IQIM Postdoctoral and Graduate Student Seminar
Abstract: Various realizations of Kitaev's surface code, such as the XY and XZZX surface codes, perform surprisingly well for biased Pauli noise. Attracted by potential gains, we study the performance of Clifford-deformed surface codes (CDSCs) that are obtained from the surface code by deforming its stabilizer group via the application of single-qubit Clifford operators. We first analyze CDSCs on the 3 by 3 square lattice and find that depending on the noise bias, their logical error rates can differ by orders of magnitude. To explain the observed behavior, we introduce the notion of the effective distance d' that subsumes the standard code distance. Then, we focus on random CDSCs and demonstrate that they can outperform the subthreshold logical error rate of the best known translationally-invariant codes, such as the XY and XZZX surface codes while maintaining thresholds that are close to the hashing bound. We also conjecture a threshold phase diagram that describes the region of random CDSCs with 50% threshold for infinite bias noise, which we support using percolation-theory arguments and tensor-network simulations.