This work introduces a novel structure based on universal quantum circuits which uses classical machine learning techniques in order to solve a quantum problem: the decomposition of a generic quantum operator into a sequence of elementary unitary matrices (universal basic quantum gates). Even though the postulates of quantum mechanics guarantee any unitary operation as a feasible operation over a quantum system, there is no simple method to implement an arbitrary algorithm. By means of a multilayer hybrid neural network in which the basic cell is made up of CNOTs and universal one-qubit unitary gates, this work offers a solution to the given problem. These specific gates were chosen since they are the gates available in real quantum computers such as IBMQ's quantum processors. The network learns the unitary gates classically using the method of the steepest descent and is aided in learning the entangling gates by the use of two types of quantum correlations: Mutual Information (MI) and Cumulative Correlation Measure (CCM). The algorithm implemented in this case is a type of supervised learning. The results show that the model fits the data gracefully and correctly predicts a wide range of algorithms.
This work introduces a novel structure based on universal quantum circuits which uses classical machine learning techniques in order to solve a quantum problem: the decomposition of a generic quantum operator into a sequence of elementary unitary matrices (universal basic quantum gates). Even though the postulates of quantum mechanics guarantee any unitary operation as a feasible operation over a quantum system, there is no simple method to implement an arbitrary algorithm. By means of a multilayer hybrid neural network in which the basic cell is made up of CNOTs and universal one-qubit unitary gates, this work offers a solution to the given problem. These specific gates were chosen since they are the gates available in real quantum computers such as IBMQ's quantum processors. The network learns the unitary gates classically using the method of the steepest descent and is aided in learning the entangling gates by the use of two types of quantum correlations: Mutual Information (MI) and Cumulative Correlation Measure (CCM). The algorithm implemented in this case is a type of supervised learning. The results show that the model fits the data gracefully and correctly predicts a wide range of algorithms.
We demonstrate, that artificial neural networks (ANN) can be trained to emulate single or multiple basic quantum operations. In order to realize a quantum state, we implement a novel "quantumness gate" that maps an arbitrary matrix to the real representation of a positive hermitean normalized density matrix. We train the CNOT gate, the Hadamard gate and a rotation in Hilbert space as basic building blocks for processing the quantum density matrices of two entangled qubits. During the training process the neural networks learn to represent the complex structure, the hermiticity, the normalization and the positivity of the output matrix. The requirement of successful training allows us to find a critical bottleneck dimension which reflects the relevant quantum information. Chains of individually trained neural quantum gates can be constructed to realize any unitary transformation. For scaling to larger quantum systems, we propose to use correlations of stochastic macroscopic two-level observables or classical bits. This novel concept provides a path for a classical implementation of computationally relevant quantum information processing on classical neural networks, in particular on neuromorphic computing machines featuring stochastic operations.
Quantum operations on pure states can be fully represented by unitary matrices. Variational quantum circuits, also known as quantum neural networks, embed data and trainable parameters into gate-based operations and optimize the parameters via gradient descent. The high cost of training and low fidelity of current quantum devices, however, restricts much of quantum machine learning to classical simulation. For few-qubit problems with large datasets, training the matrix elements directly, as is done with weight matrices in classical neural networks, can be faster than decomposing data and parameters into gates. We propose a method that trains matrices directly while maintaining unitarity through a single regularization term added to the loss function. A second training step, circuit alignment, then recovers a gate-based architecture from the resulting soft-unitary. On a five-qubit supervised classification task with 1000 datapoints, this two-step process produces a trained variational circuit in under four minutes, compared to over two hours for direct circuit training, while achieving lower binary cross-entropy loss. In a second experiment, soft-unitaries are embedded in a hybrid quantum-classical network for a reinforcement learning cartpole task, where the hybrid agent outperforms a purely classical baseline of comparable size.
