Variational noise mitigation in quantum circuits: the case of Quantum Fourier Transform

TL;DR

This paper introduces a variational quantum algorithm approach to improve the fidelity of the Quantum Fourier Transform under realistic noise conditions, demonstrating potential as an effective error mitigation strategy for near-term quantum devices.

Contribution

It presents a novel variational method incorporating Mutually Unbiased Bases to enhance QFT fidelity in noisy environments, especially with coherent noise.

Findings

Variational circuits outperform traditional QFT under coherent noise.

Incorporating MUBs improves generalization and robustness.

Method adapts to specific device noise profiles.

Abstract

We propose using variational quantum algorithms (VQAs) to simulate established quantum algorithms under realistic noise conditions, aiming to surpass the fidelity of theoretical circuits in noisy environments. Focusing on the Quantum Fourier Transform (QFT), we perform numerical simulations for two qubits under both coherent and incoherent noise. To enhance generalization, we further introduce the use of Mutually Unbiased Bases (MUBs) during the optimization. Our results show that the variational circuit can reproduce the QFT with higher fidelity in scenarios dominated by coherent noise. This demonstrates the potential of the approach as an effective error-mitigation strategy for small- to medium-scale quantum systems, particularly in settings where coherent noise strongly impacts performance. Beyond mitigating noise and improving fidelity, the method can be adapted to the noise profile of a specific device, providing a versatile and practical route to enhance the reliability of quantum algorithms in near-term quantum hardware.