Superfast encodings for fermionic quantum simulation

TL;DR

This paper introduces generalized superfast encodings for fermionic quantum simulation that improve error correction and reduce Hamiltonian complexity, making near-term quantum simulations more feasible.

Contribution

It proposes new GSEs that maintain qubit count while enhancing error correction and reducing Pauli weight of Hamiltonians.

Findings

GSE can correct single-qubit errors for graphs with degree ≥ 6.

GSE reduces Pauli weight from O(d) to O(log d).

Application to 2D Hubbard model demonstrates practical benefits.

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 (GSE) 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 $d\ge 6$. In contrast, we prove that the original Superfast Encoding lacks the error correction property for $d\le 6$. Secondly, we describe a GSE that reduces the Pauli weight of the simulator Hamiltonian from $O(d)$ to $O(\log{d})$. 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.