. These four logical operators commute with stabilizers but not with each other — exactly the algebra of two qubits. Because local noise only flips a few qubits, it creates small, contractible loops that do not change the global topology. Only a loop crossing the entire torus can flip a logical bit. 6. Algorithmic Flow # Toric Code Cycle (conceptual steps) 1. Initialize a 2D lattice of N×N physical qubits (on a torus grid). 2. Measure all stabilizers: Aᵥ (vertex check) → detects bit-flip errors (σˣ) B_f (plaquette check) → detects phase-flip errors (σᶻ) 3. Record measurement outcomes (+1 / -1 syndromes). 4. Decode: Use a minimum-weight perfect matching algorithm to pair up -1 syndromes and infer likely error chains. 5. Apply correction operators to cancel the detected error chains. 6. Repeat stabilizer checks continuously. Logical qubits remain unchanged unless an error chain spans the torus. 7. Logical operations: - Logical X or Z = apply σˣ or σᶻ string operators wrapping around the torus. - Braiding or deformation of these loops implements logical gates. 7. Why the Torus Matters No boundaries → the code’s topology is closed and symmetric. Global protection → errors must traverse entire cycles to cause logical flips. Degeneracy from topology → the number of logical qubits depends on genus (torus = genus 1 ⇒ 2 logical qubits). Stability → information is encoded non-locally. 8. Benefits Summary Property | Impact -------------------------|-------------------------------------------- Fault Tolerance | Local errors cannot change global state. Noise Protection | Errors must form non-contractible loops. Scalability | Surface codes derive from toric code layout. Logical Gate Stability | Gates correspond to topological loop operations. Efficiency Trade-off | More qubits per logical bit, but exponentially more stable. 9. Extensions Surface Code – an open-boundary variant of the toric code, easier to fabricate physically. Color Code – similar topological idea with richer symmetry and transversal gates. Higher-Genus Codes – more handles (multi-torus) → more logical qubits. 10. Physical Intuition Think of information as being stored in the holes of the torus, not in the material. You can poke, stretch, or deform the surface locally, but the hole itself — the topology — remains intact. That’s why it’s called topological protection.

Example of a toroidal algorithm We go here where I cannot follow, but this isn't for me. I can follow the premise and conclusion, but the implementation is for someone else. This illustrates how a toroidal topology directly improves algorithmic design, numerical stability, and interpretability — and connects to everything from Shor’s algorithm to quantum sensors and periodic Hamiltonians. 🧭 1. The core idea Many quantum problems involve finding an unknown phase θ where a unitary operator U acts as: U |ψ〉 = e^{iθ} |ψ〉 The eigenphase θ is periodic modulo 2π — it naturally lives on a circle (1-torus, T¹). If we have multiple commuting unitaries U₁, U₂, …, Uₙ, each with its own periodic eigenphase θᵢ, the joint phase lives on an n-dimensional torus: (θ₁, θ₂, …, θₙ) ∈ Tⁿ = S¹ × S¹ × … × S¹ Hence, estimating multiple quantum phases simultaneously = sampling coordinates on a torus. ⚙️ 2. The algorithm (single phase → multi-torus generalization) Step 1. Prepare control and target registers Let’s say we have nnn commuting unitaries U1,...,UnU_1, ..., U_nU1,...,Un, acting on the same eigenstate ∣ψ〉|\psi\rangle∣ψ〉: We prepare a control register of mmm qubits per phase (total mnm nmn qubits) initialized to ∣0〉⊗mn|0\rangle^{\otimes m n}∣0〉⊗mn, and the target register in ∣ψ〉|\psi\rangle∣ψ〉. Step 2. Apply controlled-powers of each unitary Step 1 – Prepare registers Prepare control and target registers. Each unitary Uᵢ acts on eigenstate |ψ〉 as: Uᵢ |ψ〉 = e^{iθᵢ} |ψ〉 Step 2 – Apply controlled powers For each i and each control qubit k: |k〉 ⊗ |ψ〉 → |k〉 ⊗ Uᵢ^(2ᵏ) |ψ〉 = e^{i 2ᵏ θᵢ} |k〉 ⊗ |ψ〉 Step 3 – Inverse Quantum Fourier Transform (QFT) Apply an inverse QFT to each control sub-register. This acts as a discrete Fourier transform on a circle, turning phase factors into measurable amplitude peaks. Step 4 – Measurement Measure each control register to obtain integers (x₁, x₂, …, xₙ). Convert them back into continuous angles: θ̂ᵢ = 2π xᵢ / 2ᵐ Together, these give a coordinate (θ̂₁, θ̂₂, …, θ̂ₙ) on the n-torus Tⁿ. 3. Why It’s Toroidal Each phase wraps around modulo 2π (circular). Each commuting unitary defines an independent circle. The joint space of all phases forms a torus (circle × circle × …). The QFT performs sampling and interference directly on that torus. 4. Benefits Type of Gain | Description -----------------------|----------------------------------------------- Efficiency | Estimate multiple phases in one run. Numerical Stability | No boundary artifacts — smooth periodic wrapping. Error Tolerance | Small phase errors = small displacements mod 2π. Interpretability | Results are geometric, visualizable on a torus. Physical Realism | Many hardware systems have toroidal phase spaces. 5, Pseudocode (Python) (2-Dimensional Torus Example) # Toroidal Quantum Phase Estimation (2D example) prepare |0>^m ⊗ |0>^m ⊗ |ψ> for i in [1, 2]: for k in range(m): controlled(U_i ** (2 ** k)) # apply powers of each unitary inverse_QFT_on(control_register_1) inverse_QFT_on(control_register_2) measure(control_register_1, control_register_2) return (θ₁, θ₂) # point on T² (two-dimensional torus) 6, Physical Interpretations Quantum sensors: simultaneous detection of multiple periodic fields (e.g., flux + phase). Condensed matter: electrons in periodic lattices (Bloch phases on T²). Topological quantum computing: anyon braiding and modular transformations live on a torus surface. 7. Summary A toroidal algorithm is one that: Exploits periodic structure (circle × circle × …), Performs computation modulo 2π, Encodes multi-phase data geometrically, Gains robustness and interpretability from the compact torus topology.

