# Exponential suppression of bit-flips in a qubit encoded in an oscillator

## TL;DR

This paper demonstrates that encoding a qubit in a superconducting resonator with non-linear dissipation exponentially suppresses bit-flip errors, advancing the development of fault-tolerant quantum computing.

## Contribution

The work introduces a novel qubit encoding in phase space with non-linear dissipation, achieving exponential suppression of bit-flips while maintaining manageable phase-flip rates.

## Key findings

- Exponential decrease in bit-flip rate with increased phase space separation
- Linear increase in phase-flip rate with separation
- Potential for scalable fault-tolerant quantum computation

## Abstract

A quantum system interacts with its environment, if ever so slightly, no matter how much care is put into isolating it. As a consequence, quantum bits (qubits) undergo errors, putting dauntingly difficult constraints on the hardware suitable for quantum computation. New strategies are emerging to circumvent this problem by encoding a qubit non-locally across the phase space of a physical system. Since most sources of decoherence are due to local fluctuations, the foundational promise is to exponentially suppress errors by increasing a measure of this non-locality. Prominent examples are topological qubits which delocalize quantum information over real space and where spatial extent measures non-locality. In this work, we encode a qubit in the field quadrature space of a superconducting resonator endowed with a special mechanism that dissipates photons in pairs. This process pins down two computational states to separate locations in phase space. As we increase this separation, we measure an exponential decrease of the bit-flip rate while only linearly increasing the phase-flip rate. Since bit-flips are continuously and autonomously corrected at the single qubit level, only phase-flips are left to be corrected via a one-dimensional quantum error correction code. This exponential scaling demonstrates that resonators with non-linear dissipation are promising building blocks for universal fault-tolerant quantum computation with drastically reduced hardware overhead.