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 it 1 . Therefore, quantum bits undergo errors, putting dauntingly difficult constraints on the hardware suitable for quantum computation 2 . 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-locality 3 , 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 pairs 5 , 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 rate 7 . 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 overhead 8 . 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.