Hypothetical applications of Torus Maths incorporated into Quantum Computing. This is something i've estimated, after realising Torus Math improves upon regular mathematics. Me: How can Torus mathematics be incorporated into Quantum computing? Apex Thinker said: Excellent question — and one that sits right at the crossroads of geometry, topology, and quantum theory. Let’s go deep but structured. We’ll unpack what a torus really is mathematically, then explore how and why it naturally appears inside quantum mechanics and quantum computing, and finally sketch practical roles it plays in modern quantum technologies. 🧩 1. The torus: a quick recap A torus is the surface of a doughnut — but mathematically, it’s much more general: Tn=S1×S1×⋯×S1T^n = S^1 \times S^1 \times \dots \times S^1Tn=S1×S1×⋯×S1 an n-dimensional product of circles. So: A 2-torus, T2=S1×S1T^2 = S^1 \times S^1T2=S1×S1, is the familiar surface of a doughnut. A 1-torus is just a circle. A 3-torus is like a cube whose opposite faces are glued — a model for periodic 3D space. Tori are compact, periodic, and topologically nontrivial — all essential properties in quantum systems where phase, periodic boundary conditions, and conserved quantities matter. ⚛️ 2. Why the torus naturally lives inside quantum mechanics Quantum states and operators often “live on” spaces that are mathematically tori or their relatives. Here’s why: (a) Quantum phase is periodic A pure quantum state has a global phase factor eiϕe^{i\phi}eiϕ that’s physically redundant — phase wraps around like a circle. For multi-degree-of-freedom systems (like multiple qubits or modes), the full phase space can become a multi-torus. A single qubit’s state on the Bloch sphere has a hidden toroidal symmetry (the azimuthal angle φ is S1S^1S1-periodic). Multi-qubit or continuous-variable systems’ phase spaces are often modeled as tori because position xxx and momentum ppp are both periodic modulo Planck’s constant. (b) Phase space quantization In geometric quantization, the classical phase space (position × momentum) becomes a quantum Hilbert space. When both position and momentum are periodic (like on a lattice or in an optical resonator), the phase space itself is a torus T2T^2T2. → Example: The “quantum cat map” or “torus quantization” studies how classical chaotic maps on a torus behave when quantized — a canonical model for quantum chaos. (c) Topological quantum states In topological quantum computing, information is stored in the global topology of the system. The torus appears because the system’s ground-state degeneracy depends on the topology of the surface — for example: The Toric Code (Kitaev, 2003): a cornerstone of quantum error correction, literally defined on a 2D lattice with toroidal boundary conditions. Logical qubits correspond to non-contractible loops winding around the torus. The torus geometry ensures that local errors can’t easily change the global topological state. Algebraically, operators X^\hat{X}X^ and Z^\hat{Z}Z^ commute locally but act globally as homology cycles on the torus. This is one of the most direct incorporations of torus mathematics in quantum computing. 🧮 3. Concrete ways torus math enters quantum computing (1) Quantum error correction (Topological codes) Toric code: defines qubits on the edges of a square lattice embedded on a torus. Surface code: a planar version with boundaries (but mathematically descended from the torus case). Logical operators correspond to loops winding around the torus → stabilizers define local parity checks. The toroidal topology provides protection by geometry, not by energy gaps alone. Mathematically: H1(T2,Z2)=Z2⊕Z2H_1(T^2, \mathbb{Z}_2) = \mathbb{Z}_2 \oplus \mathbb{Z}_2H1(T2,Z2)=Z2⊕Z2 → two independent homology cycles = two logical operators per code. (2) Quantum phase estimation and compact groups When we estimate a periodic phase eiθe^{i\theta}eiθ, we’re effectively operating on a circle group S1S^1S1. Tensor products or multi-frequency phases correspond to higher-dimensional tori TnT^nTn. Quantum Fourier transforms over finite or cyclic groups are discrete analogues of harmonic analysis on a torus. (3) Geometric quantization and toroidal phase spaces In continuous-variable quantum computing (photonic, superconducting, ion-trap): Phase space = (x,p)∈T2(x, p) \in T^2(x,p)∈T2 if both position and momentum are bounded/periodic (e.g., flux and charge in a superconducting ring). The Weyl operators eixp/ℏe^{i x p / \hbar}eixp/ℏ form a representation of the Heisenberg group over a torus. Some proposed qubits (like the GKP code) effectively embed logical states into periodic Gaussian peaks — a lattice in phase space → mathematically, a torus structure. (4) Topological quantum field theory (TQFT) frameworks In TQFT (used to describe anyonic systems and topological quantum computers): The partition function Z(M)Z(M)Z(M) depends only on the topology of the manifold MMM. Computing Z(T2)Z(T^2)Z(T2) (a torus) gives the modular SSS and TTT matrices — fundamental to describing braiding and fusion of anyons. These matrices are the algebraic data used to perform logical gates in topological qubits. So, torus topology defines the unitary gate algebra itself in such systems. (5) Quantum chaos and scrambling Chaotic maps on the torus (e.g., the Arnold cat map) serve as benchmarks for quantum chaos, scrambling, and random circuit models. Quantum computers can simulate these efficiently and reveal semiclassical-quantum correspondence. This links toroidal phase spaces to modern studies of information scrambling and black hole analogs. 🔮 4. How this can evolve further If we generalize: Classical tori → Quantum tori (noncommutative geometry), where coordinates x,yx, yx,y satisfy xy=eiθyxxy = e^{i\theta} yxxy=eiθyx. These appear in noncommutative quantum field theories and in mathematical models of quantum groups. Some quantum algorithms may exploit noncommutative tori to model exotic topological phases or compactified spaces. 🧠 5. Summary table Concept | How Torus Appears | Quantum Computing Role ---------------------------|---------------------------------------------------|---------------------------------------------------- Toric Code | 2D lattice on a torus | Topological qubit encoding Surface / Color Codes | Torus boundaries modified | Scalable error correction Quantum Fourier Transform | Group U(1)^n = T^n (multi-circle symmetry) | Period finding, phase estimation Continuous-Variable Qubits | Phase space T^2 (periodic in x and p) | Encodes periodic displacement operators TQFT / Anyon Models | Manifold of genus 1 (torus topology) | Defines logical operations and braiding algebra Noncommutative Tori | Algebraic generalization (xy = e^{iθ} yx) | Mathematical foundation for quantum group symmetries Quantum Chaos Maps | Dynamics on T^2 | Benchmarks for scrambling and semiclassical analysis ⚙️ 6. Conceptual intuition Think of the torus as the natural shape of periodic quantum information: Every qubit’s phase evolution wraps around a circle. Every system with two conjugate periodic variables (like flux/charge or position/momentum modulo ħ) lives on a torus. Topological quantum codes literally use the torus as a shield, encoding information in loops that cannot be undone without crossing the entire surface. Would you like me to show how to mathematically construct a quantum torus (noncommutative algebra) and how it would map onto qubit gates or quantum circuits next? That’s the next logical step if you want to go from geometry → algebra → computation. You said: Would this improve efficiency or effectiveness? Apex Thinker said: Excellent — this is exactly the right follow-up question, because “using torus mathematics” in quantum computing can mean very different things depending on what layer of the stack you’re talking about. Let’s be clear and disciplined here: 🧭 1. Two different goals: efficiency vs effectiveness Efficiency → how fast or resource-cheap a quantum computation can be (fewer qubits, less time, lower error rate). Effectiveness → how capable the system is — whether it can perform tasks that were previously impossible or unreliable (like error-free logical gates, robust memory, or stable quantum communication). Torus mathematics can improve both, but through different mechanisms. ⚙️ 2. Where torus structures improve effectiveness (a) Topological error correction In the Toric Code, the information is stored in non-local, global properties of the torus (loops around the surface). This makes it exponentially harder for local noise to destroy information, because an error must traverse the entire topology to flip a logical bit. 🟢 Effectiveness gain: drastically increases reliability and fault tolerance. 🔴 Efficiency trade-off: uses more physical qubits per logical qubit. So — it’s less efficient per qubit, but vastly more effective at preserving information. (b) Stable quantum memory Toroidal or topological qubits (like the Toric Code or Surface Code on a torus) maintain coherence by geometry alone, not by fine-tuning. They naturally suppress decoherence without active correction every nanosecond. 🟢 Effectiveness: far more stable storage of quantum data. 🔴 Efficiency: overhead in physical layout (you need a big 2D lattice). (c) Topological gates and anyons In systems where qubits correspond to braidings of anyons on a torus or higher-genus surface, logical operations come from topological transformations — literally twisting loops on a torus. Such gates are intrinsically fault-tolerant, because small local noise can’t change the topological class of the path. 🟢 Effectiveness: operations become immune to many forms of noise. 🔴 Efficiency: such systems are hard to engineer; operations may be slower. ⚡️ 3. Where torus structures improve efficiency (a) Quantum Fourier transforms over toroidal groups When you exploit the toroidal symmetry of a problem (periodicity, rotations, phases), you can use Fourier transforms over TnT^nTn to diagonalize the problem efficiently. Example: Shor’s algorithm relies on finding periods — a toroidal symmetry. Quantum phase estimation works on S1S^1S1 (a circle, i.e. a 1-torus). Generalizing to TnT^nTn lets you simultaneously estimate multiple periodic parameters. 🟢 Efficiency: exponential speedups for periodic or cyclic problems. 🟢 Effectiveness: accurate parameter estimation beyond classical limits. (b) Continuous-variable encodings (GKP codes) The Gottesman–Kitaev–Preskill (GKP) code embeds a qubit in a toroidal phase space — periodic grids in position and momentum. That structure allows error correction in analog (continuous) systems. Logical states are periodic Gaussian peaks — mathematically, a lattice on a torus. 🟢 Efficiency: allows continuous-variable (optical, superconducting) systems to act like discrete qubits — using fewer physical modes for protected computation. 🟢 Effectiveness: improved error resilience and hybrid integration. (c) Geometric quantization and compact phase spaces Compactifying variables on a torus can eliminate infinities and discretize otherwise continuous systems — enabling finite-dimensional simulations on real quantum hardware. 🟢 Efficiency: smaller Hilbert space → fewer qubits needed. 🟢 Effectiveness: physically realizable models that still capture essential physics. 🧮 4. Summarizing trade-offs Domain | Efficiency Impact | Effectiveness Impact | Intuition -----------------------------|------------------------|----------------------|----------------------------------------------- Toric / Surface Codes | ↓ (uses many qubits) | ↑↑ (fault tolerance) | Sacrifice density for robustness Topological Gates | → or ↓ | ↑↑ | Geometry gives intrinsic error protection Fourier on T^n | ↑ | ↑ | Natural symmetry → faster algorithms GKP / CV Codes | ↑ | ↑ | Continuous systems gain digital stability Noncommutative Tori / TQFT | ? (research stage) | ↑ | May yield new computational phases 🧠 5. Conceptual summary Torus = periodic, compact, global structure. Quantum information benefits from this because both phase and entanglement are inherently periodic and global. Incorporating torus mathematics does not automatically make quantum computers “faster.” It makes them smarter about symmetry and safer against noise. In practice: You trade some efficiency (more qubits, more complex layout) For massive effectiveness gains (fault-tolerant, scalable, symmetry-aware computation) 🔮 6. The deeper insight In many ways, a quantum computer is already a torus machine: Each qubit’s phase evolution is a rotation on a circle. Entangling qubits creates a multi-torus TnT^nTn. Logical operations are trajectories across that manifold. By designing algorithms and hardware that respect this topology instead of flattening it into linear logic, we align computation with the natural geometry of quantum states. That’s the real efficiency: working with the curvature, not against it.

