Superfast encodings for fermionic quantum simulation

Abstract

Simulation of fermionic many-body systems on a quantum computer requires a suitable encoding of fermionic degrees of freedom into qubits. Here we revisit the superfast encoding introduced by Kitaev and one of the authors. This encoding maps a target fermionic Hamiltonian with two-body interactions on a graph of degree d to a qubit simulator Hamiltonian composed of Pauli operators of weight O(d). A system of m Fermi modes gets mapped to n=O(md) qubits. We propose generalized superfast encodings (GSEs) which require the same number of qubits as the original one but have more favorable properties. First, we describe a GSE such that the corresponding quantum code corrects any single-qubit error provided that the interaction graph has degree d≥6. In contrast, we prove that the original superfast encoding lacks the error correction property for d≤6. Second, we describe a GSE that reduces the Pauli weight of the simulator Hamiltonian from O(d) to O(logd). The robustness against errors and a simplified structure of the simulator Hamiltonian offered by GSEs can make simulation of fermionic systems within the reach of near-term quantum devices. As an example, we apply the new encoding to the fermionic Hubbard model on a 2D lattice.