Various realizations of Kitaev's surface code perform surprisingly well for biased Pauli noise. Attracted by these potential gains, we study the performance of Clifford-deformed surface codes (CDSCs) obtained from the surface code by the application of single-qubit Clifford operators. We first analyze CDSCs on the 3×3 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 effective distance d′, which reduces to the standard distance for unbiased noise. To study CDSC performance in the thermodynamic limit, we focus on random CDSCs. Using the statistical mechanical mapping for quantum codes, we uncover a phase diagram that describes random CDSCs with 50% threshold at infinite bias. In the high-threshold region, we further demonstrate that typical code realizations at finite bias outperform the thresholds and subthreshold logical error rates of the best known translationally invariant codes.

%8 1/19/2022 %G eng %U https://arxiv.org/abs/2201.07802 %R 10.48550/ARXIV.2201.07802 %0 Journal Article %D 2022 %T Three-dimensional quantum cellular automata from chiral semion surface topological order and beyond %A Shirley, Wilbur %A Chen, Yu-An %A Dua, Arpit %A Ellison, Tyler D. %A Tantivasadakarn, Nathanan %A Williamson, Dominic J. %K FOS: Physical sciences %K Mathematical Physics (math-ph) %K Quantum Physics (quant-ph) %K Strongly Correlated Electrons (cond-mat.str-el) %XWe construct a novel three-dimensional quantum cellular automaton (QCA) based on a system with short-range entangled bulk and chiral semion boundary topological order. We argue that either the QCA is nontrivial, i.e. not a finite-depth circuit of local quantum gates, or there exists a two-dimensional commuting projector Hamiltonian realizing the chiral semion topological order (characterized by U(1)2 Chern-Simons theory). Our QCA is obtained by first constructing the Walker-Wang Hamiltonian of a certain premodular tensor category of order four, then condensing the deconfined bulk boson at the level of lattice operators. We show that the resulting Hamiltonian hosts chiral semion surface topological order in the presence of a boundary and can be realized as a non-Pauli stabilizer code on qubits, from which the QCA is defined. The construction is then generalized to a class of QCAs defined by non-Pauli stabilizer codes on 2n-dimensional qudits that feature surface anyons described by U(1)2n Chern-Simons theory. Our results support the conjecture that the group of nontrivial three-dimensional QCAs is isomorphic to the Witt group of non-degenerate braided fusion categories.

%8 2/10/2022 %G eng %U https://arxiv.org/abs/2202.05442 %R 10.48550/ARXIV.2202.05442