Born probability estimation via gate merging and dynamic frame optimisation

Abstract

Outcome probability estimation via classical methods is an important task for validating quantum computing devices. Outcome probabilities of any quantum circuit can be estimated using Monte Carlo sampling, where the amount of negativity present in the circuit frame representation quantifies the overhead on the number of samples required to achieve a certain precision. In this paper, we propose two classical sub-routines: circuit gate merging and dynamic frame optimisation, which optimise the circuit representation to reduce the sampling overhead. We show that the runtimes of both sub-routines scale polynomially in circuit size and gate depth. Our methods are applicable to general circuits, regardless of generating gate sets, qudit dimensions and the chosen frame representations for the circuit components. We numerically demonstrate that our methods provide improved scaling in the negativity overhead for all tested cases of random circuits with Clifford+T and Haar-random gates, and that the performance of our methods compares favourably with prior quasiprobability samplers as the number of non-Clifford gates increases.

Scalable measures of magic resource for quantum computers

“…The degree of non-stabilizerness is called magic. Magic can be related to the difficulty of classical simulation of quantum states [3][4][5][6][7] and to quantum chaos [8][9][10]. Further, magic is a precious resource required to realize universal unitaries [11,12] in faulttolerant quantum computers [13][14][15][16].…”