Quantum computers can exploit a Hilbert space whose dimension increases exponentially with the number of qubits. In experiment, quantum supremacy has recently been achieved by the Google team by using a noisy intermediate-scale quantum (NISQ) device with over 50 qubits. However, the question of what can be implemented on NISQ devices is still not fully explored, and discovering useful tasks for such devices is a topic of considerable interest. Hybrid quantum-classical algorithms are regarded as well-suited for execution on NISQ devices by combining quantum computers with classical computers, and are expected to be the first useful applications for quantum computing. Meanwhile, mitigation of errors on quantum processors is also crucial to obtain reliable results. In this article, we review the basic results for hybrid quantum-classical algorithms and quantum error mitigation techniques. Since quantum computing with NISQ devices is an actively developing field, we expect this review to be a useful basis for future studies.
In this work, the global white-noise model is proved from first principles. The adherence of NISQ hardware to the global white-noise model is used to perform noise mitigation using Classical White-noise Extrapolation (CLAWE).
Hybrid Quantum Error Correction and Mitigation by Purification
New York University Shanghai（纽约大学上海分校）；NYU-ECNU Institute of Physics at NYU Shanghai（纽约大学上海纽约大学-华东师范大学物理研究所）；Department of Physics, New York University（纽约大学物理系）；Center for Quantum and Topological Systems (CQTS), NYUAD Research Institute, New York University Abu Dhabi（阿布扎比纽约大学研究学院量子与拓扑系统中心）；New York University（纽约大学）
Using quantum devices supported by classical computational resources is a promising approach to quantum-enabled computation. One example of such a hybrid quantum-classical approach is the variational quantum eigensolver (VQE) built to utilize quantum resources for the solution of eigenvalue problems and optimizations with minimal coherence time requirements by leveraging classical computational resources. These algorithms have been placed among the candidates for first to achieve supremacy over classical computation. Here, we provide evidence for the conjecture that variational approaches can …
We introduce an error mitigation framework that mitigates errors in a quantum circuit using circuit cutting. Our framework can be implemented in polynomial time for a wide variety of quantum circuits. Our technique involves cutting the circuit in such a way that we run the circuit that needs to be executed on the quantum hardware whereas the error mitigation circuit is run on a simulator. We perform error mitigation qubit by qubit and then provide a way to combine the different probabilities from each of the individual qubit error mitigation runs such that the full circuit is error mitigated. …
A standard approach to quantum computing is based on the idea of promoting a classically simulable and fault-tolerant set of operations to a universal set by the addition of `magic' quantum states. In this context, we develop a general framework to discuss the value of the available, non-ideal magic resources, relative to those ideally required. We single out a quantity, the Quantum-assisted Robustness of Magic (QRoM), which measures the overhead of simulating the ideal resource with the non-ideal ones through quasiprobability-based methods. This extends error mitigation techniques, originally…
We investigate the effects of noise on parameterised quantum circuits using spectral analysis and classical signal processing tools. For different noise models, we quantify the additional, higher frequency modes in the output signal caused by device errors. We show that filtering these noise-induced modes effectively mitigates device errors. When combined with existing methods, this yields an improved reconstruction of the noiseless variational landscape. Moreover, we describe the classical and quantum resource requirements for these techniques and test their effectiveness for application moti…
We propose a simple scheme to reduce readout errors in experiments on quantum systems with finite number of measurement outcomes. Our method relies on performing classical post-processing which is preceded by Quantum Detector Tomography, i.e., the reconstruction of a Positive-Operator Valued Measure (POVM) describing the given quantum measurement device. If the measurement device is affected only by an invertible classical noise, it is possible to correct the outcome statistics of future experiments performed on the same device. To support the practical applicability of this scheme for near-te…
We present an error mitigation scheme which corrects readout errors on Noisy Intermediate-Scale Quantum (NISQ) computers [1,2]. After a short review of applying the method to one qubit, we proceed to discuss the case when correlations between different qubits occur. We demonstrate how the readout error can be mitigated in this case. By performing experiments on IBMQ hardware, we show that such correlations do not have a strong effect on the results, justifying to neglect them.
