Mid-Circuit Measurements for Clifford Noise Reduction in Hamiltonian Simulations

TL;DR

This paper introduces a mid-circuit measurement-based noise reduction method for quantum Hamiltonian simulation, achieving significant error rate reductions on near-term hardware by combining encoding, Clifford noise reduction, and stabilizer verification.

Contribution

It presents a novel device-matched noise reduction framework that leverages mid-circuit measurements and stabilizer verification to improve quantum simulation accuracy without full error correction.

Findings

Encoded CliNR reduces logical error rate by up to 54%.

Mid-circuit stabilizer readout is essential for error reduction.

Machine learning can optimize stabilizer verification operators.

Abstract

Quantum simulation of fermionic Hamiltonians is a leading application of quantum computing, but accurate execution on present-day hardware is limited by error accumulation in deep Trotter circuits. We present a device-matched noise-reduction framework for encoded Hamiltonian simulation that combines symplectic-transvection-based Trotter synthesis in the Generalized Superfast Encoding (GSE) with Clifford Noise Reduction (CliNR) and Shor-style stabilizer verification enabled by mid-circuit measurement. We implement this approach for a six-qubit encoded Clifford Trotter step on a Barium development system similar to the forthcoming IonQ Tempo line and benchmark it against direct execution using both hardware experiments and a calibrated device-level noise model. The encoded CliNR execution achieves up to 54% lower logical error rate. Crucially, this advantage disappears when stabilizer readout is deferred to the end of the circuit, showing that timely mid-circuit fault detection, rather than verification overhead alone, drives the improvement. As a proof of concept, we further show that machine-learning-guided stabilizer selection can identify verification operators that outperform random choices. These results demonstrate that encoding-native verification combined with dynamic-circuit primitives can materially improve application-motivated quantum simulation without the full overhead of quantum error correction.