Efficient charge-preserving excited state preparation with variational quantum algorithms

TL;DR

This paper introduces a charge-preserving VQD algorithm that incorporates symmetry to efficiently compute excited states in quantum systems, demonstrated through GPU-accelerated simulations up to 24 qubits.

Contribution

The study presents a novel charge-preserving VQD method that reduces computational complexity by leveraging symmetry, improving excited state calculations in quantum physics and chemistry.

Findings

Enhanced efficiency in excited state computations.

Successful GPU-accelerated simulations up to 24 qubits.

Applications demonstrated in physics and chemistry contexts.

Abstract

Determining the spectrum and wave functions of excited states of a system is crucial in quantum physics and chemistry. Low-depth quantum algorithms, such as the Variational Quantum Eigensolver (VQE) and its variants, can be used to determine the ground-state energy. However, current approaches to computing excited states require numerous controlled unitaries, making the application of the original Variational Quantum Deflation (VQD) algorithm to problems in chemistry or physics suboptimal. In this study, we introduce a charge-preserving VQD (CPVQD) algorithm, designed to incorporate symmetry and the corresponding conserved charge into the VQD framework. This results in dimension reduction, significantly enhancing the efficiency of excited-state computations. We present benchmark results with GPU-accelerated simulations using systems up to 24 qubits, showcasing applications in high-energy physics, nuclear physics, and quantum chemistry. This work is performed on NERSC's Perlmutter system using NVIDIA's open-source platform for accelerated quantum supercomputing - CUDA-Q.