Quantum Utility-Scale Error Mitigation for Quantum Quench Dynamics in Heisenberg Spin Chains

Abstract: We propose a quantum error mitigation method termed self-mitigation, which is comparable with zero-noise extrapolation, to achieve quantum utility on near-term, noisy quantum computers. We investigate the effectiveness of several quantum error mitigation strategies, including self-mitigation, by simulating quantum quench dynamics for Heisenberg spin chains with system sizes up to 104 qubits using IBM quantum processors. In particular, we discuss the limitations of zero-noise extrapolation and the advantages offered by self-mitigation at a large scale. The self-mitigation method shows stable accuracy with the large systems of 104 qubits with more than 3,000 CNOT gates. Also, we combine the discussed quantum error mitigation methods with practical entanglement entropy measuring methods, and it shows a good agreement with the theoretical estimation. Our study illustrates the usefulness of near-term noisy quantum hardware in examining the quantum quench dynamics of many-body systems at large scales, and lays the groundwork for surpassing classical simulations with quantum methods prior to the development of fault-tolerant quantum computers.