Readout errors are among the most dominant errors on current noisy intermediate-scale quantum devices. Recently, an efficient and scaleable method for mitigating such errors has been developed, based on classical bit-flip correction. In this talk, we compare the performance of this method for IBM's and Rigetti's quantum devices, demonstrating how the method improves the noisy measurements of observables obtained on the quantum hardware. Moreover, we examine the variance amplification to the data after applying of our mitigation procedure, which is common to all mitigation strategies. We derive…
While we expect quantum computers to surpass their classical counterparts in the future, current devices are prone to high error rates and techniques to minimise the impact of these errors are indispensable. There already exists a variety of error mitigation methods addressing this quantum noise that differ in effectiveness, and scalability. But for a more systematic and comprehensible approach we propose the introduction of modelling, in particular for representing cause-effect relations as well as for evaluating methods or combinations thereof with respect to a selection of relevant criteria…
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 obs…
Noisy intermediate-scale quantum (NISQ) computers could solve quantum-mechanical simulation problems that are beyond the capabilities of classical computers. However, NISQ devices experience significant errors which, if not corrected, can render physical quantities measured in these simulations inaccurate or meaningless. Here we describe a method of reducing these errors which is tailored to quantum algorithms for simulating fermionic systems. The method is based on executing quantum circuits in the model of fermionic linear optics, which are known to be efficiently simulable classically, to i…
Quantum computers are becoming increasingly accessible, and may soon outperform classical computers for useful tasks. However, qubit readout errors remain a significant hurdle to running quantum algorithms on current devices. We present a scheme to more efficiently mitigate these errors on quantum hardware and numerically show that our method consistently gives advantage over previous mitigation schemes. Our scheme removes biases in the readout errors allowing a general error model to be built with far fewer calibration measurements. Specifically, for reading out $n$-qubits we show a factor of…
Reducing errors is critical to the application of modern quantum computers. In the current Letter, we investigate the quantum error mitigation considering parametric circuits accessible by classical computations in some range of their parameters. We present a method of global randomized error cancellations (GREC) mitigating quantum errors by summing a linear combination of additionally randomized quantum circuits with weights determined by comparison with the referent classically computable data. We illustrate the performance of this method on the example of the $n = 4$ spins anti-ferromagneti…
We investigate the performance of error mitigation via measurement of conserved symmetries on near-term devices. We present two protocols to measure conserved symmetries during the bulk of an experiment, and develop a zero-cost post-processing protocol which is equivalent to a variant of the quantum subspace expansion. We develop methods for inserting global and local symetries into quantum algorithms, and for adjusting natural symmetries of the problem to boost their mitigation against different error channels. We demonstrate these techniques on two- and four-qubit simulations of the hydrogen…
Error-correcting codes were invented to correct errors on noisy communication channels. Quantum error correction (QEC), however, may have a wider range of uses, including information transmission, quantum simulation/computation, and fault-tolerance. These invite us to rethink QEC, in particular, about the role that quantum physics plays in terms of encoding and decoding. The fact that many quantum algorithms, especially near-term hybrid quantum-classical algorithms, only use limited types of local measurements on quantum states, leads to various new techniques called Quantum Error Mitigation (…
Photon loss is destructive to the performance of quantum photonic devices and therefore suppressing the effects of photon loss is paramount to photonic quantum technologies. We present two schemes to mitigate the effects of photon loss for a Gaussian Boson Sampling device, in particular, to improve the estimation of the sampling probabilities. Instead of using error correction codes which are expensive in terms of their hardware resource overhead, our schemes require only a small amount of hardware modifications or even no modification. Our loss-suppression techniques rely either on collecting…
Correlations are a valuable resource for quantum information processing and quantum thermodynamics. However, the preparation of some correlated states can carry a substantial cost that should be compared against its value. We show that classical correlations can be catalytically exploited, which enables to mitigate heat and entropy dissipation in information erasure. These correlations are naturally generated by the erasure process, and thus can be considered free. Although we also show that maximum erasure with minimum dissipation and no correlations is theoretically possible, catalysts are a…
Sample-efficient quantum error mitigation via classical learning surrogates
Henan Key Laboratory of Quantum Information（量子信息与密码学重点实验室）；College of Computing and Data Science（计算与数据科学学院）；Nanyang Technological University（南洋理工大学）；School of Physical and Mathematical Science（物理与数学科学学院）
We develop a classical bit-flip correction method to mitigate measurement errors on quantum computers. This method can be applied to any operator, any number of qubits, and any realistic bit-flip probability. We first demonstrate the successful performance of this method by correcting the noisy measurements of the ground-state energy of the longitudinal Ising model. We then generalize our results to arbitrary operators and test our method both numerically and experimentally on IBM quantum hardware. As a result, our correction method reduces the measurement error on the quantum hardware by up t…
Constrained Hamiltonian description of the classical limit is utilized in order to derive consistent dynamical equations for hybrid quantum-classical systems. Starting with a compound quantum system in the Hamiltonian formulation conditions for classical behavior are imposed on one of its subsystems and the corresponding hybrid dynamical equations are derived. The presented formalism suggests that the hybrid systems have properties that are not exhausted by those of quantum and classical systems.
