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arXiv:2307.11156 · Physical Review A

Mitigating quantum gate errors for variational eigensolvers using hardware-inspired zero-noise extrapolation

Alexey Uvarov, Daniil Rabinovich, Olga Lakhmanskaya, Kirill Lakhmanskiy, Jacob Biamonte, Soumik Adhikary

Published Jul 1, 2024• 5 citations
arXivHTMLPDF

Abstract

Variational quantum algorithms have emerged as a cornerstone of contemporary quantum algorithms research. Practical implementations of these algorithms, despite offering certain levels of robustness against systematic errors, show a decline in performance due to the presence of stochastic errors and limited coherence time. In this work, we develop a recipe for mitigating quantum gate errors using zero-noise extrapolation. We introduce an experimentally amenable method to control error strength in the circuit. We utilize the fact that gate errors in a physical quantum device are distributed inhomogeneously over different qubits and qubit pairs. As a result, one can achieve different circuit error sums based on the manner in which abstract qubits in the circuit are mapped to a physical device. We apply the proposed protocol to variational quantum algorithms and find that the estimated energy is approximately linear with respect to the circuit error sum (CES). Consequently, a linear fit through the energy-CES data, when extrapolated to zero CES, can approximate the energy estimated by a noiseless variational algorithm. We demonstrate this numerically and investigate the applicability range of the technique.

DOI
10.1103/physreva.110.012404

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Variational quantum algorithms have emerged as a cornerstone of contemporary quantum algorithms research. Practical implementations of these algorithms, despite offering certain levels of robustness against systematic errors, show a decline in performance due to the presence of stochastic errors and limited coherence time. In this work, we develop a recipe for mitigating quantum gate errors using zero-noise extrapolation. We introduce an experimentally amenable method to control error strength in the circuit. We utilize the fact that gate errors in a physical quantum device are distributed inhomogeneously over different qubits and qubit pairs. As a result, one can achieve different circuit error sums based on the manner in which abstract qubits in the circuit are mapped to a physical device. We apply the proposed protocol to variational quantum algorithms and find that the estimated energy is approximately linear with respect to the circuit error sum (CES). Consequently, a linear fit through the energy-CES data, when extrapolated to zero CES, can approximate the energy estimated by a noiseless variational algorithm. We demonstrate this numerically and investigate the applicability range of the technique.
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Abstract Quantum computers have the potential to help solve a range of physics and chemistry problems, but noise in quantum hardware currently limits our ability to obtain accurate results from the execution of quantum-simulation algorithms. Various methods have been proposed to mitigate the impact of noise on variational algorithms, including several that model the noise as damping expectation values of observables. In this work, we benchmark various methods, including a new method proposed here. We compare their performance in estimating the ground-state energies of several instances of the 1D mixed-field Ising model using the variational-quantum-eigensolver algorithm with up to 20 qubits on two of IBM’s quantum computers. We find that several error-mitigation techniques allow us to recover energies to within 10% of the true values for circuits containing up to about 25 ansatz layers, where each layer consists of CNOT gates between all neighboring qubits and Y -rotations on all qubits.
A common approach to deal with gate errors in modern quantum-computing hardware is zero-noise extrapolation. By artificially amplifying errors and extrapolating the expectation values obtained with different error strengths towards the zero-error (zero-noise) limit, the technique aims at rectifying errors in noisy quantum computing systems. For accurate extrapolation, it is essential to know the exact factors of the noise amplification. In this article, we propose a simple method for estimating the strength of errors occurring in a quantum circuit and demonstrate improved extrapolation results. The method determines the error strength for a circuit by appending to it the inverted circuit and measuring the probability of the initial state. The estimation of error strengths is easy to implement for arbitrary circuits and does not require previous characterization of noise properties. We compare this method with the conventional zero-noise extrapolation method and show that our method leads to a more accurate calculation of expectation values on current quantum hardware, showcasing its suitability for near-term quantum computing applications. Published by the American Physical Society 2024
Machine Learning-based quantum error mitigation (ML-QEM) has emerged as a promising approach for improving the performance of noisy quantum algorithms. However, existing ML-QEM methods often have restricted applicability to variational circuits and rely on inaccessible noiseless training data. In this work, we propose a practical ML-QEM protocol tailored to variational quantum algorithms, which generates training data by simulating (near-)Clifford circuits. This data is used for model selection and training, producing a mitigation model that can correct variational circuits with arbitrary parameters and transfer across different target Hamiltonians of similar structure. We benchmark the proposed method on the Variational Quantum Eigensolver (VQE) task for the Sherrington-Kirkpatrick Hamiltonian of up to n=12n=12n=12 qubits under various noise models, analyzing its effect on trainability and comparing its performance against standard Zero-Noise Extrapolation (ZNE). The results demonstrate consistent several-fold error suppression across all tested settings and superior performance over ZNE in the high-noise regime, providing evidence for the applicability of the proposed protocol to present-day NISQ processors.
Abstract We present a method to improve the convergence of variational algorithms based on hidden inverses (HIs) to mitigate coherent errors. In the context of error mitigation, this means replacing the hardware implementation of certain Hermitian gates with their inverses. Doing so results in noise cancellation and a more resilient quantum circuit. This approach improves performance in a variety of two-qubit error models where the noise operator also inverts with the gate inversion. We apply the mitigation scheme on superconducting quantum processors running the variational quantum eigensolver (VQE) algorithm to find the H 2 ground-state energy. When implemented on superconducting hardware we find that the mitigation scheme effectively reduces the energy fluctuations in the parameter learning path in VQE, reducing the number of iterations for a converged value. We also provide a detailed numerical simulation of VQE performance under different noise models and explore how HIs and randomized compiling affect the underlying loss landscape of the learning problem. These simulations help explain our experimental hardware outcomes, helping to connect lower-level gate performance to application-specific behavior in contrast to metrics like fidelity which often do not provide an intuitive insight into observed high level performance.
Variational quantum algorithms are tailored to perform within the constraints of current quantum devices, yet they are limited by performance-degrading errors. In this study we consider a noise model that reflects realistic gate errors inherent to variational quantum algorithms. We investigate the decoherence of a variationally prepared quantum state due to this noise model, which causes a deviation from the energy estimation in the variational approach. By performing a perturbative analysis of optimized circuits, we determine the noise threshold at which the criterion set by the stability lemma is met. We assess our findings against the variational quantum eigensolver and quantum approximate optimization algorithm for various problems with up to 14 qubits. Moreover, we show that certain gate errors have a significantly smaller impact on the coherence of the state, allowing us to reduce the execution time without compromising performance.