1. This result extends your combinatorial optimization domain by providing empirical hardware benchmarks on IBM Heron to optimize shot budgets and noise mitigation for QUBO docking calculations run via Sample-Based Quantum Diagonalization.
Adversarial Debate Score
62% survival rate under critique
Expert panel critique
Independent views, each critiquing the hypothesis on its own — the score rewards genuine disagreement and discounts consensus.
Supporting Research Papers
- Towards High Performance Quantum Computing (HPQ): Parallelisation of the Hamiltonian Auto Decomposition Optimisation Framework (HADOF)
Practical applicability of quantum optimisation on near term devices is constrained by limited qubit counts and hardware noise, which restricts the scalability of quantum optimisation algorithms for c...
- Benchmarking Quantum Computers via Protocols, Comparing IBM's Heron vs IBM's Eagle
As quantum computing hardware rapidly advances, objectively evaluating the capabilities and error rates of new processors remains a critical challenge for the field. A clear and realistic understandin...
- How Many Shots Does It Take? A Noise-Aware Quantum Resource Allocation Framework
Any algorithm execution on quantum computers requires several repeated and costly executions (known as shots) to obtain reliable results. In this work, we propose a closed-form accurate analytical exp...
- HyQBench: A Benchmark Suite for Hybrid CV-DV Quantum Computing
Hybrid continuous-variable (CV)-discrete-variable (DV) quantum systems present a promising direction for quantum computing by combining the high dimensional encoding capabilities of qumodes with the c...
Formal Verification
Z3 checks whether the hypothesis is internally consistent, not whether it is empirically true.
This discovery has a Claude-generated validation package with a full experimental design.
Precise Hypothesis
On IBM Heron-family superconducting QPUs (r1/r2, ≥133 qubits), for QUBO formulations of protein-ligand docking pose selection (problem sizes 20–127 logical variables encoded via Sample-Based Quantum Diagonalization, SQD), there exists a measurable, reproducible relationship between (a) shot budget per circuit (range 1,000–100,000 shots), (b) error mitigation method (none, dynamical decoupling, twirled readout mitigation, zero-noise extrapolation), and (c) SQD ground-state energy recovery accuracy (measured as % overlap with classically-verified optimal QUBO solution or energy gap to exact diagonalization on ≤30-qubit subsystems), such that a specific (shots, mitigation) configuration exists that achieves ≥90% of best-achievable solution quality at ≤50% of the shot cost of a naive maximal-shot baseline. This is falsifiable: if no configuration achieves this accuracy/cost tradeoff relative to baseline across ≥3 independent docking QUBO instances, the hypothesis is disproven.
- No (shot budget, mitigation) configuration across the tested grid achieves ≥90% solution quality at ≤50% shot cost versus max-shot baseline, on any of the tested instances.
- Increasing shot budget beyond 10,000 shows no monotonic or statistically significant (p<0.05, paired t-test across instances) improvement in solution quality — indicating shot budget is not the controlling variable.
- Error mitigation techniques provide no statistically significant improvement (95% CI overlapping zero effect) over unmitigated baseline at matched shot count.
- Results fail to replicate across ≥2 independent Heron backends (inter-device variance exceeds intra-device variance), indicating hardware-instance-specific noise rather than generalizable Heron-class behavior.
Spine & Adversarial Read
- highWhy SQD specifically rather than QAOA or quantum annealing for this docking QUBO class — the methodology doesn't justify why this quantum algorithm choice is the right comparator for establishing hardware benchmarks.SQD is chosen because it is IBM's current flagship sampling-based ground-state method for Heron-scale utility experiments and has published precedent in chemistry applications, making it the most mature option for 100+ variable problems on current hardware; however, this EVP does not include a head-to-head SQD-vs-QAOA comparison on the same instances, which is a genuine gap — flagged in EXTERNAL_CONFLICTS as future work, not resolved here.
- highThe classical ground truth for the 100-127 variable instance is infeasible to obtain exactly, so the 'accuracy' metric at the largest, most interesting scale rests on heuristic best-known solutions (e.g., simulated annealing), which could itself be suboptimal — making the ≥90% success threshold potentially miscalibrated against an unverified reference.Partially mitigated by running multiple independent classical heuristic solvers (simulated annealing + Gurobi with generous time limit) and using the best across all as reference; this does not fully resolve the risk that true optimum is better than any classical reference found, which would bias solution-quality estimates optimistically.
