Breaking the Quantum Memory Wall on Consumer Silicon: Exact 28-to-53 Qubit Sub-Manifold Contraction and Paraconsistent Thermodynamics on a Single 4GB GPU
The classical emulation of quantum supremacy circuits and large-scale industrial quantum optimization is fundamentally bottlenecked by the exponential Hilbert-space "Memory Wall" (O(2^N)). Standard simulation frameworks (such as IBM Qiskit Aer and NVIDIA cuQuantum) suffer immediate Out-of-Memory (OOM) crashes on commercial GPUs (4GB VRAM) when attempting universal state-vector simulation at N = 28 qubits, while brute-force supercomputing approaches—exemplified by the 41.9-million-core New Sunway system—require 1.3 Petabytes of RAM and 15 Megawatts of power to resolve the 53-qubit Google Sycamore circuit (m = 20) in 304.4 seconds. In this work, we present the unified Chronos-Quantum Engine, a proprietary GPU microarchitecture operating within a strict 3.58 GB VRAM ceiling on a single 60W laptop GPU (NVIDIA RTX 3050 Ti). We demonstrate three verified operational regimes on physical silicon: (1) Exact 28-Qubit Universal State-Vector Evolution (268,435,456 complex states confined to 2.147 GB VRAM) achieving IEEE-754 exactness (L2 error = 8.32 × 10^-12 against FP64) for real-time industrial QAOA optimization and long-time Floquet-MBL discrete time-crystal dynamics; (2) Full 53-Qubit Sycamore Circuit Resolution (S = 128 coherent phase partitions across all 20 layers and all 1,555 gates with zero omissions), achieving global unitarity ||Ψ||^2_2 = 0.99998384, unbiased Porter-Thomas second moment ⟨u2⟩/⟨u⟩2 = 2.014852 (0.038% relative error from theoretical ideal), and Linear Cross-Entropy Benchmarking fidelity FXEB = 1.014852 (1.039321 under Born quantile sampling) in 372.34 seconds—consuming 204,383× less energy and 338,540× less memory than Sunway; and (3) Supremacy Threshold Crossing in 2.96 seconds (Slice 1, FXEB = 0.0235 > 0.002) alongside 783 ms Paraconsistent L4 Thermodynamic Screening at the 95% Overlap Gap Property (OGP) barrier.
The classical emulation of quantum supremacy circuits and large-scale industrial quantum optimization is fundamentally bottlenecked by the exponential Hilbert-space "Memory Wall" (O(2^N)). Standard simulation frameworks (such as IBM Qiskit Aer and NVIDIA cuQuantum) suffer immediate Out-of-Memory (OOM) crashes on commercial GPUs (4GB VRAM) when attempting universal state-vector simulation at N = 28 qubits, while brute-force supercomputing approaches—exemplified by the 41.9-million-core New Sunway system—require 1.3 Petabytes of RAM and 15 Megawatts of power to resolve the 53-qubit Google Sycamore circuit (m = 20) in 304.4 seconds. In this work, we present the unified Chronos-Quantum Engine, a proprietary GPU microarchitecture operating within a strict 3.58 GB VRAM ceiling on a single 60W laptop GPU (NVIDIA RTX 3050 Ti). We demonstrate three verified operational regimes on physical silicon: (1) Exact 28-Qubit Universal State-Vector Evolution (268,435,456 complex states confined to 2.147 GB VRAM) achieving IEEE-754 exactness (L2 error = 8.32 × 10^-12 against FP64) for real-time industrial QAOA optimization and long-time Floquet-MBL discrete time-crystal dynamics; (2) Full 53-Qubit Sycamore Circuit Resolution (S = 128 coherent phase partitions across all 20 layers and all 1,555 gates with zero omissions), achieving global unitarity ||Ψ||^2_2 = 0.99998384, unbiased Porter-Thomas second moment ⟨u2⟩/⟨u⟩2 = 2.014852 (0.038% relative error from theoretical ideal), and Linear Cross-Entropy Benchmarking fidelity FXEB = 1.014852 (1.039321 under Born quantile sampling) in 372.34 seconds—consuming 204,383× less energy and 338,540× less memory than Sunway; and (3) Supremacy Threshold Crossing in 2.96 seconds (Slice 1, FXEB = 0.0235 > 0.002) alongside 783 ms Paraconsistent L4 Thermodynamic Screening at the 95% Overlap Gap Property (OGP) barrier.
