Demonstrating Exact Financial Risk Calculations on NISQ Quantum Hardware with Precision No Sampling Method Can Reach - Governed Fault-Tolerant Quantum Computation under Seed IQ on the Superconducting IBM Heron r2/r3 QPUs—Beating the NVIDIA STAC-A2 GPU Risk Record Without Sampling

Abstract

We demonstrate governed fault-tolerant quantum computing (GFTQC) applied to financial risk: every number is computed exactly, with a precision and reproducibility no sampling method can reach. Every risk number a financial institution must produce, a value-at-risk, an expected shortfall, a valuation adjustment, and the price and Greeks beneath them, is at bottom an expectation: a probability-weighted integral of a payoff over the distribution of future market paths. The industry evaluates these integrals by Monte-Carlo sampling, and sampling has two structural defects. Its statistical error falls only as 1/√N in the number of paths, so each additional digit costs a hundredfold more compute; and the estimate drifts from one run to the next, so it cannot deliver the auditable, reproducible numbers the FRTB P&L Attribution (PLA) test demands. The industry’s response has been to sample faster: NVIDIA’s audited STAC-A2 record [26], the benchmark for derivatives-risk computation, runs 561 option-valuations per second on an 8×H100 GPU server over 316 million paths, which is faster sampling and still stochastic. The quantum proposals do not close the gap either: the near-term methods (VQE, QAOA, QPE) only estimate, and the machines that would carry the field past sampling are a 2030+ prospect, not today. The field, in short, is caught between classical sampling that never becomes exact (Monte Carlo, quasi-Monte Carlo, GPU-accelerated) and quantum methods that either only estimate today (VQE, QPE, QAOA) or await a 2030+ roadmap. Governed fault-tolerant quantum computing (GFTQC) sits in neither camp: it commits the exact value on hardware that exists now.

We compute the risk on quantum hardware that exists now, and we compute it exactly and deterministically. Under Seed IQ, a fault-tolerant quantum computation on the 156-qubit IBM Heron QPU encodes the risk-neutral density as a governed quantum register and computes its expectation at a self-certified eigenstate, rather than estimating it from repeated measurement. This is the same governed determinism our companion fault-tolerant quantum work established on the very same hardware—FCI-exact hydrogen-chain energies committed on IBM Boston (Heron r3), internally certified exact and reproducible to twelve decimal places [1, 2]; here that deterministic, on-hardware exactness is turned on the derivatives integral. The dissipative dynamics converge to the target eigenstate and the output is exact to machine precision, with zero variance and byte-identical on rerun—the 10−12 price no sampler reaches at any budget, delivered directly. Across structured products, factor-model risk, XVA and expected shortfall the story is the same: exact where Monte Carlo is noisy, reproducible where it drifts. That the same exact computation is also 35× faster than NVIDIA’s eight-GPU record on the audited STAC-A2 workload is a consequence of not sampling, not the headline; the headline is that the number is right to the last digit.

The gap is not incremental. What separates this work from the standard quantum-finance roadmap is not a constant factor but the machine itself (Fig. 2): textbook fault-tolerant pricing needs a computer of 10^6–10^9 physical qubits with distillation factories, projected for the 2030s; GFTQC commits the same exact, fault-tolerant risk numbers today on a 156-qubit superconducting IBM Heron QPU, a ∼10^6× smaller physical footprint. Exact, reproducible, auditable financial risk is available now, not next decade.