Adaptive variational ground state preparation for spin-1 models on qubit-based architectures

TL;DR

This paper explores the use of adaptive variational quantum imaginary time evolution to efficiently prepare ground states of spin-1 models on quantum computers, analyzing different encodings and their resource costs.

Contribution

It compares various spin-to-qubit encodings for AVQITE in spin-1 models, providing insights into their resource scaling and performance on quantum hardware.

Findings

CNOT gate count scales cubically for Blume-Capel model and quartically for XXZ model.

Multiplet and Gray encodings have smaller scaling prefactors.

Resource requirements depend on encoding, initial state, and operator pool choices.

Abstract

We apply the adaptive variational quantum imaginary time evolution (AVQITE) method to prepare ground states of one-dimensional spin $S=1$ models. We compare different spin-to-qubit encodings (standard binary, Gray, unary, and multiplet) with regard to the performance and quantum resource cost of the algorithm. Using statevector simulations we study two well-known spin-1 models: the Blume-Capel model of transverse-field Ising spins with single-ion anisotropy, and the XXZ model with single-ion anisotropy. We consider system sizes of up to $20$ qubits, which corresponds to spin-$1$ chains up to length $10$. We determine the dependence of the number of CNOT gates in the AVQITE state preparation circuit on the encoding, the initial state, and the choice of operator pool in the adaptive method. Independent on the choice of encoding, we find that the CNOT gate count scales cubically with the number of spins for the Blume-Capel model and quartically for the anistropic XXZ model. However, the multiplet and Gray encodings present smaller prefactors in the scaling relations. These results provide useful insights for the implementation of AVQITE on quantum hardware.