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International Conference on Advanced Technologies for Communications

Efficient Parameter-Shift Rule Implementation for Computing Gradient on Quantum Simulators

Vu Tuan Hai, Vu Trung Duong Le, Pham Hoai Luan, Yasuhiko Nakashima

Published Oct 17, 2024• 1 citation
Publisher

Abstract

Quantum computing is an active research interest in the new computational area with various applications. In the quantum machine learning field, the parameterized quantum circuit is a core learnable model; this model is updated iteratively by the general Parameter-Shift Rule (PSR) technique. In many qubits and parameter scenarios, using PSR consumes significant computational resources, particularly in the quantum simulator. Therefore, this research proposes a method to perform the PSR more efficiently for matrix multiplication and state-based real-world quantum simulators. The results show that our method is faster than baseline matrix multiplication-based 12 times and baseline state-based 39 times on average experiment.

DOI
10.1109/atc63255.2024.10908246

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Quantum computing is an active research interest in the new computational area with various applications. In the quantum machine learning field, the parameterized quantum circuit is a core learnable model; this model is updated iteratively by the general Parameter-Shift Rule (PSR) technique. In many qubits and parameter scenarios, using PSR consumes significant computational resources, particularly in the quantum simulator. Therefore, this research proposes a method to perform the PSR more efficiently for matrix multiplication and state-based real-world quantum simulators. The results show that our method is faster than baseline matrix multiplication-based 12 times and baseline state-based 39 times on average experiment.
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Parameter shift rules (PSRs) are useful methods for computing arbitrary-order derivatives of the cost function in parameterized quantum circuits. The basic idea of PSRs is to evaluate the cost function at different parameter shifts, then use specific coefficients to combine them linearly to obtain the exact derivatives. In this work, we propose an extended parameter shift rule (EPSR) which generalizes a broad range of existing PSRs and has the following two advantages. First, EPSR offers an infinite number of possible parameter shifts, allowing the selection of the optimal parameter shifts to minimize the final derivative variance and thereby obtaining the more accurate derivative estimates with limited quantum resources. Second, EPSR extends the scope of the PSRs in the sense that EPSR can handle arbitrary Hermitian operator HHH in gate U(x)=exp⁡(iHx)U(x) = \exp (iHx)U(x)=exp(iHx) in the parameterized quantum circuits, while existing PSRs are valid only for simple Hermitian generators HHH such as simple Pauli words. Additionally, we show that the widely used ``general PSR'', introduced by Wierichs et al. (2022), is a special case of our EPSR, and we prove that it yields globally optimal shifts for minimizing the derivative variance under the weighted-shot scheme. Finally, through numerical simulations, we demonstrate the effectiveness of EPSR and show that the usage of the optimal parameter shifts indeed leads to more accurate derivative estimates.
Abstract Currently, variational quantum classification algorithms (VQCAs) generally rely on traditional optimization techniques such as Powell and SLSQP in the parameter optimization session. However, the performance of these methods shows limitations in practical applications. Although the parameter-shift rule can efficiently compute the parameter gradient with quantum circuits, it needs to run the quantum circuit twice repeatedly, which significantly reduces the computation efficiency. In order to overcome this challenge, this paper innovatively integrates the principle of unitary operation in quantum mechanics with the technical characteristics of superconducting quantum chips and elaborately designs some new parameterized quantum gates (PQGs). These PQGs strictly follow the rules of unitary operation, which ensures the stability and accuracy of quantum state evolution while realizing an efficient solution to the parameter gradient. Especially for the gradient calculation of a single qubit and single-angle PQGs, the new method can be completed with only a single quantum circuit run, which greatly improves the computation efficiency. Experimental validation on benchmark datasets such as breast cancer and iris shows that the method proposed in this paper exhibits excellent performance on quantum classification tasks. Compared with the parameter-shift rule, the computation efficiency of the new method is improved by 40%. And the classification accuracy, precision, and other key performance metrics are improved by an average of 5% in comparison with traditional optimization algorithms. This work not only enriches the methodology of quantum machine learning theoretically but also demonstrates its remarkable superiority in practical applications, which indicates that the method has great potential in scientific research and industrial applications.
Finding gradients is a crucial step in training machine learning models. For quantum neural networks, computing gradients using the parameter-shift rule requires calculating the cost function twice for each adjustable parameter in the network. When the total number of parameters is large, the quantum circuit must be repeatedly adjusted and executed, leading to significant computational overhead. Here we propose an approach to compute all gradients using a single circuit only, significantly reducing both the circuit depth and the number of classical registers required. We experimentally validate our approach on both quantum simulators and IBM's real quantum hardware, demonstrating that our method significantly reduces circuit compilation time compared to the conventional approach, resulting in a substantial speedup in total runtime.
In this proceedings we present quantum machine learning optimization experiments using stochastic gradient descent with the parameter shift rule algorithm. We first describe the gradient evaluation algorithm and its optimization procedure implemented using the Qibo framework. After numerically testing the implementation using quantum simulation on classical hardware, we perform successfully a full quantum hardware optimization exercise using a single superconducting qubit chip controlled by Qibo. We show results for a quantum regression model by comparing simulation to real hardware optimization.
Abstract In this study, we study the Variational Quantum Eigensolver (VQE) application for the Ising model as a test bed model, in which we pivotally delved into several optimization methods, both classical and quantum, and analyzed the quantum advantage that each of these methods offered, and then we proposed a new combinatorial optimization scheme, deemed as QN-SPSA+PSR which combines calculating approximately Fubini-study metric (QN-SPSA) and the exact evaluation of gradient by Parameter-Shift Rule (PSR). The QN-SPSA+PSR method integrates the QN-SPSA computational efficiency with the precise gradient computation of the PSR, improving both stability and convergence speed while maintaining low computational consumption. Our results provide a new potential quantum supremacy in the VQAs's optimization subroutine, even in Quantum Machine Learning's optimization section, and enhance viable paths toward efficient quantum simulations on Noisy Intermediate-Scale Quantum Computing (NISQ) devices. Additionally, we also conducted a detailed study of quantum circuit ansatz structures in order to find the one that would work best with the Ising model and NISQ, in which we utilized the properties of the investigated model.