Quantum circuits for the preparation of spin eigenfunctions on quantum computers

TL;DR

This paper presents quantum circuits for preparing total spin eigenfunctions on quantum computers, using recursive and heuristic methods, demonstrated on IBM devices for small spin systems.

Contribution

It introduces two strategies for constructing spin eigenfunctions on quantum computers, enhancing simulation capabilities for many-particle quantum systems.

Findings

Successful implementation on IBM quantum devices for 3- and 5-spin systems

Comparison of exact recursive and heuristic approximation methods

Improved understanding of spin eigenfunction preparation on quantum hardware

Abstract

The application of quantum algorithms to the study of many-particle quantum systems requires the ability to prepare wavefunctions that are relevant in the behavior of the system under study. Hamiltonian symmetries are an important instrument, to classify relevant many-particle wavefunctions, and to improve the efficiency of numerical simulations. In this work, quantum circuits for the exact and approximate preparation of total spin eigenfunctions on quantum computers are presented. Two different strategies are discussed and compared: exact recursive construction of total spin eigenfunctions based on the addition theorem of angular momentum, and heuristic approximation of total spin eigenfunctions based on the variational optimization of a suitable cost function. The construction of these quantum circuits is illustrated in detail, and the preparation of total spin eigenfunctions is demonstrated on IBM quantum devices, focusing on 3- and 5-spin systems on graphs with triangle connectivity.