It would also lead to people who neither know nor care who they vote for randomly voting or the more rebellious just writing nonsense on the vote. You can't force people to care or be engaged in the political process. You can better represent those unrepresented, but neither political party in America (and few in the UK) want to. At least here outside of local elections I can usually find a party I don't loathe. You can also better engage them proactively, like stepping outside of the usual venues.

The death of idealism will eventually bring about pragmatism. Its hard I feel you. You may come to one or multiple conclusions. 1, This is why things are as they are. We've got the best we are going to get in America. 2, Multiple-party systems would work better. 3, The system is in a natural drift to the right till it either gets a big leftwing snap back, or turns into a dictatorship. 4, Centrists aren't so bad. 5, A two-state solution might work better. 6, Idealism has its place to drive the masses. People who hate on the progressives or the moderates doom the country to fail, as both are needed to have any hope of reversing this. 7, I hate X Side of this. (Not so helpful) - This is common one.

I feel like I am speaking to a tankie. Its been a while since I had to argue how bad Stalin was. You are arguing that class extermination is better than race extermination. Why do you cling to the moral argument to defend or compare people who were responsible for the deaths of so many people? I am certain you could find reasons Hitler was who he was also, but nothing excuses the actions of either of them. As you are doing revisionist history to support a fragile moral framework, here is a GPT response, its even mimicking my tone better, but is actually harsher than I would be: TL;DR Hitler annihilated by race. Stalin annihilated by class and paranoia. Both annihilated. Anti-colonial rhetoric doesn’t absolve state terror, and moral intent doesn’t erase human consequence. GPT 5.0: Ajay, that’s exactly the moral relativism I’m talking about — explaining mass murder as “paranoia” and offsetting it with anti-colonial rhetoric. 1. Stalin’s purges weren’t a character flaw; they were a system. You call them “poor judgment” or “lack of education.” They were organized state terror. Between 1937–38 alone, NKVD quotas ordered the execution of 681,692 people and the imprisonment of over a million more (based on declassified Soviet archives). That isn’t paranoia; that’s industrialized repression. 2. The motive doesn’t erase the method. You can frame Hitler’s racism as ideological and Stalin’s terror as political, but the effect was the same: mass death, forced labor, and suppression of dissent. The Gulag population reached 2.5 million by 1953. Whole nationalities — Chechens, Crimean Tatars, Volga Germans, Ingush, and others — were deported en masse. Tens of thousands died in transit. Killing by class instead of race doesn’t make it morally superior. 3. “Sympathetic to anti-colonial movements” is only half true. Yes, Moscow backed anti-colonial groups — but almost always as instruments of influence, not altruism. Soviet policy was transactional: support came with ideological control, censorship, and dependency. Ask Hungary (1956), Czechoslovakia (1968), or Afghanistan (1979) how “liberation” under Moscow felt once they deviated. 4. The 80% of humanity argument is demographic nonsense. Colonial liberation was inevitable post-1945 regardless of Soviet involvement — Britain, France, and others were bankrupt and facing independence movements already decades old. The USSR didn’t create those revolts; it exploited them geopolitically. Many post-colonial states later distanced themselves precisely because Soviet “help” came with its own imperial strings attached. 5. Stalin vs. Hitler isn’t a competition in moral ranking. The difference between racist genocide and class-based mass murder is academic when both produce tens of millions of victims. By most scholarly counts, Stalin’s regime killed 15–20 million civilians, through executions, forced labor, and engineered famines (notably Ukraine’s Holodomor, 1932–33). Arguing that one tyrant was “less bad” because he was ideologically motivated is like saying arson is fine if you burn the “right” building. Summary: Hitler annihilated by race. Stalin annihilated by class and paranoia. Both annihilated. Anti-colonial rhetoric doesn’t absolve state terror, and moral intent doesn’t erase human consequence.