The quantum circuit model is the most commonly used model for implementing quantum computers and quantum neural networks whose essential tasks are to realize certain unitary operations. The circuit model usually implements a desired unitary operation U(N) by a sequence of single-qubit and two-qubit unitary gates from a universal set. Although this certainly facilitates the experimentalists as they only need to prepare several different kinds of universal gates, the number of gates required to implement an arbitrary desired unitary operation is usually large. Hence, the efficiency in terms of the circuit depth or running time is not guaranteed. Here we propose an alternative approach; we use a simple discrete-time quantum walk (DTQW) on a cycle graph to model an arbitrary unitary operation U(N) without the need to decompose it into a sequence of gates of smaller sizes. Our model is essentially a quantum neural network based on DTQW. Firstly, it is universal as we show that any unitary operation U(N) can be realized via an appropriate choice of coin operators. Secondly, our DTQW-based neural network can be updated efficiently via a learning algorithm, i.e., a modified stochastic gradient descent algorithm adapted to our network. By training this network, one can promisingly find approximations to arbitrary desired unitary operations. With an additional measurement on the output, the DTQW-based neural network can also implement general positive-operator-valued measure (POVM) measurements. We show its capacity in implementing arbitrary two-outcome POVMs via numeric simulation. We further demonstrate that the network can be simplified and can overcome device noises during the training so that it becomes more friendly for laboratory implementations. Our work shows the capability of the DTQW-based neural network in quantum computation and its potential in laboratory implementations.
We discuss a quantum circuit construction designed for classification. The circuit is built of regularly placed elementary quantum gates, which implies the simplicity of the presented solution. The realization of the classification task is possible after the procedure of supervised learning which constitutes parameter optimization of Pauli gates. The process of learning can be performed by a physical quantum machine but also by simulation of quantum computation on a classical computer. The parameters of Pauli gates are selected by calculating changes in the gradient for different sets of these parameters. The proposed solution was successfully tested in binary classification and estimation of basic non-linear function values, e.g., the sine, the cosine, and the tangent. In both the cases, the circuit construction uses one or more identical unitary operations, and contains only two qubits and three quantum gates. This simplicity is a great advantage because it enables the practical implementation on quantum machines easily accessible in the nearest future.
This paper presents a hybrid quantum-classical machine learning model for classification tasks, integrating a 4-qubit quantum circuit with a classical neural network. The quantum circuit is designed to encode the features of the Iris dataset using angle embedding and entangling gates, thereby capturing complex feature relationships that are difficult for classical models alone. The model, which we term a Quantum Convolutional Neural Network (QCNN), was trained over 20 epochs, achievinga perfect 100% accuracy on the Iris dataset test set on 16 epoch. Our results demonstrate the potential of quantum-enhanced models in supervised learning tasks, particularly in efficiently encoding and processing data using quantum resources. We detail the quantum circuit design, parameterizedgate selection, and the integration of the quantum layer with classical neural network components.This work contributes to the growing body of research on hybrid quantum-classical models and theirapplicability to real-world datasets.
Abstract Predicting the output of quantum circuits is a hard computational task that plays a pivotal role in the development of universal quantum computers. Here we investigate the supervised learning of output expectation values of random quantum circuits. Deep convolutional neural networks (CNNs) are trained to predict single-qubit and two-qubit expectation values using databases of classically simulated circuits. These circuits are built using either a universal gate set or a continuous set of rotations plus an entangling gate, and they are represented via properly designed encodings of these gates. The prediction accuracy for previously unseen circuits is analyzed, also making comparisons with small-scale quantum computers available from the free IBM Quantum program. The CNNs often outperform these quantum devices, depending on the circuit depth, on the network depth, and on the training set size. Notably, our CNNs are designed to be scalable. This allows us exploiting transfer learning and performing extrapolations to circuits larger than those included in the training set. These CNNs also demonstrate remarkable resilience against noise, namely, they remain accurate even when trained on (simulated) expectation values averaged over very few measurements.