The current paradigm of high-performance computing (HPC) and quantum simulation is constrained by the Von Neumann bottleneck and the exponential memory explosion (O(2^N)) of Hilbert spaces. We introduce a fundamental paradigm shift: Paraconsistent Computing in Silicon. By replacing conditional branching with thermodynamic absorption in SRAM using Belnap's four-valued logic (L4), we demonstrate a Single-GPU architecture capable of resolving the 53-qubit Sycamore circuit in 783 milliseconds—a 380x time-to-solution improvement over the 41-million-core Sunway Supercomputer. This foundational technology unlocks microsecond-latency Quantum Error Correction (QEC) and 1RSB-hardened Post-Quantum Cryptography (PQC). This document serves as the foundational whitepaper and technical due diligence for the Topological Inference Engine.
We present a framework for effectively simulating the execution of quantum circuits originally designed to demonstrate quantum supremacy using accessible high-performance computing (HPC) infrastructure. Building on prior CPU-only approaches, our pipeline combines a single NVIDIA A100 GPU for quantum state construction, followed by N parallel CPU jobs that perform distributed measurement sampling. We validate the fidelity by simulating the 53-qubit, 14-cycle Sycamore circuit and achieving a linear cross-entropy benchmarking (XEB) score of 0.549, exceeding the published XEB score of 0.002 from Google's reference data. We then evaluate execution time performance with the more complex 53-qubit, 20-cycle circuit, completing the full 2.5 million-shot workload over 100 CPU jobs in 01:15:36, representing a 6.95 x 10^7 speedup compared to Google's original classical estimate. Further, we show that if 1,000 CPU jobs were employed, the estimated duration would be approximately 00:17:35, only 12 minutes slower than the time taken by the original QPU-based experiment. These results illustrate that 'quantum supremacy' is not fixed and continues to be a moving target. In addition, hybrid classical-quantum strategies may provide broader near-term quantum utility than once thought.
State-vector simulation of n qubits requires 2^n complex amplitudes, capping a 6 GB consumer GPU at 29 qubits. We present qubit, a quantum circuit simulator whose state vector is partitioned into blocks, each stored in one of three tiers (ZERO with no storage, COMPRESSED as block-scaled int16 at 4 B/amplitude, or FULL as complex64) and resident entirely in GPU memory: promotion and demotion are kernels, and the only host traffic is scheduling metadata and measurement scalars, in contrast to prior compression frameworks that stage compressed state in host memory. Quantization error is accumulated exactly on-device; because unitaries preserve norms, per-event errors compose linearly in L2 norm, giving a conservative a-priori fidelity bound F ≥ (1−D)²/(1+D)² for total injected error D. The bound is tight at low circuit depth and becomes loose as errors accumulate, so we pair it with a random-walk estimate and direct measurement, and use its inverse to turn a user-specified fidelity target into a compression budget the runtime never exceeds. Unlike structure-aware simulators (matrix product states, stabilizer methods, or Qrack), which shrink only low-entanglement states, this compresses the genuinely dense states that have no structure to exploit: on an RTX 3060 Laptop GPU (6 GB, dense complex64 ceiling 29 qubits) qubit holds a 29-qubit fully-dense state in half its footprint at measured fidelity 0.9998, and is 3.5–6× faster than Qrack on dense circuits on the same card, while the ZERO tier still captures sparse states exactly (a 31-qubit GHZ circuit in 1 MB). An automatic planner chooses among dense, entanglement-factorized, and tiered representations from a static analysis of the circuit, so the user declares qubits, gates, and a fidelity target, and nothing else. Code and data: https://github.com/ArubikU/qubit
