Biaspreserving gates with stabilized cat qubits
Abstract
The code capacity threshold for error correction using qubits which exhibit asymmetric or biased noise channels is known to be much higher than with qubits without such structured noise. However, it is unclear how much this improvement persists when realistic circuit level noise is taken into account. This is because implementations of gates which do not commute with the dominant error unbias the noise channel. In particular, a native biaspreserving controlledNOT (CX) gate, which is an essential ingredient of stabilizer codes, is not possible in strictly twolevel systems. Here we overcome the challenge of implementing a biaspreserving CX gate by using stabilized cat qubits in driven nonlinear oscillators. The physical noise channel of this qubit is biased towards phaseflips, which increase linearly with the size of the cat, while bitflips are exponentially suppressed with cat size. Remarkably, the error channel of this native CX gate between two such cat qubits is also dominated by phaseflips, while bitflips remain exponentially suppressed. This CX gate relies on the topological phase that arises from the rotation of the cat qubit in phase space. The availability of biaspreserving CX gates opens a path towards faulttolerant codes tailored to biasednoise cat qubits with high threshold and low overhead. As an example, we analyze a scheme for concatenated error correction using cat qubits. We find that the availability of CX gates with moderately sized cat qubits, having mean photon number <10, improves a rigorous lower bound on the faulttolerance threshold by a factor of two and decreases the overhead in logical Clifford operations by a factor of 5. We expect these estimates to improve significantly with further optimization and with direct use of other codes such as topological codes tailored to biased noise.
 Publication:

Science Advances
 Pub Date:
 August 2020
 DOI:
 10.1126/sciadv.aay5901
 arXiv:
 arXiv:1905.00450
 Bibcode:
 2020SciA....6.5901P
 Keywords:

 Quantum Physics
 EPrint:
 doi:10.1126/sciadv.aay5901