Unitary-Coupled Restricted Boltzmann Machine Ansatz for Quantum Simulations

TL;DR

This paper introduces a novel quantum circuit protocol for generating complex-valued neural network quantum states using a unitary-coupled RBM, enabling more scalable and efficient quantum simulations of complex wave functions.

Contribution

It presents the first method to generate complex-valued RBM-based neural quantum states in quantum circuits, improving scalability and modeling capabilities.

Findings

Modeling of complex-valued wave functions achieved

Use of only one ancilla qubit for multiple hidden spins

Elimination of post-selections enhances scalability

Abstract

Neural-Network Quantum State (NQS) has attracted significant interests as a powerful wave-function ansatz to model quantum phenomena. In particular, a variant of NQS based on the restricted Boltzmann machine (RBM) has been adapted to model the ground state of spin lattices and the electronic structures of small molecules in quantum devices. Despite these progresses, significant challenges remain with the RBM-NQS based quantum simulations. In this work, we present a state-preparation protocol to generate a specific set of complex-valued RBM-NQS, that we name the unitary-coupled RBM-NQS, in quantum circuits. This is a crucial advancement as all prior works deal exclusively with real-valued RBM-NQS for quantum algorithms. With this novel scheme, we achieve (1) modeling complex-valued wave functions, (2) using as few as one ancilla qubit to simulate $M$ hidden spins in an RBM architecture, and (3) avoiding post-selections to improve scalability.