Joint Mitigation of Algorithmic and Physical Errors in Noisy Hamiltonian Simulation

• URL: http://arxiv.org/abs/2609.11508v1
• Date: Thu, 10 Sep 2026 13:15:37 GMT
• Title: Joint Mitigation of Algorithmic and Physical Errors in Noisy Hamiltonian Simulation
• Abstract summary: Product-formula Hamiltonian simulation is naturally suited to near-term quantum processors.<n>But its accuracy is set by two competing errors: finite-step Trotter bias and physical hardware noise.<n>We introduce a joint extrapolation strategy that ties the tunable per-layer noise strength to the Trotter step size.<n>We demonstrate the protocol for Ising dynamics on a superconducting quantum computer using learned noise.
• Score: 22.28754738497284
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $s^p$ 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.

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