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

TL;DR

The results show that the variational circuit can reproduce the QFT with higher fidelity in scenarios dominated by coherent noise, demonstrating 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.

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.

Figures (20)

• Figure 1: The quantum circuit for the 2-qubit QFT, where $|\psi\rangle$ denotes the initial state before applying the QFT, implemented using the Pennylane library.
• Figure 2: The quantum circuit for the 2-qubit variational Ansatz used to simulate the QFT, where $|\psi\rangle$ denotes the initial state before applying the Ansatz, implemented using the Pennylane library.
• Figure 3: The quantum circuit for the variational Ansatz used to simulate the QFT with 2 qubits, with random superposition states as input, implemented using the Pennylane library.
• Figure 4: Evolution of the cost function, corresponding to the noiseless case, presented on a logarithmic scale, during optimization over 5000 steps, showing quick convergence. However, we trained for additional steps to achieve higher fidelity.
• Figure 5: Evolution of the average fidelity during optimization. The big panel shows the complete optimization for 5000 steps, demonstrating quick convergence. Nevertheless, we trained for additional steps to achieve higher fidelity. The small panel displays the evolution of the fidelity after 200 steps, zooming-in.