Simulating quantum error mitigation in fermionic encodings

TL;DR

This paper explores stabilizer postselection as an error mitigation technique for fermionic quantum simulations, demonstrating significant fidelity improvements on systems up to 42 qubits with manageable resource overhead.

Contribution

It introduces and evaluates a stabilizer postselection method for error mitigation in fermionic encodings, supported by new classical simulation algorithms.

Findings

Fidelity can be significantly increased at reasonable noise levels.

Error mitigation outperforms standard Jordan-Wigner transformation.

Classical algorithms scale with logical Hilbert space, enabling larger simulations.

Abstract

The most scalable proposed methods of simulating lattice fermions on noisy quantum computers employ encodings that eliminate nonlocal operators using a constant factor more qubits and a nontrivial stabilizer group. In this work, we investigated the most straightforward error mitigation strategy using the stabilizer group, stabilizer postselection, that is very natural to the setting of fermionic quantum simulation. We numerically investigate the performance of the error mitigation strategy on a range of systems containing up to 42 qubits and on a number of fundamental quantum simulation tasks including non-equilibrium dynamics and variational ground state calculations. We find that at reasonable noise rates and system sizes, the fidelity of computations can be increased significantly beyond what can be achieved with the standard Jordan-Wigner transformation at the cost of increasing the number of shots by less than a factor of 10, potentially providing a meaningful boost to near-term quantum simulations. Our simulations are enabled by new classical simulation algorithms that scale with the logical Hilbert space dimension rather than the physical Hilbert space dimension.