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

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Abstract

The problem of simulating through quantum walks the curved space-time propagation of Dirac fermions is revisited, taking the \((1 + 1)\)D case as an example. New quantum walks are introduced which encode the space-time geometry, not in the mixing operators, but in new unitary shift operators which carry out a position-dependent translation of the wave function components. These walks simulate Dirac fermions in arbitrary curved space-times and coordinates. Contrary to previously proposed general alternatives, the wave functions of the new walks have as many components as usual Dirac spinors, and not twice that number. 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. The possible usefulness of the new shift operators and quantum walks in other more general contexts is also discussed.

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  1. LERMA, Sorbonne Université, Observatoire de Paris, Université PSL, CNRS, 75005, Paris, France

    Fabrice Debbasch

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  1. Fabrice Debbasch
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Correspondence to Fabrice Debbasch.

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Debbasch, F. Minimal quantum walk simulation of Dirac fermions in curved space-times. Quantum Stud.: Math. Found. 10, 317–327 (2023). https://doi.org/10.1007/s40509-023-00297-1

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