Quantum computing has the potential to outperform classical computers, and is expected to play an active role in various fields. On quantum machine learning, it is difficult to learn only on quantum computing. Classical-quantum hybrid algorithms are proposed in recent years. Classical computer is used for calculation of parameter tuning in quantum circuit. In this paper, we propose a backpropagation algorithm that can efficiently calculate gradient in optimization of parameter in quantum circuit, which outperforms the current parameter search algorithm while presents the same or even higher accuracy.
Quantum computing has the potential to outperform classical computers, and is expected to play an active role in various fields. On quantum machine learning, it is difficult to learn only on quantum computing. Classical-quantum hybrid algorithms are proposed in recent years. Classical computer is used for calculation of parameter tuning in quantum circuit. In this paper, we propose a backpropagation algorithm that can efficiently calculate gradient in optimization of parameter in quantum circuit, which outperforms the current parameter search algorithm while presents the same or even higher accuracy.
Quantum computing has the potential to outperform classical computers and is expected to play an active role in various fields. In quantum machine learning, a quantum computer has been found useful for enhanced feature representation and high dimensional state or function approximation. Quantum-Classical hybrid algorithms are proposed in recent years for this purpose under the Noisy-Intermediate Scale Quantum computer (NISQ) environment. Under this scheme, the role played by classical computer is the parameter tuning, parameter optimization, and parameter update for the quantum circuit. In this paper, we propose a gradient descent based backpropagation algorithm that can efficiently calculate the gradient in parameter optimization and update the parameter for quantum circuit learning, which outperforms the current parameter search algorithms in terms of computing speed while presents the same or even higher test accuracy.
Quantum computing has the potential to outperform classical computers and is expected to play an active role in various fields. In quantum machine learning, a quantum computer has been found useful for enhanced feature representation and high dimensional state or function approximation. Quantum-Classical hybrid algorithms are proposed in recent years for this purpose under the Noisy-Intermediate Scale Quantum computer (NISQ) environment. Under this scheme, the role played by classical computer is the parameter tuning, parameter optimization, and parameter update for the quantum circuit. In this paper, we propose a gradient descent based backpropagation algorithm that can efficiently calculate the gradient in parameter optimization and update the parameter for quantum circuit learning, which outperforms the current parameter search algorithms in terms of computing speed while presents the same or even higher test accuracy.
Quantum computing has the potential to outperform classical computers and is expected to play an active role in various fields. In quantum machine learning, a quantum computer has been found useful for enhanced feature representation and high-dimensional state or function approximation. Quantum–classical hybrid algorithms have been proposed in recent years for this purpose under the noisy intermediate-scale quantum computer (NISQ) environment. Under this scheme, the role played by the classical computer is the parameter tuning, parameter optimization, and parameter update for the quantum circuit. In this paper, we propose a gradient descent-based backpropagation algorithm that can efficiently calculate the gradient in parameter optimization and update the parameter for quantum circuit learning, which outperforms the current parameter search algorithms in terms of computing speed while presenting the same or even higher test accuracy. Meanwhile, the proposed theoretical scheme was successfully implemented on the 20-qubit quantum computer of IBM Q, ibmq_johannesburg. The experimental results reveal that the gate error, especially the CNOT gate error, strongly affects the derived gradient accuracy. The regression accuracy performed on the IBM Q becomes lower with the increase in the number of measurement shot times due to the accumulated gate noise error.
We develop a backpropagation algorithm for evaluating parameter gradients in quantum circuits using Pauli propagation simulation. The method has computational complexity comparable to that of standard sparse Pauli simulation techniques, while producing gradients whose accuracy is of the same order as the corresponding observable expectation values. By exploiting the reversibility of quantum circuits, the algorithm reduces the memory cost by a factor of O(nparam) compared with conventional reverse-mode automatic differentiation, where nparam denotes the number of parameters in the circuit. Compared with finite difference methods, the algorithm is O(nparam) more efficient in function evaluations. These features enable efficient and accurate classical optimization of quantum circuits for applications such as state preparation and time-evolution compression, while also allowing operator-complexity measures such as the operator stabilizer Rényi entropy to be monitored and regularized during optimization. We demonstrate the method by optimizing low-energy state-preparation circuits for transverse-field Ising models in one, two, and three dimensions and for the three-dimensional Heisenberg model, and by compressing two-dimensional time-evolution circuits.
The discovery of the backpropagation algorithm ranks among one of the most important moments in the history of machine learning, and has made possible the training of large-scale neural networks through its ability to compute gradients at roughly the same computational cost as model evaluation. Despite its importance, a similar backpropagation-like scaling for gradient evaluation of parameterised quantum circuits has remained elusive. Currently, the most popular method requires sampling from a number of circuits that scales with the number of circuit parameters, making training of large-scale quantum circuits prohibitively expensive in practice. Here we address this problem by introducing a class of structured circuits that are not known to be classically simulable and admit gradient estimation with significantly fewer circuits. In the simplest case – for which the parameters feed into commuting quantum gates – these circuits allow for fast estimation of the gradient, higher order partial derivatives and the Fisher information matrix. Moreover, specific families of parameterised circuits exist for which the scaling of gradient estimation is in line with classical backpropagation, and can thus be trained at scale. In a toy classification problem on 16 qubits, such circuits show competitive performance with other methods, while reducing the training cost by about two orders of magnitude.
Quantum Machine Learning (QML) has emerged as a promising field, offering potential advantages over classical machine learning in terms of speed, scalability, and the ability to model complex systems. One significant challenge lies in optimizing model parameters—a crucial step in achieving optimal performance. Traditional parameter tuning methods often rely on grid search, random search, or gradient-based optimization, which can be computationally expensive and time-consuming. This paper introduces a novel quantum machine learning parameter adjustment algorithm, leveraging quantum computing's unique properties to automate the parameter optimization process. The proposed algorithm utilizes a quantum circuit to efficiently explore the parameter space, leading to improved model accuracy and generalization capabilities. This work explores the potential of quantum computing to revolutionize the parameter tuning process, offering a more efficient and robust approach compared to classical methods. The core mechanism involves quantum state manipulation to represent and update model parameters, achieving a significant improvement in performance.