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

Understand

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.