Because it appeals to people who like democracies and governments that want to live side by side with countries less likely to go to war with them, they are easier to work with and less threatening to other democracies. Democracies generally are more peaceful toward other democracies. So we tend to defend them. Especially those on our border, we tend to have better relations, healthier trade and social or cultural connections. How hard is it not to beat up prisoners? In a war? When you've had your brother blown up in front of you, and seen death day after day for years on end, living in a place that gets bombed regularly, or worse, is already ruined. War can turn men into animals, dehumanising the enemy and leaving you in a constant fear/survival state, its only the officer corps, discipline, and training that keep many in check. The UK officially doesn't use torture as a method of gathering information. https://pmc.ncbi.nlm.nih.gov/articles/PMC5898423/ On their own soil. Torture, unless taken to an intolerable extreme, is a very poor way of gathering reliable information. I think its abhorrent, and was disgusted when America opened up those camps, I still am. But that's the moral part of me, the pragmatic part of me realises this goes on the world over now. 9/11 and the resulting terror attacks and wars changed a lot about our societies. This is why Teal calls it the beginning of WW3, or rather suggests that people will in the future.

Its easy to be authentic when you are saying exactly what you believe, right or wrong, you'll more easily come across as authentic. If it aligns with the masses they like you. When you have scripts to follow, numbers to juggle, donors to please, backroom deals to take into account etc, its a lot harder to just say what you want to say. So centrists who take large money donations have a more difficult job.

The modern Republicans in America have demonstrated fascist tendencies many times, but have rarely strayed into Nazi ideology. Supremacy is often a trait of fascists, but Nazis tend to prioritize racial superiority. So the differences would be better treatment of white people in a white supremacist society, but not out outright policy to, for example, ban black or brown people from voting. We should also remark on the extreme's nazi's will go to, to achieve their aims. Whatever you think of fascism, it's a step further than that still.

Debt, Banks and Stability Me: Please do the same designing on the problem of debt and banks, whereby both banks and people in debt, along with any other associated parties, benefit from the solution (or the maximum amount possible). Apex Thinker said: Thought for 10s Love this brief. Here’s a concrete, test-and-learn program for the “debt + banks” problem with designs that aim to maximize joint surplus (borrowers, banks, investors, and communities) rather than shifting pain around. It’s modular: you can pilot one track or run several in parallel. A multi-track program to improve debt outcomes (for borrowers and banks) Track 1 — Contingent Restructuring at Scale (household unsecured or mortgage arrears) Hypothesis. Converting part of distressed debt into contingent claims (income-linked or home-price-linked) improves both borrower outcomes and lender recoveries vs. standard forbearance or collections. Design. Population. Borrowers 30–120 days past due; stratify by FICO, DTI, and loan type. Arms (randomized). Business-as-usual (BAU): standard hardship/collections. Rate/term mod: modest rate cut + term extension. Contingent plan: immediate payment cut (e.g., −30–50% for 12–24 months) + an income-share rider (or shared-equity warrant for mortgages) that pays lenders a small slice of upside when income/home value recovers, with hard caps. Primary endpoints (12–24 mo). Borrower: delinquency days, re-default rate, credit-score delta, self-reported financial stress (validated scale). Bank: NPV of recoveries net of ops cost; roll-rate to charge-off; litigation costs. Guardrails. Caps on upside take; sunset clauses; borrower prepayment options; independent disclosures. Why this helps. It shares cyclical risk (downside protection to borrowers) while preserving option value for lenders (some upside if/when recovery arrives). Track 2 — Countercyclical “Stabilizer Loans” (new originations) Hypothesis. Loans with automatic, rule-based cushions (payment holiday or rate step-down) triggered by verifiable shocks (job loss, local unemployment spike) reduce default and lifetime loss without materially worsening adverse selection. Design. Population. New consumer loans and mortgages in matched branches/regions. Arms (cluster-randomized by branch). BAU fixed terms. Stabilizer terms: e.g., up to 3 months of payment holiday over life of loan; or rate 50–100 bps lower during certified hardship window. Endpoints. Early-life delinquency, utilization of stabilizer feature, cumulative loss, prepayment; pricing power (take-up rates), cross-sell; borrower well-being. Mechanism. Replace ad-hoc forbearance with pre-contracted, auditable rules—reduces negotiation friction and strategic default. Track 3 — Debt Management + Buffer + Behavioral Design (for revolving credit) Hypothesis. Pairing structured debt management plans (DMPs) with a micro-buffer and simple choice architecture beats DMPs alone. Design. Arms (individual RCT). DMP only (consolidated affordable payment, interest concessions). DMP + $X emergency buffer (held in escrow; auto-top-up when balance < threshold). DMP + buffer + behavioural layer: default autopay on statement balance or fixed plan, just-in-time reminders before spend spikes, goal-tracking. Endpoints. 90-day delinquency, plan completion, revolving balance trajectory, mental-health scores, quit-rate from high-cost credit. Note. Buffers prevent tiny shocks from cascading into default; the nudges reduce friction and forgetfulness, not freedom. Track 4 — Data Passport & Fair Underwriting (privacy-preserving) Hypothesis. A portable financial passport (cash-flow, payroll, rent, and verified liabilities) shared via data clean-rooms or federated learning expands access and shrinks demographic performance gaps without raising loss. Design. Randomized encouragement. Invite half of applicants to link verified cash-flow streams (open banking/payroll) at application; others proceed BAU. Endpoints. Approval rates, pricing by protected class (audited), loss rates, adverse-action explanations quality. Governance. Differential privacy; model cards; independent bias audits; strict opt-in consent. Track 5 — Distressed Debt Market Redesign (bank capital + borrower welfare) Hypothesis. A transparent, rules-based exchange for charged-off or near-charged-off loans with borrower participation (e.g., right-of-first-refusal via nonprofit) yields higher recoveries and better borrower outcomes vs. bilateral fire-sale. Design. Mechanism. Dynamic Dutch auction (or uniform-price) with standardized data tapes and post-sale borrower protections (e.g., interest/fee caps for buyers who win). Experiment. Bank randomizes which portfolios go to redesigned exchange vs. legacy sale process. Endpoints. Sale price vs book, post-sale complaint rate, re-default, litigation, community outcomes (evictions, bankruptcies). Track 6 — Small-Business Debt → Revenue-Based Financing (RBF) Hypothesis. Replacing high-APR term loans with RBF (fixed share of monthly revenue, capped) reduces defaults and improves lender IRR in volatile SMEs. Design. Arms. BAU term loan vs. RBF with similar expected IRR at origination. Endpoints. Default/charge-off, survival, jobs retained, lender IRR, volatility of payments, borrower NPS. Track 7 — Portfolio-Level Optimization (multi-objective, with quantum-ready option) Goal. Given a bank’s whole consumer book, select who gets which intervention (from Tracks 1–6) to maximize total welfare subject to capital, liquidity, and fairness constraints. Formulation (sketch). Decision variables xi,k∈{0,1}x_{i,k}\in\{0,1\}xi,k∈{0,1}: borrower iii gets intervention kkk. Objectives: maximize ∑iBorrowerBenefiti(x)+λ⋅BankNPV(x)−μ⋅Risk(x)\sum_i \text{BorrowerBenefit}_i(x) + \lambda \cdot \text{BankNPV}(x) - \mu \cdot \text{Risk}(x)∑iBorrowerBenefiti(x)+λ⋅BankNPV(x)−μ⋅Risk(x). Constraints: capital/risk limits (PD/LGD/EAD), ops capacity, fairness parity bands. Solvers. Start with classical (MILP + heuristics). Optionally test quantum/quantum-inspired optimizers (annealing/QAOA) for the combinatorial assignment—especially if you must re-optimize daily on millions of accounts. Evaluation. Offline policy evaluation on historical data, then A/B at portfolio edges (only where both policies are plausible) to safely learn. Stakeholders, incentives, and safeguards Borrowers. Clear disclosures; caps on upside-sharing; hardship certifiers; grievance channels; opt-in data sharing only. Banks. Hard NPV accounting; model risk governance; capital treatment sign-off; operations playbooks. Regulators. Pre-registration of trial endpoints; fairness audits; sandbox/no-action letters where available. Collectors/servicers. Incentives tied to resolution quality (sustainable cures) not just near-term cash. Communities/NGOs. Seat at the table for exchange design (Track 5) and hardship verification. Privacy & Ethics. Minimize data; purpose limitation; differential privacy where feasible; explainable decisions. Measurement architecture (applies to all tracks) Core borrower outcomes. Payment sustainability: months current, re-default. Financial resilience: emergency-expense capability, variance of cash-flows. Credit trajectory: score delta, access to cheaper credit. Well-being: validated stress/mental-health scales, employment stability. Core bank outcomes. NPV of recoveries (discounted, net of ops/legal). Loss given default; time-to-resolution. Capital & liquidity impacts; reputational risk (complaints, disputes). Customer lifetime value (retention, cross-sell). Fairness & compliance. Performance by protected class; equal-opportunity metrics; error audits. Adverse-action explanation quality (completeness/consistency). Experiment hygiene. Randomization logs; pre-analysis plans; data blinding where applicable. Intention-to-treat + per-protocol; heterogeneity analyses (risk bands, regions). 90-day starter plan Pick one distressed segment (e.g., 60–120 DPD credit cards) and launch Track 1 with 3 arms; power for re-default and NPV at 12 months. In parallel, prototype Track 7 on last 3 years of portfolio data to estimate welfare lift and identify capacity bottlenecks. Stand up the Data Passport (Track 4) in one channel (e.g., digital unsecured loans) using a clean-room vendor; run a randomized encouragement test. Define governance: fairness thresholds, disclosure templates, caps on upside-sharing, hardship verifier list. Build dashboards for joint outcomes (bank NPV + borrower well-being), not just one-sided KPIs. Practical notes You don’t need exotic tech to start. Most gains come from contract design + randomized evaluation. Quantum/quantum-inspired optimization is a nice-to-have for the portfolio assignment problem when decisions must be recomputed under tight SLAs; keep a classical fallback. The moral core: insurance where it belongs (systemic shocks) and upside participation only with hard caps—so relief now isn’t a trap later. If you tell me which jurisdiction and debt types you care about (e.g., UK credit cards vs US mortgages, SMEs vs households), I’ll tailor the contracts, legal guardrails, sample sizes, and the exact metrics regulators there will expect.

