Adiabatic quantum computing with parameterized quantum circuits

TL;DR

This paper introduces a novel discrete adiabatic quantum computing approach that is suitable for near-term devices, offering robustness against initialization issues and outperforming variational algorithms on classical and quantum problems.

Contribution

It develops a new method to analyze Hamiltonian perturbations and implement adiabatic quantum computing on near-term devices, improving robustness and performance.

Findings

Outperforms Variational Quantum Eigensolver on MaxCut and Number Partitioning.

Demonstrates superior performance on Transverse-Field Ising Chain.

Provides a practical algorithm for near-term quantum hardware.

Abstract

Adiabatic quantum computing is a universal model for quantum computing whose implementation using a gate-based quantum computer requires depths that are unreachable in the early fault-tolerant era. To mitigate the limitations of near-term devices, a number of hybrid approaches have been pursued in which a parameterized quantum circuit prepares and measures quantum states and a classical optimization algorithm minimizes an objective function that encompasses the solution to the problem of interest. In this work, we propose a different approach starting by analyzing how a small perturbation of a Hamiltonian affects the parameters that minimize the energy within a family of parameterized quantum states. We derive a set of equations that allow us to compute the new minimum by solving a constrained linear system of equations that is obtained from measuring a series of observables on the unperturbed system. We then propose a discrete version of adiabatic quantum computing that can be implemented in a near-term device while at the same time is insensitive to the initialization of the parameters and to other limitations hindered in the optimization part of variational quantum algorithms. We compare our proposed algorithm with the Variational Quantum Eigensolver on two classical optimization problems, namely MaxCut and Number Partitioning, and on a quantum-spin configuration problem, the Transverse-Field Ising Chain model, and confirm that our approach demonstrates superior performance.