Error-corrected fermionic quantum processors with neutral atoms

TL;DR

This paper proposes a method to implement error correction in fermionic quantum processors with neutral atoms, overcoming superselection constraints and enabling more reliable quantum simulations of many-body fermionic systems.

Contribution

It introduces a blueprint for an error-corrected fermionic quantum computer using current experimental capabilities, including logical fermionic modes and error correction protocols.

Findings

Quadratic suppression of logical error rate demonstrated

Logical fermionic gates constructed for particle-number conserving processes

Protocol applicable to current neutral-atom quantum processors

Abstract

Many-body fermionic systems can be simulated in a hardware-efficient manner using a fermionic quantum processor. Neutral atoms trapped in optical potentials can realize such processors, where non-local fermionic statistics are guaranteed at the hardware level. Implementing quantum error correction in this setup is however challenging, due to the atom-number superselection present in atomic systems, that is, the impossibility of creating coherent superpositions of different particle numbers. In this work, we overcome this constraint and present a blueprint for an error-corrected fermionic quantum computer that can be implemented using current experimental capabilities. To achieve this, we first consider an ancillary set of fermionic modes and design a fermionic reference, which we then use to construct superpositions of different numbers of referenced fermions. This allows us to build logical fermionic modes that can be error corrected using standard atomic operations. Here, we focus on phase errors, which we expect to be a dominant source of errors in neutral-atom quantum processors. We then construct logical fermionic gates, and show their implementation for the logical particle-number conserving processes relevant for quantum simulation. Finally, our protocol is illustrated using a minimal fermionic circuit, where it leads to a quadratic suppression of the logical error rate.