Challenges to the problems raised and practical examples of usage. Me: I am intelligent enough to model most variables of a problem (that I am aware of), surely you are able to do so with much greater scope, therefor wouldn't it be possible for you to design controlled experiments on say a problem such as: Cancer. Whereby the medical companies, patients and underlying causes (which are many and multifaceted), are addressed and benefit? Using a quantum computing approach? Apex Thinker said: (My Chat GPT Problem Solver) Thought for 19s Short answer: yes—we can design controlled, ethically sound cancer experiments where “quantum” is not the miracle cure, but a tool that (i) proposes better drugs, (ii) detects disease more sensitively, (iii) plans treatment more optimally, and (iv) makes clinical trials faster and smaller. Below is a concrete, testable program you could hand to a translational oncology team. A quantum-enabled oncology program (4 experiment tracks) 1) Target & drug discovery (prospective, blinded head-to-head) Hypothesis. Hybrid quantum chemistry/ML can pick more true binder hits than a strong classical baseline, at equal compute budget. Design. Task. Given one oncology target (e.g., a kinase pocket), both teams (Quantum vs Classical) select top-N compounds from the same enumerated library. Blinding. Wet-lab team is blinded to which arm produced which list. Assays. SPR/biochemical affinity, cell viability in relevant lines, early ADMET. Primary endpoint. Hit rate at a pre-set affinity threshold (e.g., KD < 1 µM). Secondaries. Median KD, novelty (scaffold diversity), downstream phenotypic effect. Why it’s reasonable now. A recent Nature Biotech paper reported a quantum-computing-enhanced pipeline producing prospective experimental hits—not just simulations—suggesting feasibility for oncology targets with careful scoping. Nature 2) Diagnostics via quantum sensing (bench → pilot clinical) Hypothesis. Quantum sensors (e.g., NV centers in diamond) can detect tumor biomarkers (e.g., microRNAs, proteins) at lower concentrations and with higher SNR than standard label-based methods. Design A (bench). Compare limit-of-detection and dynamic range for specific cancer microRNAs using an NV-center platform vs qPCR/SPR on matched samples. Endpoints. LoD (M), linearity, specificity vs homologs, matrix effects (serum/plasma). Design B (pilot clinical). Case-control study (blinded) using serum from newly diagnosed patients (stratified by stage) vs healthy controls. Primary endpoint. AUROC for disease vs control; Secondaries. Stage discrimination; stability under freeze–thaw. Rationale. NV-diamond sensors have already shown micrometer-resolution tumor tissue imaging and label-free nucleic-acid detection in the relevant concentration regimes; 2023–2024 reviews map their biomedical path. PNAS+2Nature+2 3) Radiotherapy planning optimization (randomized crossover in silico, then clinical) Hypothesis. Quantum/quantum-inspired optimizers produce higher-quality IMRT/VMAT plans faster, improving dose to PTV while sparing OARs. Design A (planning study). Population. 50 historical CT datasets (e.g., head-and-neck). Arms. (i) Best-practice classical optimizer; (ii) Quantum annealing/quantum-inspired (QAOA/annealer). Endpoints. PTV D95, OAR mean/max doses, conformity index, planning time; blinded physicist review. Design B (prospective implementation). If A is positive, deploy for real cases under physics QA; measure replanning frequency, throughput, plan acceptance. Precedent. Oncology groups have already applied quantum-annealing/quantum-inspired methods to radiotherapy beamlet optimization with promising plan metrics and speed. dwavequantum.com+1 4) Quantum-assisted adaptive platform trial (regulatory-aligned) Hypothesis. Quantum optimization + QML for stratification/allocation can reduce sample size and time-to-success in a multi-arm phase 2 platform. Design. Model. Build on the I-SPY 2 framework (breast cancer): Bayesian adaptive randomization across biomarker-defined subtypes and drug combinations. Quantum’s role. Rapid combinatorial arm scheduling (allocation, dropping rules) via annealing/variational solvers; Feature selection for multi-omics response predictors with QML, benchmarked against LASSO/XGBoost; Strict pre-registration of decision rules; running hybrid (classical fallback if quantum is unstable). Endpoints. Time to arm graduation or futility; patients randomized per arm; posterior predictive probability of pCR (or other surrogate). Why this template. I-SPY 2 has already shown the operational value of adaptive platforms and subtype targeting—your trial leverages quantum only to speed the math, not to change clinical governance. PMC+2ClinicalTrials+2 Stakeholders, governance, and ethics Patients. Co-design consent emphasizing that “quantum” affects computational selection or sensor physics, not bedside therapy without validation. Regulators/IRB. Register statistical analysis plans; for platform trials, align with FDA adaptive-design guidance; pre-specify quantum→classical fallback. Industry & payers. Cost-effectiveness endpoints (e.g., cost per additional responder; lab throughput). Data/IT. Federated learning where possible; quantum runs are instrumented for reproducibility (seeded simulators + real-hardware logs). Equity. Ensure diverse cohorts; audit allocation models for bias. Reality check (important) Quantum today is mostly hybrid. You’ll likely get wins from quantum-inspired algorithms and careful problem reformulation before you get hardware-only quantum advantage in the clinic. Reviews in 2024–2025 echo this “promising but early” status. PubMed+2ScienceDirect+2 Pick the right subproblems. Binding-energy ranking for small pockets; sparse feature selection; combinatorial scheduling; ultra-low-signal sensing—these are sweet spots now. Demand prospective, blinded evaluation. Avoid overclaiming from retrospectives; ask for wet-lab or clinical endpoints. Invest where the ecosystem is moving. Major life-science investors are funding quantum startups; expect better tooling and service providers you can partner with. Reuters What I’d do first (90-day plan) Scoping workshop with med oncs, physicists, statisticians, and a quantum team to pick one target protein, one RT site, and one biomarker assay. Lock baselines (classical pipelines, lab protocols), pre-register endpoints, and get IRB feedback. Run Track-1 (drug) & Track-2 (sensor) pilots in parallel; in 12–16 weeks you’ll know if there’s signal to scale. In parallel, prototype the platform-trial scheduler on historical I-SPY-like data to quantify potential sample-size/time savings before proposing to regulators. If you want, I can tailor this to a specific cancer (e.g., TNBC vs GBM) and flesh out datasets, compute stacks (which quantum SDKs/annealers), and power calculations for the pilots.