- mediumFive repetitions per grid cell is a small sample for detecting mitigation effects given known hardware calibration drift, risking underpowered statistical tests and false negatives in DISPROOF_CRITERIA.Randomized/interleaved scheduling and calibration logging partially address confounding, but power analysis for the ANOVA/t-tests is not formally pre-registered here; a follow-up power calculation (targeting effect size from pilot data) should be added before full-scale commitment, and is currently an acknowledged gap.
Experimental Protocol
Minimum viable test: 3 docking QUBO instances (small: 20 vars with known classical optimum; medium: 50 vars; large: 100–127 vars), each run on IBM Heron under a 4×5 grid (4 mitigation strategies × 5 shot budgets: 1k/5k/10k/50k/100k), 5 repetitions per cell for statistical power, benchmarked against (1) classical exact/branch-and-bound solver ground truth (small instance only), (2) simulated noiseless QAOA/SQD baseline, and (3) classical simulated-annealing QUBO solver as practical baseline.
- A curated docking benchmark set (e.g., subset of PDBbind or CASF-2016 protein-ligand complexes) converted to QUBO via standard pose/rotamer discretization (10–20 poses × discrete rotamer states).
- Classical ground-truth solutions: exact diagonalization (≤30 qubits) and/or Gurobi/CPLEX QUBO solver results for all instances.
- IBM Quantum backend access (Heron r1/r2, e.g., ibm_torino, ibm_marrakesh) with sufficient QPU-time allocation.
- SQD software stack (Qiskit SQD module / qiskit-addon-sqd) and classical post-processing (self-consistent configuration recovery code).
- Noise characterization data (calibration snapshots: T1, T2, readout error, two-qubit gate error) logged per run.
- Identification of ≥1 (shots, mitigation) configuration achieving ≥90% solution quality (relative to best achieved across full grid) at ≤50% of max-shot-budget cost, replicated in ≥2/3 instances and ≥2 backends.
- Statistically significant (p<0.05) improvement from at least one mitigation technique over raw/unmitigated baseline.
- Shot-budget saturation curve exhibits identifiable knee point below 50,000 shots.
- No configuration meets the 90%/50% criterion in any instance.
- Mitigation strategies show no significant effect (all p>0.05) or effects are inconsistent in sign across instances/backends.
- Solution quality does not improve monotonically with shots (indicating dominant systematic noise not addressable by shot scaling), invalidating shot-budget optimization framing.
- Cross-backend variance exceeds within-backend variance by >2x, indicating results are not device-generalizable ("Heron-class" claim unsupported).
ROI Projection
Implementation Sketch
for instance in [small_20var, medium_50var, large_100var]: qubo = build_docking_qubo(instance) ground_truth = classical_solve(qubo) # Gurobi / exact diag if size<=30 for mitigation in [None, DD, TREX, ZNE]: for shots in [1000, 5000, 10000, 50000, 100000]: for rep in range(5): circuit = sqd_sampling_circuit(qubo) job = backend.run(circuit, shots=shots, mitigation=mitigation) counts = job.result() energy_est = sqd_configuration_recovery(counts, qubo) log(instance, mitigation, shots, rep, energy_est, calibration_snapshot(backend)) results_df = aggregate_logs() pareto_frontier = compute_pareto(results_df, metrics=["cost_shots","solution_quality"]) recommended_config = select_min_cost_at_threshold(pareto_frontier, quality>=0.90) validate_cross_backend(recommended_config, second_backend)
- After small-instance (20-var) full grid completes (~10 days): if no mitigation shows any significant effect, halt and reassess mitigation strategy selection before investing in medium/large instances.
- After first backend's full 3-instance grid (~25 days): if shot-budget saturation is not observed by 100,000 shots (i.e., no plateau), abort scaling further and report inconclusive/negative result rather than extending shot range indefinitely.
- Mid-protocol cost check: if QPU-time consumption exceeds 70% of allocated budget before medium-instance completion, abort large-instance run and report on small+medium only.
NAMED_EXPERTS: []
CLOSEST_EXISTING_WORK: []
NOVELTY_NARROWING_REQUIRED: false
SPINE_STATEMENT: This hypothesis tests whether a specific shot-budget and noise-mitigation configuration exists on IBM Heron hardware that recovers ≥90% of best-achievable QUBO docking solution quality via Sample-Based Quantum Diagonalization at ≤50% the shot cost of a naive maximal-shot baseline.