Minimal quantum walk simulation of Dirac fermions in curved space-times

TL;DR

This paper introduces a novel quantum walk framework that accurately simulates Dirac fermions in curved space-times using minimal qubits, enabling practical quantum simulations on current devices.

Contribution

It develops a new shift operator for quantum walks that accounts for arbitrary geometries, reducing the qubit requirement and aligning wave functions with standard Dirac spinors.

Findings

Successfully simulates Dirac dynamics in curved space-times

Requires only one qubit per lattice point in (1+1)D

Demonstrates simulations in Gravitoelectromagnetism regime

Abstract

The problem of simulating through quantum walks Dirac fermions in arbitrary curved space-times and coordinates is revisited, taking (1 + 1)D space-times as an example. A new shift or translation operator on the grid is introduced, to take into account arbitrary geometries. The new, generalised quantum walks built with this operator can simulate Dirac fermions in arbitrary curved space-times and coordinates, and their wave functions have exactly the same number of components as standard Dirac spinors, and not twice that number, as previously believed. In particular, in $(1 + 1)$D space-times, only one qubit is needed at each lattice point, which makes it easier to perform quantum simulations of the Dirac dynamics on current NISQs quantum devices. Numerical simulations of the Dirac dynamics in the post Newtonian, so-called Gravitoelectromagnetism regime are presented as an illustration.