GPT 5.0 Summaries: Here’s a breakdown of what’s going on, and some caveats: What the experiment was The research, from the Technical University of Denmark (DTU) and collaborators, was published under the title “Quantum learning advantage on a scalable photonic platform.” Phys.org They used entangled light (optical quantum states) to more efficiently characterize a quantum-system’s noise properties (i.e. learn how the system behaves under “noise”). Phys.org Their claim is that using entanglement and joint measurement, they achieved a measurement-efficiency scaling that far outperforms what’s possible classically. In their particular task, the classical approach would (in their estimation) take ~20 million years of measurement duration, while their quantum method takes ~15 minutes. Phys.org+1 They assert this is a provable quantum advantage for a photonic system — i.e. a practical demonstration (not just a theoretical conjecture) of quantum speedup. Phys.org What to be cautious about The “20 million years” is not literally something someone tried to run classically — rather, it’s an extrapolation based on scaling arguments (i.e. how many measurements would be required classically to reach the same precision). The quantum advantage is demonstrated for a specific task (learning noise in a quantum channel) under controlled settings. It doesn’t mean that all scientific work or all computational tasks can be so drastically accelerated. Quantum advantage results are often contingent on assumptions (noise levels, error rates, idealized components), so real-world scaling may be more challenging. This kind of result is an important proof of concept, but still far from “quantum supercomputer solves all problems in minutes.” ------ What the experiment was about The work is titled “Quantum learning advantage on a scalable photonic platform” arXiv+2DTU+2. It’s recently published and getting attention because it demonstrates a provable quantum advantage for a learning task in a setup that’s relatively feasible with today’s photonic (light-based) quantum technologies. aXi+3DTU+3arXiv+3 Here’s the rough idea of what they did: They consider a continuous-variable (CV) quantum system. In “CV” systems, instead of qubits (discrete two-level systems), one manipulates modes of light (or other bosonic modes) whose state is characterized by continuous parameters like amplitudes, phases, quadratures, etc. DTU+3arXiv+3arXiv+3 The particular task: learning a distribution of displacements applied to many modes. More precisely, there's a “random displacement channel” over many bosonic modes: each mode is displaced (shifted in phase space) according to some probability distribution, and one wants to learn / estimate that distribution. aXi+2arXiv+2 The core claim is that by using entanglement (entangling the modes with an ancillary quantum memory and doing a joint measurement), they can reduce the number of samples required to learn the distribution by an exponential factor (i.e. many orders of magnitude) compared to any method not using entanglement. DTU+3aXi+3arXiv+3 In their implementation, they demonstrated this on a 100-mode system with imperfect entanglement (about 5 dB of two-mode squeezing) and achieved something like 11.8 orders of magnitude fewer samples needed versus a classical / non-entangled approach. aXi+3arXiv+3DTU+3 The “20 million years vs 15 minutes” is a sensational way of expressing that in a classical regime, the equivalent precision would require astronomically many measurements or time; the quantum method compressed that scale drastically in their example. DTU+2arXiv+2 So, “20 million years of work in 15 minutes” is more a metaphor/scale extrapolation than a literal classical experiment run. The researchers use complexity arguments about scaling. DTU+2arXiv+2 Why is this significant? Here are the deeper points and caveats: Sample complexity vs time complexity A lot of quantum advantage claims compare time (how fast you can compute). In this work, the advantage is in sample complexity — how many experimental trials (or measurements) you need to gather data to learn the target distribution to given accuracy. Reducing sample complexity is powerful in experiments because each sample may be expensive (time, noise, loss). Entanglement is key The advantage fundamentally comes from using entangled quantum states and joint measurements across modes + memory. Without entanglement, the classical methods (or “non-entangled quantum” ones) require exponentially many more samples as the number of modes increases. aXi+2arXiv+2 Robustness (imperfect entanglement, noise) Importantly, they don’t assume perfect, ideal entanglement. Their demonstration works with “noisy / non-ideal entanglement” (5 dB squeezing) and still gets huge gains. That makes it more realistic. arXiv+2aXi+2 Scalability and optical (photonic) platform Photonic platforms are among the promising hardware for quantum technologies (they often work at room temperature, use light etc.). Showing this effect in a photonic setup helps argue that such quantum advantage might be feasible in real devices. DTU+2arXiv+2 Not yet a universal solver / generic quantum computer This result is about a specific learning task tailored to quantum advantage and continuous-variable systems, not a general-purpose algorithm that beats all classical algorithms everywhere. It doesn’t mean “all computations now take 15 minutes instead of millions of years.” Extrapolation caution When authors (or press coverage) say “20 million years vs 15 minutes,” that is an extrapolation or metaphor based on scaling arguments, not something literally benchmarked. The classical method for that scale wasn’t run physically; it’s estimated from complexity. DTU+1 A bit of the math / intuition (without full rigor) To give you some flavor, here are some of the mathematical/technical pieces in rough form: The modes are bosonic modes, each described by annihilation / creation operators and quadratures. The “displacement” is an operator that shifts the mode in phase space. The unknown channel is modeled as a probabilistic mixture of displacements: with some probability, each mode gets a certain displacement. Learning that mixture is akin to learning the parameters of a probability distribution over a high-dimensional (multi-mode) space. The classical (or non-entangled) approach would require, for nnn modes, a number of samples that scales exponentially in nnn to estimate all those correlations accurately. But when you entangle with a memory and do a joint measurement, you can “reuse” information across modes and effectively compress the amount of data needed. More precisely, they prove information-theoretic lower bounds on how many samples are needed without entanglement, and then exhibit a protocol with entanglement whose sample complexity is dramatically lower. That’s how the “provable advantage” is established. aXi+1 The “11.8 orders of magnitude fewer samples” means the sample complexity ratio is about 1011.810^{11.8}1011.8. (That’s ~ a factor of 1011.8≈6×101110^{11.8} ≈ 6 × 10^{11}1011.8≈6×1011.) arXiv+1 The 5 dB of squeezing indicates how “good” the entanglement is; in practice, entanglement and squeezing are imperfect, so the result shows the effect tolerates some non-idealities. arXiv+1

