Nikolas P Breuckmann

Quantum error correction is essential for the development of scalable quantum computers; however, it introduces redundancy that results in large resource requirements for useful quantum computation. In this work, we construct error-correcting codes that are up to times more efficient than surface codes for architectures with native two-qubit measurements and some long-range connections.

Abstract In this work, we study the single-shot performance of higher-dimensional hypergraph product codes decoded using belief propagation and ordered-statistics decoding [P. Panteleev and G. Kalachev, Quantum 5, 585 (2021)]. We find that decoding data-qubit and syndrome-measurement errors together in a single stage leads to single-shot thresholds that greatly exceed all previously observed single-shot thresholds for these codes.

Abstract We analyze the thermodynamic properties of the random-bond Ising model (RBIM) on closed hyperbolic surfaces using Monte Carlo and high-temperature series expansion techniques. We also analyze the dual-RBIM, that is, the model that in the absence of disorder is related to the RBIM via the Kramers-Wannier duality. Even on self-dual lattices this model is different from the RBIM, unlike in the Euclidean case. We explain this anomaly by a careful rederivation of the Kramers-Wannier duality.