TBNQuantum
Quantum-Classical Iterative Refinement for the Pressure-Poisson Equation on NISQ Hardware
Publication: quant-ph updates on arXiv.org
Author: Doyeol "David" Ahn (Department of Electrical and Computer Engineering, University of Seoul, Seoul, Republic of Korea 2 Singularity Quantum Inc., Newport Beach, CA, USA 3 Center for Quantum Information
Source published: 20/10/2026, 04:00:00 UTC
Briefing created: 21/10/2026, 02:45:16 UTC
Based on a feed excerpt; full article content has not been acquired. Source evidence retrieved 21/10/2026, 02:43:24 UTC.
Briefings
A hybrid quantum-classical iterative refinement method solves the pressure-Poisson equation on NISQ hardware by repeatedly solving the residual equation and scaling quantum directions via least-squares fitting. This approach treats quantum noise as a convergence rate limiter rather than an accuracy floor, allowing residual convergence without requiring state infidelity below 10^-7. On IBM's ibm_cleveland processor, a four-qubit problem achieved a relative residual below 10^-7 in eight to ten corrections, whereas a single solve with similar shots stopped at 0.33-0.59. On the IonQ Forte processor, a benchmark reached 5.6e-8 in nine corrections.
Key points
- The method uses a hybrid quantum-classical iterative refinement where the pressure equation is solved repeatedly for the normalized residual, with quantum directions scaled by a least-squares fit to the physical residual.
- On IBM's ibm_cleveland processor, a four-qubit (16x16) problem reached a relative residual below 10^-7 within eight to ten corrections in all 20 runs of a pre-registered experiment.
Context
This work represents a significant step toward solving the pressure-Poisson equation on noisy quantum hardware, enabling more accurate simulations of incompressible Navier-Stokes flows. The key finding is that quantum noise limits convergence speed rather than accuracy, allowing residual convergence without stringent infidelity requirements.
Limitations
The study is limited to a single pre-registered experiment on IBM's ibm_cleveland processor and a six-qubit pilot on IonQ Forte. Results are based on limited shots and may not generalize to larger systems or different noise models. The specific hardware and processor details are not fully disclosed.
Generated by Bittrees-hosted qwen35-2b sha256:aaf42c8b7c3c on 21/10/2026, 02:45:16 UTC. Based on publisher-provided feed evidence; may not cover the full original article. Check the source for details.
View archived briefing on IPFS
bafybeidcta5j3snj4yuhcoponabmt47zqb4ztpoivfmnqe4rxmeqdr4bo4