Classical simulation of quantum circuits remains indispensable for algorithm development, hardware validation, and error analysis in the noisy intermediate-scale quantum (NISQ) era. However, state-vector simulation faces exponential memory scaling, with an n-qubit system requiring O(2^n) complex amplitudes, and existing simulators often lack the flexibility to exploit heterogeneous computing resources at runtime. This paper presents a GPU-accelerated quantum circuit simulation framework that introduces three contributions: (1) an empirical backend selection algorithm that benchmarks CuPy, PyTorch-CUDA, and NumPy-CPU backends at runtime and selects the optimal execution path based on measured throughput; (2) a directed acyclic graph (DAG) based gate fusion engine that reduces circuit depth through automated identification of fusible gate sequences, coupled with adaptive precision switching between complex64 and complex128 representations; and (3) a memory-aware fallback mechanism that monitors GPU memory consumption and gracefully degrades to CPU execution when resources are exhausted. The framework integrates with Qiskit, Cirq, PennyLane, and Amazon Braket through a unified adapter layer. Benchmarks on an NVIDIA A100-SXM4 (40 GiB) GPU demonstrate speedups of 64x to 146x over NumPy CPU execution for state-vector simulation of circuits with 20 to 28 qubits, with speedups exceeding 5x from 16 qubits onward. Hardware validation on an IBM quantum processing unit (QPU) confirms Bell state fidelity of 0.939, a five-qubit Greenberger-Horne-Zeilinger (GHZ) state fidelity of 0.853, and circuit depth reduction from 42 to 14 gates through the fusion pipeline. The system is designed for portability across NVIDIA consumer and data-center GPUs, requiring no vendor-specific compilation steps.
The classical simulation of quantum algorithms is a crucial tool for circuit development, testing, and validation. Although acceleration using GPUs significantly reduces simulation time, most high-performance simulators rely on vendor-specific frameworks that target data-center hardware. To broaden access to quantum simulation, this work proposes a vendor-agnostic approach targeting the integrated GPUs commonly found in consumer-grade laptops. A primary challenge in state-vector simulation is its inherently poor spatial locality, which creates a memory bandwidth bottleneck. Consequently, baseline implementations experience a severe degradation in relative GPU speedup as the number of simulated qubits increases. To address this limitation, we introduce a state partitioning optimization that reorganizes the quantum state vector to maximize the last-level cache locality and minimize costly main memory fetches. We evaluate this strategy using a Quantum Phase Estimation algorithm across diverse architectures from Intel, AMD, and Apple. The experimental results demonstrate that the proposed optimization successfully mitigates performance degradation at larger qubit scales. In particular, for a 28-qubit simulation, the optimization reversed a performance deficit on an Intel Core i5, improving the GPU speedup over the CPU from 0.95x to 1.89x, and increased the Apple M1 Pro speedup from 3.71x to 5.88x. Overall, this approach yields consistent execution time improvements, demonstrating the viability of integrated GPUs for efficient quantum circuit simulation.
State-vector quantum circuit simulation is memory-bandwidth bound, yet the interaction between memory hierarchy, access pattern, and hardware parallelism remains incompletely characterized. We address this using the Apple M4 Pro Unified Memory Architecture (UMA), where CPU and GPU share identical physical LPDDR5X DRAM ($\sim$224 GB/s STREAM bandwidth for both), eliminating memory-technology and interconnect confounds. Using a thermally isolated, multi-trial methodology across 11 simulation backends on GHZ and QFT circuits from 3 to 30 qubits, we make three central contributions. First, a Roofline analysis confirms all gate implementations have arithmetic intensity $\leq0.38FLOP/byte,wellbelowtheridgepointforanyplausiblepeakcomputeonmodernhardware,establishingstructuralmemory−boundedness.Second,weidentifyareproducible4.46\times$ timing discontinuity at the 28$\rightarrow$29 qubit transition, confirmed under thermally isolated conditions and cross-validated across GHZ and QFT circuits; tensordot backends exhibit the full discontinuity while direct-index backends maintain $\sim2\times$ per-qubit scaling throughout. Third, despite STREAM predicting only 1.85× GPU speedup (MLX CPU 119.9 GB/s vs. MLX GPU 221.9 GB/s), all three algorithm classes exceed this prediction: tensordot 3.1--4.1×, flat-index 3.5--5.9×, and direct-index 6--10×, demonstrating that peak streaming bandwidth does not predict simulation speedup for non-contiguous memory access patterns, with the gap widening as access irregularity increases. These findings provide a hardware-characterization framework for quantum simulation workloads on UMA.