Dual-state purification for practical quantum error mitigation

TL;DR

This paper introduces a practical dual-state purification protocol for quantum error mitigation that enhances fidelity without additional qubits, improving accuracy especially for larger quantum circuits.

Contribution

It presents a novel error mitigation method using dual states, requiring minimal qubit overhead, and demonstrates its effectiveness on real quantum hardware.

Findings

Reduces error by a factor decreasing with qubit number and circuit depth

Effective on cloud quantum computers with variational circuits

Improves fidelity without extra qubits or significant overhead

Abstract

Quantum error mitigation is essential for computing on the noisy quantum computer with a limited number of qubits. In this paper, we propose a practical protocol of error mitigation by virtually purifying the quantum state without qubit overhead or requiring only one ancillary qubit. In dual-state purification, we effectively generate a purified state with increased fidelity using the erroneous state and its dual state, respectively, prepared with the noisy quantum circuit and the dual map of its inverse circuit. Combined with tomography purification, we can make sure that the final estimate of an observable is obtained from a pure state. The numerical result suggests that our protocol reduces the error by a rescaling factor decreasing with the qubit number and circuit depth, i.e. the performance of purification is better for larger circuits. On a cloud quantum computer, we successfully demonstrate the reduced error with a quantum variational eigensolver circuit.