Quantum codes for quantum simulation of fermions on a square lattice of qubits

Mark Steudtner and Stephanie Wehner
Phys. Rev. A 99, 022308 – Published 8 February 2019

Abstract

Quantum simulation of fermionic systems is a promising application of quantum computers, but to program them, we need to map fermionic states and operators to qubit states and quantum gates. While quantum processors may be built as two-dimensional qubit networks with couplings between nearest neighbors, standard fermion-to-qubit mappings do not account for that kind of connectivity. In this work we concatenate the (one-dimensional) Jordan-Wigner transform with specific quantum codes defined under the addition of a certain number of auxiliary qubits. This yields a class of mappings with which any fermionic system can be embedded in a two-dimensional qubit setup, fostering scalable quantum simulation. Our technique is demonstrated on the two-dimensional Fermi-Hubbard model, which we transform into a local Hamiltonian. What is more, we adapt the Verstraete-Cirac transform and Bravyi-Kitaev superfast simulation to the square lattice connectivity and compare them to our mappings. An advantage of our approach in this comparison is that it allows us to encode and decode a logical state with a simple unitary quantum circuit.

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  • Received 23 October 2018

DOI:https://doi.org/10.1103/PhysRevA.99.022308

©2019 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Mark Steudtner1,2 and Stephanie Wehner2

  • 1Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands
  • 2QuTech, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands

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Issue

Vol. 99, Iss. 2 — February 2019

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