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

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

Steudtner, M. (TU Delft QuTech Advanced Research Centre; TU Delft QID/Wehner Group; Universiteit Leiden)
Wehner, S.D.C. (TU Delft Quantum Internet Division; TU Delft Quantum Information and Software; TU Delft QuTech Advanced Research Centre)

Quantum Internet Division

2019

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.

Quantum algorithms
Quantum computation
Quantum simulation
Quantum Information

http://resolver.tudelft.nl/uuid:421a52e1-8c6c-482d-b288-e272c087587f

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

2469-9926

Physical Review A: covering atomic, molecular, and optical physics and quantum information, 99 (2)

Institutional Repository

journal article

© 2019 M. Steudtner, S.D.C. Wehner