Efficient State Preparation for the Schwinger Model with a Theta Term

TL;DR

This paper compares quantum state preparation algorithms for the Schwinger model with a theta term, highlighting the efficiency of the blocked QAOA combined with the rodeo algorithm for large systems.

Contribution

It introduces a blocked Hamiltonian modification for QAOA and demonstrates the effectiveness of combining QAOA with the rodeo algorithm for efficient state preparation.

Findings

QAOA with blocked Hamiltonian reduces algorithm length as system size grows.

Combining QAOA and rodeo algorithm yields high-quality initial states efficiently.

ASP is effective but requires high CNOT counts in practice.

Abstract

We present a comparison of different quantum state preparation algorithms and their overall efficiency for the Schwinger model with a theta term. While adiabatic state preparation (ASP) is proved to be effective, in practice it leads to large CNOT gate counts to prepare the ground state. The quantum approximate optimization algorithm (QAOA) provides excellent results while keeping the CNOT counts small by design, at the cost of an expensive classical minimization process. We introduce a ``blocked'' modification of the Schwinger Hamiltonian to be used in the QAOA that further decreases the length of the algorithms as the size of the problem is increased. The rodeo algorithm (RA) provides a powerful tool to efficiently prepare any eigenstate of the Hamiltonian, as long as its overlap with the initial guess is large enough. We obtain the best results when combining the blocked QAOA ansatz and the RA, as this provides an excellent initial state with a relatively short algorithm without the need to perform any classical steps for large problem sizes.