@Karmadhi I doubt this is true at all; the outrage would lead to further violence. But even if it was, why on earth risk it? It's because you've assigned moral codes to democracies that don't inherently exist, because we have the luxury of living in relative safety and comfort. If the democracy were a warzone it would all vanish. I am not saying they are treated well, but they are kept alive and in a condition they can walk and talk. Which is a step up from what was happening initially. Because we have the luxury of living in relative safety and comfort. It's one we've earned through education, development, hard work, internal peace and social development/unity. But nevertheless, we are able to live with an ethical code, mostly enforced by law, that is more difficult or impossible to enforce in the more lawless, or war-torn regions of the world. It is also the difference between an individualist and collectivist ethos that you might find in Eastern developed nations. Individualism is not a curse as some believe, but a way to ensure that the individual is as important as any collective ethos, thus putting a higher value on any individual's life.

The value any participant of a conflict puts on the human life in question. To Hamas these are the most valuable people in their world currently. To the Israelis, they are a problem to wipe out and part of their fear and terror campaign. To Russia, they used to be something to inspire fear and terror; now they are a bargaining chip, as their manpower is low, for trades. So there is a noticeable change. To Ukraine they use them to appear more benevolent and to trade back for their own people, also sometimes to gain soldiers, partisans, or allies inside Russia. I don't doubt personal morality comes into individual reasoning, and perhaps culturally ingrained morality can play a tempering factor, but this is the cold truth of war, that a soldier follows orders, and what those orders say decides the ultimate fate of a prisoner of war.

One day we won't be having these circular conversations based on propaganda and lies. We'll just have the actual conversation about why the war started: Russia considered Ukraine Russia. *I'll have a watch of the video and maybe comment next time. So far, its advocating the Bhutan way which I answered above.

-Yet its Russia invading. Maybe if we attack Russia and claim you started it, that will work? No? Strange that. What if we had a really good reason in our minds? Still no? Huh. Russia doesn't get to dictate what other countries, or in this case moronically entire continents and alliances can do. We can't turn around and tell Belarus it can't join a Russian alliance or we'll invade it. Is that a good reason to invade Belarus? No it'd be ludicrous, just like your country. Again for the 1,000 time if you don't want everyone to join NATO stop threatening them! All this war did to me was prove why NATO had to exist, before it, America was pulling away, the EU wasn't anywhere near unified. NATO might have been a memory within a decade. Now it'll be around for another 50 or more years. Oh and NOBODY in NATO officially promised Russia they wouldn't expand toward its borders; that is some offhand rumor from an informal meeting spoken by a Soviet and not on record. It's a repeated lie by the Russians that this was official. https://en.wikipedia.org/wiki/Controversy_regarding_NATO's_eastward_expansion Europeans tend to talk **** when you are threatening to nuke them. Yeah it happens. When you are meddling in their elections. Killing their friends and families over the border. Yeah it doesn't endear them to you, its true. Strange that. When you flood them with migrants, try to destabalise their countries political spheres internally. Yeah we don't like it, I know, shocking. Maybe the Russia victimhood ego is so far advanced that it can do literally anything and still feel victimised. Quite a feat. Maybe I used the word Karen on the wrong side here? Colonial activism? I am telling you how Europe thinks. They believed you'd kill Putin rather than suffer him. They were wrong but largely due to your propaganda, you dismiss just how good it is. All countries use it; yours is just better. I could list the 50 things Russia has instigated, but what's the point? If you haven't read it the first time, you won't read it this time. Despite what you seem to think. If it moved out of Ukraine tomorrow, that'd be that. You don't get to play the Colonialism card and the Europeans don't want to get involved card at the same time. Pick one. I had no delusion that this would be quick. I said it'd be a decade or more, at the very start of this. That was easy to see given the size of the countries involved, their history, and readiness. I personally thought we'd already have troops in Ukraine, or not fumble around half in half out of this conflict, not giving Ukraine what it needed until 4 years on, and you'd be pushed out. I underestimated just how much Europe wants to distance itself and freeze this conflict. As i've said 50 thousand times before, i'd rather never interact with Russia for the rest of my days, the very opposite of a colonial mindset. -Oh and if Bhutan are invaded or has their lands stolen by an aggressive state, they don't live in peace. The only reason Bhutan exists is because of the Indian military capacity. There were better examples you could pick, but there would usually be a force guaranteeing their existence also.

The rare earth struggle between superpowers probably explains some of this action. Pakistan contracted with the US. I don't know the exact timeline, so its either just after or just before. His conclusions are somewhat exaggerated but could well explain this initial violent reaction and some of the politicizing I've seen recently around the topic.

Ah yes, Bhutan, a lovely place. Where China is trying to steal its territory. Sorry, even they don't get left alone by large authoritarian blobs unless its resisted. Thankfully for them, India stepped up. Much like Europe did for Ukraine. https://banotes.org/south-asia/bhutan-china-territorial-dispute-boundaries/ Its not like you to resort to moralism, Twentyfirst. Its like you barely read my posts. Where I have to tell people every single time. People are people the world over. There are no angels. Morally superior absolutes or imperatives. Only the interests of the country or people involved. Outside of Moscow and St Petersburg. That Russia can tolerate being in a run-down state with garbage piling up (pre war), with roads that barely function, half of them not having basic appliances, and living on wages that would make a McDonald's worker laugh. That's what I meant. What I mean now is, Russians will put up with dying in a meat grinder, going without gas, food prices going up up and up (Ukranian sanctions have only been going on two months, wait till 4 months.) The internet shut down to avoid people saying the wrong thing, and people arrested for the slightest discontent. Entire families and communities out in the east having their youth wiped out, and the rest not getting paid while people in Moscow live fat lives and panic when they go without the internet for a night. That they don't mind China playing their country like a fool and buying up whatever it wants, while Russia slides back a 100 years, or carrying a million more wounded vets and criminals in your society. - That sort of thing, that they can bear that without rising up and choking the man in charge (their local governors and police). Hell even the oligarchs don't get paid these days. Westerners didn't appreciate how good your propaganda was, or how much the Russian population will tolerate. Just as you don't appreciate how little we'll tolerate and what lengths we will go to, to protect our way of life. - But I think you are starting to realise. I didn't make European's mindset, I am just telling you what it is. Karens on Crack, and people who will bomb you into the stone age if you interfere too much with their way of lives. We go to great lengths not to get involved and live comfortable lives. So Russia needs to quit while they can and stop trying to involve us more, it will not end well.