Kernel methods are the basis of most classical machine learning algorithms such as Gaussian Process (GP) and Support Vector Machine (SVM). Computing kernels using noisy intermediate scale quantum (NISQ) devices has attracted considerable attention due to recent progress in the design of NISQ devices. However noise and errors on current NISQ devices can negatively affect the predicted kernels. In this paper we utilize two quantum kernel machine learning (ML) algorithms to predict the labels of a Breast Cancer dataset on two different NISQ devices: quantum kernel Gaussian Process (qkGP) and quan…
A hybrid formalism is proposed for interacting classical and quantum sytems. This formalism is mathematically consistent and reduces to standard classical and quantum mechanics in the case of no interaction. However, in the presence of interaction, the correspondence principle is violated.
We discuss two approaches that are used frequently to describe quantum-classical hybrid system. One is the well-known mean-field theory and the other adopts a set of hybrid brackets which is a mixture of quantum commutators and classical Poisson brackets. We prove that these two approaches are equivalent.
A general framework describing the statistical discrimination of an ensemble of quantum channels is given by the name of quantum reading. Several tools can be applied in quantum reading to reduce the error probability in distinguishing the ensemble of channels. Classical and quantum codes can be envisioned for this goal. The aim of this paper is to present a simple but fruitful protocol for this task using classical error-correcting codes. Three families of codes are considered: Reed-Solomon codes, BCH codes, and Reed-Muller codes. In conjunction to the use of codes, we also analyze the role o…
Several techniques have been recently introduced to mitigate errors in near-term quantum computers without the overhead required by quantum error correcting codes. While most of the focus has been on gate errors, measurement errors are significantly larger than gate errors on some platforms. A widely used {\it transition matrix error mitigation} (TMEM) technique uses measured transition probabilities between initial and final classical states to correct subsequently measured data. However from a rigorous perspective, the noisy measurement should be calibrated with perfectly prepared initial st…
We present a scheme to neutralize the dephasing effect induced by classical noise on a qubit. The scheme builds upon the key idea that this kind of noise can be recorded by a classical device during the qubit evolution, and that its effect can be undone by a suitable control sequence that is conditioned on the measurement result. We specifically demonstrate this scheme on a nitrogen-vacancy (NV) center that strongly couples to current noise in a nearby conductor. By conditioning the readout observable on a measurement of the current, we recover the full qubit coherence and its intrinsic cohere…
Reducing measurement errors in multi-qubit quantum devices is critical for performing any quantum algorithm. Here we show how to mitigate measurement errors by a classical post-processing 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 parameterizing these noise models can be extracted from the measurement calibration data using a simple formula. Error mitigation is achieved by ap…
We investigate new features, especially of entanglement dynamics, which arise in a quantum-classical hybrid. As a model, we study the coupling between two quantum mechanical two-level systems, i.e. two q-bits, and a classical harmonic oscillator. Their interaction is described by a hybrid coupling, in accordance with a recently developed quantum-classical hybrid theory. We discuss various situations in which entanglement of the q-bits does (not) evolve. Furthermore, we point out an experimental application in a hybrid cooling scheme and indicate topics for future study.
A canonical formulation of coupled classical-quantum dynamics is presented. The theory is named symmetric hybrid dynamics. It is proved that under some general conditions its predictions are consistent with the full quantum ones. Moreover symmetric hybrid dynamics displays a fully consistent canonical structure. Namely, it is formulated over a Lie algebra of observables, time evolution is unitary and the solution of a hybrid type Schrödinger equation. A quantization prescription from classical mechanics to hybrid dynamics is presented. The quantization map is a Lie algebra isomorphism. Finally…
