Variational Noise Mitigation Reproduces Quantum Fourier Transform with Higher Fidelity under Coherent Noise Conditions

Quantum circuits, despite their promise, remain vulnerable to errors introduced by environmental noise, hindering the development of reliable quantum computation. Rafael Gómez-Lurbe, Alexander Bernal, and Armando Pérez, alongside their colleagues, address this challenge by exploring a novel approach to error mitigation using variational quantum algorithms. The team investigates how these algorithms can simulate quantum circuits, specifically the Quantum Fourier Transform, even under realistic and disruptive noise conditions. Their results demonstrate that this method surpasses the fidelity of standard circuits in noisy environments, particularly when coherent noise dominates, and offers a versatile pathway to improve the reliability of near-term quantum hardware by adapting to specific device characteristics. This achievement represents a significant step towards building practical and robust quantum computers capable of tackling complex computational problems.

Focusing on the Quantum Fourier Transform (QFT), they perform numerical simulations for two qubits under both coherent and incoherent noise, and introduce the use of Mutually Unbiased Bases (MUBs) during the optimisation process. 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.

Variational Circuits Enhance Quantum Fourier Transform Fidelity

Scientists have demonstrated a novel approach to enhance the fidelity of quantum computations in the presence of noise, achieving improved performance for the Quantum Fourier Transform (QFT). The research focuses on utilising variational quantum circuits to simulate the QFT for a two-qubit system, operating under both coherent and incoherent noise conditions. Through numerical simulations, the team successfully reproduced the QFT with higher fidelity specifically in scenarios where coherent noise predominates. This breakthrough delivers a practical method for error mitigation, particularly relevant for small- to medium-scale quantum systems where classical simulation remains feasible.

The method involves optimising a variational circuit, guided by comparisons between classically computed ideal QFT states and the noisy outputs generated by the circuit, within a classical optimisation loop. This process allows the circuit parameters to be tuned to minimise the impact of noise and maximise fidelity. Measurements confirm that the use of Mutually Unbiased Bases (MUBs) during optimisation enhances the generalisation capability of the circuit, enabling it to accurately reproduce the QFT across a broader range of input states. The optimised variational circuit surpasses the fidelity of the original QFT circuit under realistic noisy conditions, demonstrating its potential as a valuable tool for certifying quantum device performance.

The team’s approach is particularly effective in mitigating coherent noise, where variational adaptation significantly improves accuracy. Furthermore, the resulting optimised circuits can be integrated as subroutines within larger quantum algorithms, increasing their robustness to hardware-specific noise and paving the way for more reliable quantum computations. This work establishes a versatile protocol tailored to the specific noise profile of a given quantum device, enabling the design of circuits that deliver enhanced fidelity for the QFT.

Variational Quantum Circuits Mitigate QFT Noise

This research demonstrates the successful use of variational quantum circuits to simulate the Quantum Fourier Transform (QFT) with improved fidelity under noisy conditions. By employing a specifically designed variational Ansatz, the team achieved higher fidelity in simulating the two-qubit QFT, particularly when coherent noise dominates. This approach offers a promising error-mitigation strategy for small- to medium-scale quantum systems, enhancing the reliability of computations in near-term quantum hardware. The key to this achievement lies in the ability of the variational circuit to adapt to specific noise profiles, offering a versatile method for improving performance.

The researchers constructed a circuit based on single-qubit rotations, allowing for optimisation of parameters to closely replicate the QFT. This simulation-based approach provides a pathway to enhance the accuracy of quantum computations in the presence of imperfections. Future research will focus on scaling this approach to multiqubit systems, leveraging the recursive structure of the QFT to build more complex circuits. Further investigation into the optimisation of the variational parameters and the exploration of different noise models are also planned to refine the method and broaden its applicability.