George Umbrarescu

Simulating universal quantum circuits is of fundamental and practical importance for the development of quantum computation. But existing simulators, despite being powerful in their own regimes, are limited for quantum error correction (QEC) tasks like testing the fault-tolerance of a QEC gadget or accurately decoding and computing logical error rates under realistic noise. In this work, we propose a simulator called SyQMA that is especially amenable to QEC-related tasks through several attractive features. SyQMA can represent Clifford circuits with incoherent Pauli noise, coherent Pauli rotations and Pauli measurements, returns expected values and probabilities as analytical functions of the error rates, rotation angles and Pauli measurement outputs, and produces samples from the outcome distribution. For QEC, this simulator can perform maximum likelihood (MLD) decoding to return exact and analytical expressions of the logical error rate in stabiliser and magic state preparations, avoiding the problem of rare-event sampling in Monte Carlo simulations. SyQMA is based on an intuitive extension of stabiliser simulators where every non-Clifford Pauli rotation and incoherent Pauli channel is compactly represented with the addition of a virtual qubit, allowing for the consumption of only polynomial memory. We demonstrate the simulator on the FT preparation of stabiliser and magic states in the Iceberg, Steane, [[15,1,3]], and [[17,1,5]] codes.