Joint Mitigation of Algorithmic and Physical Errors in Noisy Hamiltonian Simulation
Abstract
Product-formula Hamiltonian simulation is naturally suited to near-term quantum processors, but its accuracy is set by two competing errors: finite-step Trotter bias and physical hardware noise. We introduce a joint extrapolation strategy that ties the tunable per-layer noise strength to the Trotter step size, λ(s)=c(sT)p+1 for a p-th order product formula. Along this one-dimensional path, the leading physical-noise and Trotter corrections over the full evolution both enter at order sp and can be canceled by a single Richardson extrapolation. Building on a previously established finite-order Baker--Campbell--Hausdorff truncation bound, we derive a provably commutator-scaling resource guarantee for the joint extrapolation. For local Hamiltonians with local Lindbladian noise, the protocol mitigates physical noise together with Trotter error with only a constant asymptotic overhead relative to noiseless Trotter extrapolation, provided the required noise strengths lie above the intrinsic device-noise floor. We experimentally demonstrate the protocol for Ising dynamics on a superconducting quantum computer using learned noise amplification. Complementary 100-qubit Sparse Pauli Dynamics (SPD) simulations achieve comparable accuracy to two-dimensional Richardson extrapolation with fewer circuit settings.
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BibTeX
@misc{zhou2026joint,
title = {{Joint Mitigation of Algorithmic and Physical Errors in Noisy Hamiltonian Simulation}},
author = {Shuo Zhou and Xinzhao Wang and Ruiqi Zhang and Xiaoyang Wang and Yi-Cong Zheng and Tongang Li and Shengyu Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11508},
eprint = {2609.11508},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11508},
}
RIS
TY - UNPB
TI - Joint Mitigation of Algorithmic and Physical Errors in Noisy Hamiltonian Simulation
AU - Shuo Zhou
AU - Xinzhao Wang
AU - Ruiqi Zhang
AU - Xiaoyang Wang
AU - Yi-Cong Zheng
AU - Tongang Li
AU - Shengyu Zhang
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11508
UR - https://arxiv.org/abs/2609.11508
AB - Product-formula Hamiltonian simulation is naturally suited to near-term quantum processors, but its accuracy is set by two competing errors: finite-step Trotter bias and physical hardware noise. We introduce a joint extrapolation strategy that ties the tunable per-layer noise strength to the Trotter step size, λ(s)=c(sT)^p+1 for a p-th order product formula. Along this one-dimensional path, the leading physical-noise and Trotter corrections over the full evolution both enter at order s^p and can be canceled by a single Richardson extrapolation. Building on a previously established finite-order Baker--Campbell--Hausdorff truncation bound, we derive a provably commutator-scaling resource guarantee for the joint extrapolation. For local Hamiltonians with local Lindbladian noise, the protocol mitigates physical noise together with Trotter error with only a constant asymptotic overhead relative to noiseless Trotter extrapolation, provided the required noise strengths lie above the intrinsic device-noise floor. We experimentally demonstrate the protocol for Ising dynamics on a superconducting quantum computer using learned noise amplification. Complementary 100-qubit Sparse Pauli Dynamics (SPD) simulations achieve comparable accuracy to two-dimensional Richardson extrapolation with fewer circuit settings.
ER -