Experimental error mitigation via symmetry verification in a variational quantum eigensolver

TLDR

Variational quantum eigensolvers offer a small‑scale testbed to demonstrate the performance of error mitigation techniques with low experimental overhead. The study applies symmetry verification to experimentally estimate the ground‑state energy and state of the hydrogen molecule, demonstrating successful error mitigation. The authors use a tunable exchange interaction between two qubits in a circuit‑QED processor to prepare parity‑respecting variational ansatz states, and employ full‑density‑matrix simulations together with convex‑optimization enforcement of positivity to dissect and correlate error contributions. Symmetry verification reduces errors from qubit relaxation and residual excitation, yielding more accurate energy and state estimates for the hydrogen molecule.

Abstract

Variational quantum eigensolvers offer a small-scale testbed to demonstrate the performance of error mitigation techniques with low experimental overhead. We present successful error mitigation by applying the recently proposed symmetry verification technique to the experimental estimation of the ground-state energy and ground state of the hydrogen molecule. A finely adjustable exchange interaction between two qubits in a circuit QED processor efficiently prepares variational ansatz states in the single-excitation subspace respecting the parity symmetry of the qubit-mapped Hamiltonian. Symmetry verification improves the energy and state estimates by mitigating the effects of qubit relaxation and residual qubit excitation, which violate the symmetry. A full-density-matrix simulation matching the experiment dissects the contribution of these mechanisms from other calibrated error sources. Enforcing positivity of the measured density matrix via scalable convex optimization correlates the energy and state estimate improvements when using symmetry verification, with interesting implications for determining system properties beyond the ground-state energy.