Fast estimation of outcome probabilities for quantum circuits Speaker(s): Hakop Pashayan
Abstract:
We present two classical algorithms for the simulation of universal quantum circuits on n qubits constructed from c instances of Clifford gates and t arbitraryangle Zrotation gates such as T gates. Our algorithms complement each other by performing best in different parameter regimes. The Estimate algorithm produces an additive precision estimate of the Born rule probability of a chosen measurement outcome with the only source of runtime inefficiency being a linear dependence on the stabilizer extent (which scales like ≈1.17^t for T gates). Our algorithm is stateoftheart for this task: as an example, in approximately 25 hours (on a standard desktop computer), we estimated the Born rule probability to within an additive error of 0.03, for a 50 qubit, 60 nonClifford gate quantum circuit with more than 2000 Clifford gates. The Compute algorithm calculates the probability of a chosen measurement outcome to machine precision with runtime O(2^t−r(t−r)t) where r is an efficiently computable, circuitspecific quantity. With high probability, r is very close to min{t,n−w} for random circuits with many Clifford gates, where w is the number of measured qubits. Compute can be effective in surprisingly challenging parameter regimes, e.g., we can randomly sample Clifford+T circuits with n=55, w=5, c=105 and t=80 Tgates, and then compute the Born rule probability with a runtime consistently less than 104 seconds using a single core of a standard desktop computer. We provide a C+Python implementation of our algorithms. Date: 31/03/2021  4:00 pm
