QUARK: A GRADIENT-FREE QUANTUM LEARNING FRAMEWORK FOR CLASSIFICATION TASKS

Abstract

As more practical and scalable quantum computers emerge, much attention has been focused on realizing quantum supremacy in machine learning. Existing quantum ML methods either (1) embed a classical model into a target Hamiltonian to enable quantum optimization or (2) represent a quantum model using variational quantum circuits and apply classical gradient-based optimization. The former method leverages the power of quantum optimization but only supports simple ML models, while the latter provides flexibility in model design but relies on gradient calculation, resulting in barren plateau (i.e., gradient vanishing) and frequent classical-quantum interactions. To address the limitations of existing quantum ML methods, we introduce Quark, a gradient-free quantum learning framework that optimizes quantum ML models using quantum optimization. Quark does not rely on gradient computation and therefore avoids barren plateau and frequent classical-quantum interactions. In addition, Quark can support more general ML models than prior quantum ML methods and achieves a dataset-sizeindependent optimization complexity. Theoretically, we prove that Quark can outperform classical gradient-based methods by reducing model query complexity for highly non-convex problems; empirically, evaluations on the Edge Detection and Tiny-MNIST tasks show that Quark can support complex ML models and significantly reduce the number of measurements needed for discovering near-optimal weights for these tasks.

1. INTRODUCTION

Quantum computing provides a new computational paradigm to achieve exponential speedups over classical counterparts for various tasks, such as cryptography (Shor, 1994) , scientific simulation (Tazhigulov et al., 2022) , and data analytics (Arute et al., 2019) . A key advantage of quantum computing is its ability to entangle multiple quantum bits, called qubits, allowing n qubits to encode a 2 n -dimensional vector, while encoding this vector in classical computing requires 2 n bits. Inspired by this potential, recent work (Jaderberg et al., 2022; Macaluso et al., 2020b; Torta et al., 2021; Kapoor et al., 2016; Bauer et al., 2020; Farhi & Neven, 2018a; Schuld et al., 2014; Cong et al., 2019b) has focused on realizing quantum speedups over classical algorithms in the field of supervised learning. Existing quantum ML work can be divided into two categories: classical model with quantum optimization (CMQO) and quantum model with classical optimization (QMCO). First, CMQO methods embed a classical ML model jointly with the optimization problem into a target Hamiltonian and optimize the model using quantum adiabatic evolution (QAE) (Finnila et al., 1994) or quantum approximate optimization algorithm (QAOA) (Farhi et al., 2014; Torta et al., 2021) . As the transition between a classical model and the target Hamiltonian only applies to loworder polynomial activations (see Figure 2 ), CMQO methods do not support ML models with nonlinear activations that cannot be represented in low-order polynomial (e.g., ReLU). Second, QMCO methods optimize variational quantum modelsfoot_0 by iteratively performing gradient descent using classical optimizers. QMCO methods are fundamentally limited by barren plateau (i.e., gradient vanishing (McClean et al., 2018) ) and the high cost of frequent quantum-classical interactions. To address the limitations of existing quantum ML methods, we introduce Quark, a gradient-free quantum learning framework for classification tasks that optimizes quantum models with quantum



They are also known as variational quantum circuits (VQC)-based models in the quantum literature.1

