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

TL;DR

This paper introduces a new class of fermion-to-qubit mappings that enable scalable quantum simulation of fermionic systems on two-dimensional qubit lattices, improving compatibility with realistic quantum hardware connectivity.

Contribution

It combines Jordan-Wigner transform with quantum codes and auxiliary qubits to embed fermionic systems into 2D qubit layouts, facilitating scalable quantum simulation.

Findings

Demonstrated on the 2D Fermi-Hubbard model with local Hamiltonian transformation.

Compared with Verstraete-Cirac and Bravyi-Kitaev transforms, showing advantages in encoding and decoding simplicity.

Provides a scalable approach compatible with 2D qubit network architectures.

Abstract

Quantum simulation of fermionic systems is a promising application of quantum computers, but in order 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 novel 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, that 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.