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

A quantum system interacts with its environment—if ever so slightly—no matter how much care is put into isolating it1. Therefore, quantum bits undergo errors, putting dauntingly difficult constraints on the hardware suitable for quantum computation2. New strategies are emerging to circumvent this problem by encoding a quantum bit non-locally across the phase space of a physical system. Because most sources of decoherence result from local fluctuations, the foundational promise is to exponentially suppress errors by increasing a measure of this non-locality3,4. Prominent examples are topological quantum bits, which delocalize information over real space and where spatial extent measures non-locality. Here, we encode a quantum bit in the field quadrature space of a superconducting resonator endowed with a special mechanism that dissipates photons in pairs5,6. This process pins down two computational states to separate locations in phase space. By increasing this separation, we measure an exponential decrease of the bit-flip rate while only linearly increasing the phase-flip rate7. Because bit-flips are autonomously corrected, only phase-flips remain to be corrected via a one-dimensional quantum error correction code. This exponential scaling demonstrates that resonators with nonlinear dissipation are promising building blocks for quantum computation with drastically reduced hardware overhead8. The choice of the physical system that represents a qubit can help reduce errors. Encoding them in the quadrature space of a superconducting resonator leads to exponentially reduced bit-flip rates, while phase-flip errors increase only linearly.