Hybrid Quantum Classical Simulations

TL;DR

This paper explores hybrid quantum-classical algorithms like QAOA and VQE, demonstrating their scalability, resource requirements, and effectiveness in approximating solutions for complex quantum problems.

Contribution

It introduces a comparative analysis of QAOA, AQA, and VQE, highlighting their scalability, resource efficiency, and improved methods for quantum state approximation.

Findings

QAOA scales better than random guessing but needs significant resources.

Approximate quantum annealing achieves similar scaling with fewer resources.

VQE provides reasonable ground state energy approximations with proper initializations.

Abstract

We report on two major hybrid applications of quantum computing, namely, the quantum approximate optimisation algorithm (QAOA) and the variational quantum eigensolver (VQE). Both are hybrid quantum classical algorithms as they require incremental communication between a classical central processing unit and a quantum processing unit to solve a problem. We find that the QAOA scales much better to larger problems than random guessing, but requires significant computational resources. In contrast, a coarsely discretised version of quantum annealing called approximate quantum annealing (AQA) can reach the same promising scaling behaviour using much less computational resources. For the VQE, we find reasonable results in approximating the ground state energy of the Heisenberg model when suitable choices of initial states and parameters are used. Our design and implementation of a general quasi-dynamical evolution further improves these results.