Bravyi-Kitaev Superfast simulation of fermions on a quantum computer

TL;DR

This paper details the Bravyi-Kitaev Superfast (BKSF) algorithm for mapping fermionic states to qubits, demonstrating its advantages over traditional methods in reducing Trotter errors in molecular simulations.

Contribution

It provides the first detailed exposition and implementation of the BKSF algorithm for molecular simulation, comparing its performance with Jordan-Wigner and Bravyi-Kitaev transforms.

Findings

BKSF achieves lower Trotter errors than previous methods.

Implementation of BKSF in OpenFermion is demonstrated.

Study focused on hydrogen molecule simulations.

Abstract

Present quantum computers often work with distinguishable qubits as their computational units. In order to simulate indistinguishable fermionic particles, it is first required to map the fermionic state to the state of the qubits. The Bravyi-Kitaev Superfast (BKSF) algorithm can be used to accomplish this mapping. The BKSF mapping has connections to quantum error correction and opens the door to new ways of understanding fermionic simulation in a topological context. Here, we present the first detailed exposition of BKSF algorithm for molecular simulation. We provide the BKSF transformed qubit operators and report on our implementation of the BKSF fermion-to-qubits transform in OpenFermion. In this initial study of the hydrogen molecule, we have compared BKSF, Jordan-Wigner and Bravyi-Kitaev transforms under the Trotter approximation. We considered different orderings of the exponentiated terms and found lower Trotter errors than previously reported for Jordan-Wigner and Bravyi-Kitaev algorithms. These results open the door to further study of the BKSF algorithm for quantum simulation.