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arXiv:2206.09933 · Physical Review A

Quantum-machine-learning channel discrimination

Andrey Kardashin, A. V. Vlasova, Anastasiia A. Pervishko, Dmitry Yudin, Jacob Biamonte

Published Sep 7, 2022• 14 citations
arXivHTMLPDF

Abstract

In the problem of quantum channel discrimination, one distinguishes between a given number of quantum channels, which is done by sending an input state through a channel and measuring the output state. This work studies applications of variational quantum circuits and machine-learning techniques for discriminating such channels. In particular, we explore (i) the practical implementation of embedding this task into the framework of variational quantum computing, (ii) training a quantum classifier based on variational quantum circuits, and (iii) applying the quantum kernel estimation technique. For testing these three channel discrimination approaches, we considered a pair of entanglement-breaking channels and the depolarizing channel with two different depolarization factors. For the approach (i), we address solving the quantum channel discrimination problem using widely discussed parallel and sequential strategies. We show the advantage of the latter in terms of better convergence with less quantum resources. Quantum channel discrimination with a variational quantum classifier (ii) allows one to operate even with random and mixed input states and simple variational circuits. The kernel-based classification approach (iii) is also found effective as it allows one to discriminate depolarizing channels associated not with just fixed values of the depolarization factor, but with ranges of it. Additionally, we discovered that a simple modification of one of the commonly used kernels significantly increases the efficiency of this approach. Finally, our numerical findings reveal that the performance of variational methods of channel discrimination depends on the trace of the product of the output states. These findings demonstrate that quantum machine learning can be used to discriminate channels, such as those representing physical noise processes.

DOI
10.1103/physreva.106.032409

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In the problem of quantum channel discrimination, one distinguishes between a given number of quantum channels, which is done by sending an input state through a channel and measuring the output state. This work studies applications of variational quantum circuits and machine-learning techniques for discriminating such channels. In particular, we explore (i) the practical implementation of embedding this task into the framework of variational quantum computing, (ii) training a quantum classifier based on variational quantum circuits, and (iii) applying the quantum kernel estimation technique. For testing these three channel discrimination approaches, we considered a pair of entanglement-breaking channels and the depolarizing channel with two different depolarization factors. For the approach (i), we address solving the quantum channel discrimination problem using widely discussed parallel and sequential strategies. We show the advantage of the latter in terms of better convergence with less quantum resources. Quantum channel discrimination with a variational quantum classifier (ii) allows one to operate even with random and mixed input states and simple variational circuits. The kernel-based classification approach (iii) is also found effective as it allows one to discriminate depolarizing channels associated not with just fixed values of the depolarization factor, but with ranges of it. Additionally, we discovered that a simple modification of one of the commonly used kernels significantly increases the efficiency of this approach. Finally, our numerical findings reveal that the performance of variational methods of channel discrimination depends on the trace of the product of the output states. These findings demonstrate that quantum machine learning can be used to discriminate channels, such as those representing physical noise processes.
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With the rapid development of quantum technology, understanding the properties of entanglement states has become an urgent task.Various classifications of entanglement states have been proposed to cater to distinct quantum applications, highlighting the significance of entanglement classification. This paper presents a variational quantum classifier for entanglement classification discrimination which can effectively reduce the measurement resources, specifically for four-qubit entanglement equivalence classifications under SLOCC (Stochastic Local Operations and Classical Communication). Through training one-to-one and one-to-many models, our proposed method achieves excellent performance in the entanglement classification. We further investigate the impact of parameterized quantum circuit layers and various measurement settings on the classifier’s performance. Considering the inherent noise present in near-term quantum computers, we also analyze how noise affects the model’s performance. Moreover, we explore the classifier’s capabilities in the context of multi-qubit entanglement systems. Numerical simulations demonstrate that high-precision entanglement classification tasks can be accomplished with shallow circuit depths, and the model exhibits resilience to noise. Additionally, the results reveal the versatility and potential application of our proposed model in larger-scale quantum systems by effectively handling entanglement classification tasks involving an increased number of qubits.
Abstract We present studies of quantum algorithms exploiting machine learning to classify events of interest from background events, one of the most representative machine learning applications in high-energy physics. We focus on variational quantum approach to learn the properties of input data and evaluate the performance of the event classification using both simulators and quantum computing devices. Comparison of the performance with standard multi-variate classification techniques based on a boosted-decision tree and a deep neural network using classical computers shows that the quantum algorithm has comparable performance with the standard techniques at the considered ranges of the number of input variables and the size of training samples. The variational quantum algorithm is tested with quantum computers, demonstrating that the discrimination of interesting events from background is feasible. Characteristic behaviors observed during a learning process using quantum circuits with extended gate structures are discussed, as well as the implications of the current performance to the application in high-energy physics experiments.
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We present algorithms for supervised classification tasks in machine learning that are inspired by quantum mechanics. They rely on the so-called problem of quantum state discrimination, which consists in identifying which one of a known set of quantum states has been prepared based on the outcome of a quantum measurement on the state. After building the quantum states associated with the training data, which are encoded as density matrices, we explore various quantum measurement strategies suited for the classification task, including those based on semi-definite programming and on the so-called Pretty GoodMeasurement.We also consider how the measurement performs on multiple copies of the quantum state, since this in principle improves quantum state discrimination at the price of a higher computational cost. For the Pretty Good Measurement classifier, an analogue of the well-known Kernel Trick in learning theory can be devised, so that the cost scales only with the number of examples in the training dataset. This allows to study the performance of this classifier on tensor products of the quantum state. Finally, thedifferent classifiers are benchmarked on the MNIST and MNIST-1D datasets.
Abstract Kernel methods have a wide spectrum of applications in machine learning. Recently, a link between quantum computing and kernel theory has been formally established, opening up opportunities for quantum techniques to enhance various existing machine-learning methods. We present a distance-based quantum classifier whose kernel is based on the quantum state fidelity between training and test data. The quantum kernel can be tailored systematically with a quantum circuit to raise the kernel to an arbitrary power and to assign arbitrary weights to each training data. Given a specific input state, our protocol calculates the weighted power sum of fidelities of quantum data in quantum parallel via a swap-test circuit followed by two single-qubit measurements, requiring only a constant number of repetitions regardless of the number of data. We also show that our classifier is equivalent to measuring the expectation value of a Helstrom operator, from which the well-known optimal quantum state discrimination can be derived. We demonstrate the performance of our classifier via classical simulations with a realistic noise model and proof-of-principle experiments using the IBM quantum cloud platform.