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IEEE Congress on Evolutionary Computation (CEC)

A Competent Memetic Algorithm for Error Mitigation in Quantum Measurement

Giovanni Acampora, Autilia Vitiello

Published Jul 1, 2023• 0 citations
Publisher

Abstract

Recently, a significant interest is arising in developing techniques capable of correcting errors in noisy quantum computations without using additional quantum resources. These techniques, known as mitigation methods, are aimed at post-processing the quantum outcome without working at quantum hardware level. Among the most error-prone operations on the current quantum devices, there is surely the quantum measurement. Currently, the most popular mitigation method for quantum measurement error consists of computing a so-called mitigation matrix to be applied on the results outputted by a quantum processor to transform them and make them closer to the ideal ones. In this paper, a new measurement error mitigation method based on a competent memetic algorithm is proposed to generate an appropriate mitigation matrix. As shown in the experimental session, the proposed measurement error mitigation method shows better results when compared with the conventional method and the state of the art among the evolutionary approaches.

DOI
10.1109/cec53210.2023.10253998

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Recently, a significant interest is arising in developing techniques capable of correcting errors in noisy quantum computations without using additional quantum resources. These techniques, known as mitigation methods, are aimed at post-processing the quantum outcome without working at quantum hardware level. Among the most error-prone operations on the current quantum devices, there is surely the quantum measurement. Currently, the most popular mitigation method for quantum measurement error consists of computing a so-called mitigation matrix to be applied on the results outputted by a quantum processor to transform them and make them closer to the ideal ones. In this paper, a new measurement error mitigation method based on a competent memetic algorithm is proposed to generate an appropriate mitigation matrix. As shown in the experimental session, the proposed measurement error mitigation method shows better results when compared with the conventional method and the state of the art among the evolutionary approaches.
Noisy Intermediate Scale Quantum (NISQ) devices are expected to demonstrate the real potential of quantum computing in solving hard problems. However, quantum noise that characterizes this kind of devices still remains an obstacle for their practical exploitation in real world scenarios. As a consequence, there is a strong emergence for error correction techniques aimed at making NISQ devices stable and fully operative. Unfortunately, current approaches for quantum error correction are prohibitive for NISQ devices because of the enormous multiplicative cost in resources that they require. For this reason, so-called quantum error mitigation methods are emerging as alternative approaches able to attenuate the quantum error as much as possible, without requiring a strong additional computational effort. Among the most error-prone operations, there is surely the quantum measurement. Conventionally, mitigation methods for quantum measurement error compute a so-called mitigation matrix capable of correcting results outputted by a quantum processor. In this paper, a new measurement error mitigation approach based on genetic algorithms is proposed to learn an appropriate mitigation matrix. As shown in the experimental session, the proposed measurement error mitigation method is comparable with or better than a conventional algebraic approach in terms of the Hellinger fidelity.
Quantum computing is a fascinating research area which promises a revolution in computing performance. Since the launch of the IBM Quantum Experience project in 2016, the research activities in this area are strongly increased. This project provides the public access to quantum processors composed of superconducting physical computing elements known as qubits. Unfortunately, qubits are sensitive to noise and, for this reason, quantum computation can be affected by errors. As a consequence, there is a strong emergence for so- called quantum error mitigation methods aimed to attenuate the quantum error as much as possible, without requiring a strong additional computational effort. Among the most error- prone operations, there is surely the quantum measurement. Conventionally, mitigation methods for quantum measurement error compute a so-called mitigation matrix capable of correcting results outputted by a quantum processor. In this paper, a new measurement error mitigation approach based on genetic algorithms whose fitness function uses Bhattacharyya distance is proposed to learn an appropriate mitigation matrix. As shown in the experimental session, the proposed measurement error mitigation method outperforms the traditional approach.
Minimizing the effect of noise is essential for quantum computers. The conventional method to protect qubits against noise is through quantum error correction. However, for current quantum hardware in the so-called noisy intermediate-scale quantum (NISQ) era, noise presents in these systems and is too high for error correction to be beneficial. Quantum error mitigation is a set of alternative methods for minimizing errors, including error extrapolation, probabilistic error cancellation, measurement error mitigation, subspace expansion, symmetry verification, virtual distillation, etc. The requirement for these methods is usually less demanding than error correction. Quantum error mitigation is a promising way of reducing errors on NISQ quantum computers. This paper gives a comprehensive introduction to quantum error mitigation. The state-of-art error mitigation methods are covered and formulated in a general form, which provides a basis for comparing, combining and optimizing different methods in future work.
Error mitigation has been one of the recently sought after methods to reduce the effects of noise when computation is performed on a noisy near-term quantum computer. Interest in simulating stochastic processes with quantum models gained popularity after being proven to require less memory than their classical counterparts. With previous work on quantum models focusing primarily on further compressing memory, this work branches out into the experimental scene; we aim to bridge the gap between theoretical quantum models and practical use with the inclusion of error mitigation methods. It is observed that error mitigation is successful in improving the resultant expectation values. While our results indicate that error mitigation work, we show that its methodology is ultimately constrained by hardware limitations in these quantum computers.
Reducing measurement errors in multiqubit quantum devices is critical for performing any quantum algorithm. Here we show how to mitigate measurement errors by a classical postprocessing of the measured outcomes. Our techniques apply to any experiment where measurement outcomes are used for computing expected values of observables. Two error-mitigation schemes are presented based on tensor product and correlated Markovian noise models. Error rates parametrizing these noise models can be extracted from the measurement calibration data using a simple formula. Error mitigation is achieved by applying the inverse noise matrix to a probability vector that represents the outcomes of a noisy measurement. The error-mitigation overhead, including the number of measurements and the cost of the classical postprocessing, is exponential in $\ensuremath{\epsilon}n$, where $\ensuremath{\epsilon}$ is the maximum error rate and nnn is the number of qubits. We report experimental demonstration of our error-mitigation methods on IBM Quantum devices using stabilizer measurements for graph states with $n\ensuremath{\le}12$ qubits and entangled 20-qubit states generated by low-depth random Clifford circuits.
The realization of fault-tolerant quantum computers remains a challenging endeavor, forcing state-of-the-art quantum hardware to rely heavily on noise mitigation techniques. Standard quantum error mitigation is typically based on post-processing strategies. In contrast, the present work explores a pre-processing approach, in which the effects of noise are mitigated before performing a measurement on the output state. The main idea is to find an observable YYY such that its expectation value on a noisy quantum state E(ρ)\mathcal{E(ρ)}E(ρ) matches the expectation value of a target observable XXX on the noiseless quantum state ρρρ. Our method requires the execution of a noisy quantum circuit, followed by the measurement of the surrogate observable YYY. The main enablers of our method in practical scenarios are Tensor Networks. The proposed method improves over Tensor Error Mitigation (TEM) in terms of average error, circuit depth, and complexity, attaining a measurement overhead that approaches the theoretical lower bound. The improvement in terms of classical computation complexity is in the order of ∼106\sim 10^6∼106 times when compared to the post-processing computational cost of TEM in practical scenarios. Such gain comes from eliminating the need to perform the set of informationally complete positive operator-valued measurements (IC-POVM) required by TEM, as well as any other tomographic strategy.