Quantum sampling architectures (QSAD) for protein structure reconstruction will exhibit power-law scaling of conformational search efficiency when constrained by the same exponent-range precision barrier governing FP32-BF16 loss-landscape mismatch (LMC) in surrogate Bayesian optimization, with the barrier magnitude inversely proportional to the number of qubits in the quantum-classical hybrid system.

This discovery has a Claude-generated validation package with a full experimental design.

Precise Hypothesis

Spine & Adversarial ReadReady for validation

“This hypothesis tests whether the scaling exponent governing conformational-search efficiency in qubit-count-varying quantum-classical hybrid protein-folding samplers is statistically indistinguishable from the scaling exponent governing the FP32-BF16 precision-mismatch barrier in classical surrogate Bayesian optimization.”

• highThe premise that a well-characterized 'FP32-BF16 LMC exponent-range precision barrier' exists as an established, reproducible phenomenon in classical surrogate Bayesian optimization is unsupported by any citation or dataset in the provided materials — the entire hypothesis may be anchoring to an undefined or non-existent baseline quantity.
  Not resolved in this EVP. Phase A of the protocol requires independently establishing/reproducing this baseline before any cross-domain comparison is meaningful; this is flagged as Abort Checkpoint Day 15. If the LMC claim cannot be sourced or reproduced, the hypothesis is untestable as stated and must be reformulated as a purely quantum-side scaling-law study.
• highWhy HP lattice models and QAOA/VQE specifically, rather than e.g. quantum annealing, more realistic coarse-grained force fields, or classical replica-exchange MD as the comparator? The methodology choice is not justified against alternatives that might show the same or opposite scaling behavior, risking a result that is an artifact of the specific (convenient, easy-to-simulate) model choice rather than a general physical law.
  Partially addressed: HP lattice models are chosen because they admit exact/brute-force ground truth at small sizes (needed for the efficiency metric) and are standard benchmarks in quantum-folding proof-of-concept literature. However, the EVP does not include a control comparing against quantum annealing (D-Wave-style) or classical replica-exchange MD baselines, which would test whether the scaling law is specific to the QAOA/VQE ansatz class or a more general property of hybrid sampling. This is a gap — recommend adding a comparator arm before treating any positive result as evidence of a general law rather than an ansatz-specific one.
• mediumWith only 4 primary qubit-count conditions and known QAOA-optimization non-convexity/barren-plateau issues at larger qubit counts, any observed power-law fit is at high risk of being a low-power, small-n curve-fitting artifact rather than a genuine scaling law, especially given the documented tendency of variational quantum algorithms to fail to show scaling advantage in independently replicated studies.
  Partially resolved via the hold-out replication step (independent qubit counts 15/30/60) and bootstrap CIs, but the underlying statistical power problem is real and not fully solved by n=4-7 conditions. Recommend escalating to at least 8-10 qubit-count conditions and pre-registering the analysis (including AIC model comparison against stretched-exponential and logarithmic alternatives) before claiming power-law confirmation, to guard against the barren-plateau phenomenon being misread as favorable scaling.

Experimental Protocol

ROI Projection

Implementation Sketch

# Phase A: Classical LMC baseline
for precision in [FP32, BF16]:
    surrogate = GaussianProcessSurrogate(precision=precision)
    loss_landscape = surrogate.fit(conformational_energy_dataset)
    lmc_deviation[precision] = compare_landscape(loss_landscape, FP32_reference)
lmc_exponent = fit_power_law(lmc_deviation_vs_bitwidth_proxy)

# Phase B: Quantum-classical hybrid sampler
for Q in [10, 20, 40, 80]:
    for seed in [1,2,3]:
        for instance in benchmark_sequences:
            ansatz = build_QAOA(num_qubits=Q, cost_hamiltonian=encode(instance))
            result = hybrid_optimize(ansatz, classical_optimizer=COBYLA, backend=tensor_network_sim)
            efficiency[Q][seed][instance] = oracle_calls_to_convergence(result, exact_baseline[instance])

quantum_exponent = fit_power_law(efficiency vs Q, log_log=True)

# Phase C: Cross-domain comparison
compare_CI_overlap(quantum_exponent, lmc_exponent)
run_noise_ablation(Q_range, noise_levels=[0, 0.01, 0.05])
run_holdout_replication(Q_holdout=[15,30,60])