Compact fermion to qubit mappings

Charles Derby, Joel Klassen, Johannes Bausch, and Toby Cubitt
Phys. Rev. B 104, 035118 – Published 8 July 2021

Abstract

Mappings between fermions and qubits are valuable constructions in physics. To date only a handful exist. In addition to revealing dualities between fermionic and spin systems, such mappings are indispensable in any quantum simulation of fermionic physics on quantum computers. The number of qubits required per fermionic mode, and the locality of mapped fermionic operators strongly impact the cost of such simulations. We present a fermion to qubit mapping that outperforms all previous local mappings in both the qubit to mode ratio and the locality of mapped operators. In addition to these practically useful features, the mapping bears an elegant relationship to the toric code, which we discuss. Finally, we consider the error mitigating properties of the mapping—which encodes fermionic states into the code space of a stabilizer code. Although there is an implicit tradeoff between low weight representations of local fermionic operators, and high distance code spaces, we argue that fermionic encodings with low-weight representations of local fermionic operators can still exhibit error mitigating properties which can serve a similar role to that played by high code distances. In particular, when undetectable errors correspond to “natural” fermionic noise. We illustrate this point explicitly both for this encoding and the Verstraete-Cirac encoding.

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  • Received 16 July 2020
  • Accepted 27 May 2021

DOI:https://doi.org/10.1103/PhysRevB.104.035118

©2021 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & TechnologyCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Charles Derby1,2,*, Joel Klassen1,†, Johannes Bausch1,3,‡, and Toby Cubitt1,§

  • 1Phasecraft Ltd, London, UK
  • 2Department of Computer Science, University College London, Gower Street, London WC1E 6BT, UK
  • 3Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Trinity Lane, Cambridge CB2 1TN, UK

  • *charlie@phasecraft.io
  • joel@phasecraft.io
  • johannes@phasecraft.io
  • §toby@phasecraft.io

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Issue

Vol. 104, Iss. 3 — 15 July 2021

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