Error correction of a logical grid state qubit by dissipative pumping

TL;DR

This paper demonstrates a dissipative error correction method for GKP encoded logical qubits in a trapped ion system, extending logical lifetime and showcasing reservoir engineering for quantum state stabilization.

Contribution

Introduces and implements a dissipative map for finite GKP codes that corrects small displacements in a single trapped ion, enhancing logical qubit coherence.

Findings

Achieved a threefold increase in logical qubit lifetime.

Implemented correction cycles involving mapping stabilizer info and coherent feedback.

Demonstrated error correction with both square and hexagonal GKP codes.

Abstract

Stabilization of encoded logical qubits using quantum error correction is key to the realization of reliable quantum computers. While qubit codes require many physical systems to be controlled, oscillator codes offer the possibility to perform error correction on a single physical entity. One powerful encoding for oscillators is the grid state or GKP encoding, which allows small displacement errors to be corrected. Here we introduce and implement a dissipative map designed for physically realistic finite GKP codes which performs quantum error correction of a logical qubit implemented in the motion of a single trapped ion. The correction cycle involves two rounds, which correct small displacements in position and momentum respectively. Each consists of first mapping the finite GKP code stabilizer information onto an internal electronic state ancilla qubit, and then applying coherent feedback and ancilla repumping. We demonstrate the extension of logical coherence using both square and hexagonal GKP codes, achieving an increase in logical lifetime of a factor of three. The simple dissipative map used for the correction can be viewed as a type of reservoir engineering, which pumps into the highly non-classical GKP qubit manifold. These techniques open new possibilities for quantum state control and sensing alongside their application to scaling quantum computing.