Quantum gates and architecture for the quantum simulation of the Fermi-Hubbard model

Abstract: Quantum computers are the ideal platform for quantum simulations. Given enough coherent operations and qubits, such machines can be leveraged to simulate strongly correlated materials, where intricate quantum effects give rise to counter-intuitive macroscopic phenomena such as high-temperature superconductivity. In this paper, we provide a gate decomposition and an architecture for a quantum simulator used to simulate the Fermi-Hubbard model in a hybrid variational quantum-classical algorithm. We propose a simple planar implementation-independent layout of qubits that can also be used to simulate more general fermionic systems. By working through a concrete application, we show the gate decomposition used to simulate the Hamiltonian of a cluster of the Fermi-Hubbard model. We briefly analyze the Trotter-Suzuki errors and estimate the scaling properties of the algorithm for more complex applications.