Hardware-efficient quantum error correction via concatenated bosonic qubits

TL;DR

This paper demonstrates a hardware-efficient quantum error correction method using concatenated bosonic cat qubits and a repetition code, achieving significant suppression of logical errors in a superconducting circuit.

Contribution

It introduces a practical implementation of concatenated bosonic qubits with an outer repetition code, showing improved error suppression and scalability for fault-tolerant quantum computing.

Findings

Logical phase-flip error decreases with code distance from 3 to 5

Logical bit-flip error is suppressed with higher photon number

Minimum logical error per cycle around 1.7% for distance-3 and 1.65% for distance-5

Abstract

In order to solve problems of practical importance, quantum computers will likely need to incorporate quantum error correction, where a logical qubit is redundantly encoded in many noisy physical qubits. The large physical-qubit overhead typically associated with error correction motivates the search for more hardware-efficient approaches. Here, using a microfabricated superconducting quantum circuit, we realize a logical qubit memory formed from the concatenation of encoded bosonic cat qubits with an outer repetition code of distance $d=5$. The bosonic cat qubits are passively protected against bit flips using a stabilizing circuit. Cat-qubit phase-flip errors are corrected by the repetition code which uses ancilla transmons for syndrome measurement. We realize a noise-biased CX gate which ensures bit-flip error suppression is maintained during error correction. We study the performance and scaling of the logical qubit memory, finding that the phase-flip correcting repetition code operates below threshold, with logical phase-flip error decreasing with code distance from $d=3$ to $d=5$. Concurrently, the logical bit-flip error is suppressed with increasing cat-qubit mean photon number. The minimum measured logical error per cycle is on average $1.75(2)\%$ for the distance-3 code sections, and $1.65(3)\%$ for the longer distance-5 code, demonstrating the effectiveness of bit-flip error suppression throughout the error correction cycle. These results, where the intrinsic error suppression of the bosonic encodings allows us to use a hardware-efficient outer error correcting code, indicate that concatenated bosonic codes are a compelling paradigm for reaching fault-tolerant quantum computation.