13pTB-10 Random plaquette gauge models and quantum memory

Takuya Ohno, Gaku Arakawa, Ikuo Ichinose +1 more

Koujin Takeda, Hidetoshi Nishimori

晃人 竹田, Koujin Takeda

Gaku Arakawa, Ikuo Ichinose, Tetsuo Matsui +1 more

Koujin Takeda, Hidetoshi Nishimori

We study the phase diagrams of random models with bimodal randomness, especially the random bond Ising model and the random plaquette gauge model from the viewpoint of quantum information theory. Using Fourier transformation in conjunction with the replica trick, we show that these models have a common structure under duality transformation. This observation enables us to derive a conjecture on the exact location of the multicritical point and lead the accuracy threshold of the toric code, which is one of the topological quantum memories.

Manuel Rispler, Davide Vodola, Markus Müller +1 more

Abstract We introduce the random coupled-plaquette gauge model (RCPGM), which enables optimal accounting for Y -errors in decoding a surface code with noisy syndrome measurements. Using Parallel Tempering Monte Carlo simulations, we determine the code’s fundamental error thresholds. For phenomenological depolarizing data and bit-flip syndrome noise we determine a threshold of 6%, to be compared to the “uncoupled” random plaquette gauge model (RPGM) with a mere 4.3%. We then tackle the circuit-level noise scenario, where an approximate reduction technique allows us to exploit the RCPGM. Within the assumptions of the reduction technique, we find a threshold of 1.4%, to be compared to 0.7% when marginalizing Y -errors for the “uncoupled” RPGM. These results crucially enlarge the landscape of statistical mechanical mappings for quantum error correction. In particular they show further room for improvement of the surface code for fault-tolerant quantum computation and should be highly encouraging for practical decoder development.