# Error-corrected gates on an encoded qubit

## TL;DR

This paper demonstrates a fault-tolerant quantum gate on a bosonic logical qubit using an error-corrected ancilla, significantly reducing gate errors and showing resilience against common noise sources, advancing scalable quantum computing.

## Contribution

It introduces a hardware-efficient, error-corrected ancilla-based gate for bosonic qubits that maintains high fidelity despite ancilla errors and decoherence.

## Key findings

- Logical gate error reduced by a factor of two under decoherence.
- Sixfold suppression of gate error with increased energy relaxation.
- Fourfold suppression of gate error with increased dephasing noise.

## Abstract

To solve classically hard problems, quantum computers need to be resilient to the influence of noise and decoherence. In such a fault-tolerant quantum computer, noise-induced errors must be detected and corrected in real-time to prevent them from propagating between components. This requirement is especially pertinent while applying quantum gates, when the interaction between components can cause errors to quickly spread throughout the system. However, the large overhead involved in most fault-tolerant architectures makes implementing these systems a daunting task, which motivates the search for hardware-efficient alternatives. Here, we present a gate enacted by a multilevel ancilla transmon on a cavity-encoded logical qubit that is fault-tolerant with respect to decoherence in both the ancilla and the encoded qubit. We maintain the purity of the encoded qubit in the presence of ancilla errors by detecting those errors in real-time, and applying the appropriate corrections. We show a reduction of the logical gate error by a factor of two in the presence of naturally occurring decoherence, and demonstrate resilience against ancilla bit-flips and phase-flips by observing a sixfold suppression of the gate error with increased energy relaxation, and a fourfold suppression with increased dephasing noise. The results demonstrate that bosonic logical qubits can be controlled by error-prone ancilla qubits without inheriting the ancilla's inferior performance. As such, error-corrected ancilla-enabled gates are an important step towards fully fault-tolerant processing of bosonic qubits.