Classical Simulation of Variational Quantum Classifiers using Tensor Rings

TL;DR

This paper introduces a tensor ring-based classical simulation method for variational quantum classifiers, significantly reducing computational resources while maintaining comparable performance on standard datasets.

Contribution

It proposes a novel tensor ring compression algorithm for simulating VQCs classically, enabling efficient benchmarking and initialization of quantum algorithms.

Findings

Achieves exponential reduction in storage and computation with respect to qubits and layers.

Demonstrates comparable performance to traditional classical simulators on Iris and MNIST datasets.

Provides a scalable approach for classical simulation of variational quantum algorithms.

Abstract

In recent times, Variational Quantum Circuits (VQC) have been widely adopted to different tasks in machine learning such as Combinatorial Optimization and Supervised Learning. With the growing interest, it is pertinent to study the boundaries of the classical simulation of VQCs to effectively benchmark the algorithms. Classically simulating VQCs can also provide the quantum algorithms with a better initialization reducing the amount of quantum resources needed to train the algorithm. This manuscript proposes an algorithm that compresses the quantum state within a circuit using a tensor ring representation which allows for the implementation of VQC based algorithms on a classical simulator at a fraction of the usual storage and computational complexity. Using the tensor ring approximation of the input quantum state, we propose a method that applies the parametrized unitary operations while retaining the low-rank structure of the tensor ring corresponding to the transformed quantum state, providing an exponential improvement of storage and computational time in the number of qubits and layers. This approximation is used to implement the tensor ring VQC for the task of supervised learning on Iris and MNIST datasets to demonstrate the comparable performance as that of the implementations from classical simulator using Matrix Product States.