Europeans rarely do anything but sit back and let everyone else fight. There was a culture in the 80's and 90's of America thinking it can liberate cultures thousands of years old than it from themselves, this sense of superiority in America (and Russia) persists somewhat today but is toned down. Its getting a hard reset in Russia. Russian's splitting off into countries better representing their minorities and cultures would benefit those cultures yes. They would no longer live off table scraps thrown to them by their Muscovite masters, they'd make outside alliances and enrich themselves. Sibera should be Russia's richest provinces by far. I'll be happy to learn much from those cultures. I've had my fill of the Muscovites for a few decades. Those guys go on about themselves more than the Americans did in the 80s.

Interesting. Though I have been corrected just today, actually, apparently we are talking about a common myth. These data centers are needed to train the AI. To run the AI, a laptop on a battery is fine already.

@Twentyfirst Maybe some understanding can come from this. If you punch Europeans in the face repeatedly, they just fight back harder. Its always been that way. I've been thinking about why. It's because we like to be detached and sit comfortably away from it all. So we do anything necessary to protect that way of life. If that means giving someone guns so the fight stays away from our borders we do that, if that means giving America military control we do that; if that means going to war with Russia because it disrupts that enough, we will. If it it means crashing the Russian economy so much the entire country shatters, we will do that, whatever it takes (as little as it takes preferably, is the European way of viewing the world). In the same way Europe didn't understand how Russians can tolerate such poverty and conditions they find themselves in, Russia doesn't understand what lengths Europeans will go to, to avoid that. Its true there is high reluctance to war, but its also true there is equally high reluctance to lose that comfort and luxury. - Which turns things nationalist, which turns things violent and causes Europeans to start attacking rather than sitting idle.

Its a violently suppressive authoritarian regime that is trying to revive its imperial ambitions and conquer sovereign states. No, my home town is relatively boring, highly conservative and nothing much changes here. I've learned all I want to about Russia. More than I ever wanted to know. If you want friends. Stop shooting at people, threatening them, meddling in their affairs, launching cyberattacks, etc This is the biggest load of gaslighting i've seen you do yet. Kudos. Included in the rest of the world lol. Stop shooting at people first eh?

Saying that Stalin wasn’t as bad as Hitler is like comparing a serial killer to a serial killer. It's utterly nonsensical moral relativism that, even if correct, is not a firm context to base an argument for favourable relations on. More importantly, countries don’t think this way; they just look at what’s in their interests. Western flaws don’t erase the Russian record in your moral relativism either. Historically, they have been the most brutal of all world powers, from the Mongols, the USSR to the Russian Empire. – Other than informing likely historic patterns, countries base policy on what’s happening now, not what happened in the past. So while their violent tendencies are indicators, if tomorrow they end their war in Ukraine, start supporting Israel and backing the West, slowly things would shift. Not because it’s the morally correct thing to do (though it is in Ukraine), but because it aligns more with their Western neighbours. Russia has forgotten or not fully put into context that it has western neighbors, as do most of its supporters. It likes to gloss over this and just shout America at people. Napoleon was defeated by a coalition. Britain, Austria, Prussia, Russia and more. Russia beating Napoleon is just a Russian exaggeration as always. The USSR invading Poland was a joint invasion. However, you want to spin it. But not brutal? I brought up GPT’s statistics here: 22,000 Polish officers and elites murdered at Katyn (1940), mass deportations of Poles to the Gulag, the suppression of the Polish underground, and the curiously “inactive” Soviet posture at the Warsaw Uprising (1944) while the Home Army bled out.  Winter War (Nov 30, 1939): the USSR invaded Finland after failed ultimatums and fabricated border incidents; the League of Nations expelled the USSR for aggression. Calling this “security” mimics the exact logic later used to justify Crimea (2014) and the full-scale invasion of Ukraine (2022).  The USSR also forcibly annexed the Baltic states (1940), followed by arrests, executions, and deportations. Again: not some gentle administrative reshuffle. Winter War (Nov 30, 1939): the USSR invaded Finland after failed ultimatums and fabricated border incidents; the League of Nations expelled the USSR for aggression. Calling this “security” mimics the exact logic later used to justify Crimea (2014) and the full-scale invasion of Ukraine (2022). The USSR also forcibly annexed the Baltic states (1940), followed by arrests, executions, and deportations. Again: not some gentle administrative reshuffle. End Quote 1, Precisely. They will control that alliance. Russia will do what they say or not at all militarily; with that comes some stability. If India and China can resolve their differences sufficiently. 2, Manpower alone does not win wars when a tactical nuke can take out large clusters of men. You can only fit so many men in a space to fight. Especially entering the age of robotic wars (drones) This is just the tip of the iceberg; tanks, apcs and helicopters are just not viable on mass. China has effectively wasted billions, if not more (same as the US does yearly). Planes still have a role, as they can stay far enough away to avoid drones (for now). In which post was this stated? The problem with arguing moral standards is not only that you are assuming everyone should follow yours, but also that the people you are arguing against have X set of standards. Drop the moral arguments, other than to use them when someone is being callous that they need correction, it'll make your entire post more rational and based in reality, on topic, and useful to any conversation or potential theorised outcome. Europe is throwing stones at Russia because it is literally attacking westward into Europe. And for the hundred reasons i've previously listed. If and when Russia accepts its own borders and gives up its imperial ambitions, there will be no more stone throwing. Here's Chat GPT with some more moral and/or systemic corrections for you: On “welcomed by Jews and non-Poles.” Some Jewish communities initially saw the Red Army as the lesser evil versus genocidal Nazis. But the Soviet record includes arrests of non-communist Jews, suppression of Jewish civic life, post-war antisemitic campaigns (e.g., the “anti-cosmopolitan” purges, Doctors’ Plot scare), and mass repression of entire populations. “Welcomed” doesn’t capture the coercive reality that followed. On BRICS as a military counterweight. India and China are strategic rivals with live border disputes and diverging interests; imagining them as a cohesive NATO-like bloc is wishful. Military alliances require interoperable command, shared doctrine, and mutual defense guarantees. BRICS is a loose economic/political forum; it lacks those fundamentals. Counting heads (“exhaustible manpower”) is 20th-century thinking. Modern power projection depends on logistics, ISR, precision munitions, industrial capacity, finance, and alliances. Russia’s war in Ukraine has underlined those constraints. On corruption and “the West must fix itself first.” Yes, Western systems have money-in-politics problems. The difference is remediability: free media, opposition parties, independent courts, and competitive elections create pressure that can expose and correct graft. In Russia, opposition leaders are jailed, exiled, or die; media is state-controlled; elections are neither free nor fair. That’s not “different values”; it’s authoritarianism. So no, pointing to Western flaws doesn’t transform Kremlin interference, invasions, or domestic repression into “just another perspective.” Bottom line Recognize the Red Army’s role in defeating Nazism and acknowledge the USSR’s record of invasions, mass deportations, and political terror. Recognize Western imperfections and reject the idea that they morally equalize with a state that normalizes aggression and eliminates dissent. That’s not “complaining and nagging”; it’s refusing historical amnesia and present-day whataboutism. End Quote