Distinguishing one quantum channel from another becomes a next natural question following the advent of quantum state discrimination. Here, we address the problem of quantum channel discrimination with the separable states and the entangled states input. Two schemes, based on the simulator for quantum networks and channels framework (SQUANCH) and the quantum machine learning toolbox (QMLT), are proposed to perform the quantum channel discrimination task. In the first scheme, we give an example of several qubit channels, verify that the performance metrics of channel discrimination can be improved by the entangled states. In the second scheme, we train a quantum circuit learning model to classify quantum channels using the Adam stochastic optimization algorithm. Although we consider the distinguishability in the case of only two possible channels, this model can be extended to any number of channels. This method can provide a good solution for distinguishing some complex quantum channels.
Distinguishing one quantum channel from another becomes a next natural question following the advent of quantum state discrimination. Here, we address the problem of quantum channel discrimination with the separable states and the entangled states input. Two schemes, based on the simulator for quantum networks and channels framework (SQUANCH) and the quantum machine learning toolbox (QMLT), are proposed to perform the quantum channel discrimination task. In the first scheme, we give an example of several qubit channels, verify that the performance metrics of channel discrimination can be improved by the entangled states. In the second scheme, we train a quantum circuit learning model to classify quantum channels using the Adam stochastic optimization algorithm. Although we consider the distinguishability in the case of only two possible channels, this model can be extended to any number of channels. This method can provide a good solution for distinguishing some complex quantum channels.
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.
In quantum state discrimination, typically the design of measurement operators or probe state is formulated assuming the set of possible states is perfectly known, but this may yield designs which are sensitive to deviations in the realized set of states. For example, the channel through which a transmitted state is sent may not be deterministic, but instead characterized by a classical distribution over quantum channels. In this paper, we consider the design of measurement schemes and probe states for quantum detection over an uncertain quantum channel. We present stochastic gradient-based algorithms to maximize the expected performance over the channel distribution under two design scenarios, joint design and two-stage design. We consider various design objectives, including the detection probability and mutual information, with the latter leading to a hybrid scheme consisting of von Neumann measurement and classical hypothesis test. Furthermore, we introduce a channel discrimination scheme which leverages the isometric extension of a quantum channel which increases the channel distinguishability, while simultaneously reducing the effective dimension and thereby reducing the optimization complexity. In addition, we apply amortized optimization to train a recurrent neural network in order to improve the convergence speed of the proposed algorithms. Finally, we apply the proposed algorithms to multi-copy channel discrimination as well as a novel joint channel-state discrimination scenario.
Abstract Recent results have demonstrated the successful applications of quantum-classical hybrid methods to train quantum circuits for a variety of machine learning tasks. A natural question to ask is consequentially whether we can also train such quantum circuits to discriminate quantum data, i.e., perform classification on data stored in form of quantum states. Although quantum mechanics fundamentally forbids deterministic discrimination of non-orthogonal states, we show in this work that it is possible to train a quantum circuit to discriminate such data with a trade-off between minimizing error rates and inconclusiveness rates of the classification tasks. Our approach achieves at the same time a performance which is close to the theoretically optimal values and a generalization ability to previously unseen quantum data. This generalization power hence distinguishes our work from previous circuit optimization results and furthermore provides an example of a quantum machine learning task that has inherently no classical analogue.
In quantum information technology, crucial information is regularly encoded in different quantum states. To extract information, the identification of one state from the others is inevitable. However, if the states are non-orthogonal and unknown, this task will become awesomely tricky, especially when our resources are also limited. Here, we introduce the quantum stochastic neural network (QSNN), and show its capability to accomplish the binary discrimination of quantum states. After a handful of optimizing iterations, the QSNN achieves a success probability close to the theoretical optimum, no matter whether the states are pure or mixed. Other than binary discrimination, the QSNN is also applied to classify an unknown set of states into two types: entangled ones and separable ones. After training with four samples, it can classify a number of states with acceptable accuracy. Our results suggest that the QSNN has the great potential to process unknown quantum states in quantum information.
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.
Discrimination between objects, in particular quantum states, is one of the most fundamental tasks in (quantum) information theory. Recent years have seen significant progress towards extending the framework to point-to-point quantum channels. However, with technological progress the focus of the field is shifting to more complex structures: Quantum networks. In contrast to channels, networks allow for intermediate access points where information can be received, processed and reintroduced into the network. In this work we study the discrimination of quantum networks and its fundamental limitations. In particular when multiple uses of the network are at hand, the rooster of available strategies becomes increasingly complex. The simplest quantum network that capturers the structure of the problem is given by a quantum superchannel. We discuss the available classes of strategies when considering n copies of a superchannel and give fundamental bounds on the asymptotically achievable rates in an asymmetric discrimination setting. Furthermore, we discuss achievability, symmetric network discrimination, the strong converse exponent, generalization to arbitrary quantum networks and finally an application to an active version of the quantum illumination problem.