A Variational Quantum Circuit for First-Quantized Simulation of Electronic States

A study conducted by Takahiro Horiba et al., was published in the Journal of Chemical Theory and Computation.

Quantum computers are currently attracting more and more attention as promising hardware for materials computation. Such materials computations with quantum computers are mostly based on the second quantized formulation, which is suitable for qubit representation. Another way to describe electronic states on a quantum computer is based on the first quantized formulation, which is expected to achieve smaller scaling with respect to the number of basis functions than the second quantized formulation. A major difficulty in the first quantized algorithm is state preparation for many-body electronic systems. This difficulty stems from the antisymmetry of electrons, and it is not straightforward to construct antisymmetric quantum states on a quantum circuit.

In this study, we have provided for the first time a design principle for constructing variational quantum circuits to prepare an antisymmetric quantum state. We performed numerical experiments on a one-dimensional hydrogen molecular system and demonstrated that the antisymmetric quantum state corresponding to the ground state can be correctly obtained by the proposed circuit. Our research is expected to contribute to the realization of highly accurate material simulations using quantum computers.

Title: Construction of Antisymmetric Variational Quantum States with Real Space Representation
Authors: Horiba, T., Shirai, S., Hirai, H.
Journal Name: Journal of Chemical Theory and Computation
Published: August 27, 2024
https://doi.org/10.1021/acs.jctc.4c00167