A Combinatorial Noise Model for Quantum Computer Simulation

Quantum computers (QCs) have many potential hardware implementations ranging from solid-state silicon-based structures to electron-spin qubits on liquid helium. However, all QCs must contend with gate infidelity and qubit state decoherence over time. Quantum error correcting codes (QECCs) have been developed to protect program qubit states from such noise. Previously, Monte Carlo noise simulators have been developed to model the effectiveness of QECCs in combating decoherence. The downside to this random sampling approach is that it may take days or weeks to produce enough samples for an accurate measurement. We present an alternative noise modeling approach that performs combinatorial analysis rather than random sampling. This model tracks the progression of the most likely error states of the quantum program through its course of execution. This approach has the potential for enormous speedups versus the previous Monte Carlo methodology. We have found speedups with the combinatorial model on the order of 100X-1,000X over the Monte Carlo approach when analyzing applications utilizing the [[7,1,3]] QECC. The combinatorial noise model has significant memory requirements, and we analyze its scaling properties relative to the size of the quantum program. Due to its speedup, this noise model is a valuable alternative to traditional Monte Carlo simulation.