Is near-term quantum supremacy feasible? A runtime-based investigation

Quantum computing sits at a tipping point: attention-grabbing supremacy headlines and major public-private investments coexist with contested claims and stubborn engineering limits. The question reviewers and practitioners alike now care about is simple: when, if ever, will a quantum device deliver a faster, better answer than the best classical systems under fair, end-to-end timing and quality constraints? This project turns that question into a disciplined program, replacing optimistic proxies with measurable runtime and solution quality, and pitting QPUs and novel hybrid methods against tuned CPU/GPU/FPGA/wafer-scale baselines. This project asks a single, field-defining question: what must be true for near-term quantum devices to achieve practical quantum supremacy under operationally meaningful conditions? We address claims across three emblematic domains: combinatorial optimization (QUBO/Ising), oracle problems (e.g., Grover and Simon), and random-circuit sampling, and test them against the strongest classical competitors on modern hardware. Our preliminary evidence indicates that several reported quantum advantages vanish when measured by end-to-end runtime and quality, and when compared to state-of-the-art classical baselines. We will establish necessary and empirical conditions for practical supremacy by (i) defining and standardizing quality-aware, end-to-end metrics (time-to-epsilon, success-probability under time budgets, fidelity, runtime trade-offs), (ii) codesigning and implementing novel hybrid quantum-classical algorithms, and (iii) benchmarking against optimized CPU/GPU/FPGA/wafer-scale (WSE) baselines. The work spans optimization on annealers and gate-model hardware, oracle algorithms with classical pre/post-processing, and random-circuit sampling at matched fidelity and energy. Research tasks. (1) Metrics and protocols: formalize and open-source a benchmarking framework that accounts for all overheads (problem prep, compilation/transpilation, queueing, execution, readout/post-processing) and energy. Build strong classical baselines and curated instance suites. (2) Hybrid optimization: design runtime-first hybrid solvers that combine quantum moves (e.g., QAOA/annealing) with accelerated classical refinement on GPUs and FPGAs; evaluate on structured QUBO/Ising families using time-to-epsilon and approximation quality. (3) Oracle problems: integrate amplitude-amplification steps with classical pruning and verification on accelerators; quantify when query-complexity advantages survive wall-clock and orchestration overheads. (4) Sampling: compare QPU random-circuit samplers to best-in-class simulators on GPUs, WSEs, and FPGAs at matched fidelity and with energy accounting; map the crossover region where classical spoofing fails. (5) Synthesis: produce empirical bounds and crossover maps delineating parameter regimes where supremacy is feasible or excluded; distill design principles for future algorithms and hardware. Classical code will be developed in Julia and C++ with CUDA and oneAPI/SYCL; linear-algebra kernels will target multi-GPU clusters and wafer-scale engines. Selected kernels (Ising/QUBO updates, Gibbs/Metropolis primitives, Grover oracles) will be accelerated on FPGAs using Bluespec SystemVerilog (BSC flow) with fixed-point, deeply pipelined designs and AXI-based I/O. Quantum experiments will use Qiskit/OpenQASM (IBM and other cloud QPUs) and D-Wave Ocean for annealing, with pinned toolchains and reproducible transpilation/embedding configs. All studies will report identical metrics on identical instances, emphasize end-to-end timing and energy, and include statistical confidence intervals. Artifacts (code, instances, logs) will be released to enable independent reproduction. The project will either demonstrate robust, quality-aware runtime advantages in well-specified niches via hybrid methods, or establish quantitative, reproducible bounds showing where current hardware cannot outperform leading classical systems. In both outcomes, we deliver community benchmarks, open tooling, and clear guidance for algorithm/hardware co-design, thereby setting a higher standard for credible quantum-supremacy claims.