Digitized-counterdiabatic quantum approximate optimization algorithm

P Chandarana,A Del Campo,Xi Chen,E Solano,N N Hegade,F Albarrán-Arriagada,K Paul

doi:10.1103/physrevresearch.4.013141

P Chandarana, A Del Campo + Show 5 more

Open Access

https://doi.org/10.1103/physrevresearch.4.013141

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Abstract

The quantum approximate optimization algorithm (QAOA) has proved to be an effective classical-quantum algorithm serving multiple purposes, from solving combinatorial optimization problems to finding the ground state of many-body quantum systems. Since QAOA is an ansatz-dependent algorithm, there is always a need to design ansatz for better optimization. To this end, we propose a digitized version of QAOA enhanced via the use of shortcuts to adiabaticity. Specifically, we use a counterdiabatic (CD) driving term to design a better ansatz, along with the Hamiltonian and mixing terms, enhancing the global performance. We apply our digitized-counterdiabatic QAOA to Ising models, classical optimization problems, and the P-spin model, demonstrating that it outperforms standard QAOA in all cases we study.

Highlights

Hybrid classical-quantum algorithms have the potential to unleash a broad set of applications in the quantum computing realm
One notable example is that of the variational quantum algorithms (VQA), which is implemented by designing variational quantum circuits to minimize the expectation value for a given problem Hamiltonian
We have introduced a quantum algorithm leveraging the strengths of shortcuts to adiabaticity for quantum approximate optimization algorithm (QAOA)

Summary

INTRODUCTION

Hybrid classical-quantum algorithms have the potential to unleash a broad set of applications in the quantum computing realm. The choice of the approximate trial state, from which the cost function is obtained, is crucial to the success of the QAOA This is done by using quantum adiabatic algorithms (QAAs) which produce near-optimal results for large p which is not suitable for current NISQ devices. Several studies have been reported in the past few years showing that high-fidelity quantum states can be prepared by assisting QAAs with additional driving interaction [34] These studies establish that, for certain problems, the inclusion of additional driving terms can reduce the computational complexity and with it the circuit depth.

DC-QAOA

ISING SPIN MODELS

CLASSICAL OPTIMIZATION PROBLEMS

P-SPIN MODEL

DISCUSSION AND CONCLUSIONS