Efficient quantum circuit for singular value thresholding

TL;DR

This paper introduces a scalable quantum circuit for singular value thresholding that significantly accelerates the process and demonstrates its potential for practical quantum computing applications.

Contribution

The paper designs a scalable quantum circuit for SVT with an adjustable parameter, enabling high fidelity results and practical implementation, advancing quantum algorithms in machine learning.

Findings

Quantum circuit for SVT achieves exponential speedup over classical algorithms.

Numerical simulations verify the circuit's capability to perform SVT accurately.

The circuit design includes an adjustable parameter for high success probability.

Abstract

Singular value thresholding (SVT) operation is a fundamental core module in many mathematical models in computer vision and machine learning, particularly for many nuclear norm minimizing-based problems. We presented a quantum SVT (QSVT) algorithm which was used as a subroutine to address an image classification problem. This algorithm runs in $O\left[\log\left(pq\right)\right]$, an exponential speed improvement over the classical algorithm which runs in $O\left[poly\left(pq\right)\right]$. In this study, we investigate this algorithm and design a scalable quantum circuit for QSVT. In the circuit design, we introduce an adjustable parameter $\alpha$ to ensure the high probability of obtaining the final result and the high fidelity of actual and ideal final states. We also show that the value of $\alpha$ can be computed ahead of implementing the quantum circuit when the inputs of the QSVT algorithm, i.e. matrix ${\bf{A}}$ and constant $\tau$, are given. In addition, we propose a small-scale quantum circuit for QSVT. We numerically simulate and demonstrate the performance of this circuit, verifying its capability to solve the intended SVT. The quantum circuit for QSVT implies a tempting possibility for experimental realization on a quantum computer.