Iain Burge

Iain Burge, Michel Barbeau, Joaquin Garcia-Alfaro

This work introduces a quantum algorithm for computing the function arcsine, with arbitrary accuracy. We leverage a technique from embedded computing and Field-Programmable Gate Arrays, called COordinate Rotation DIgital Computer (CORDIC). CORDIC is a family of iterative algorithms that, in a classical context, can approximate various trigonometric, hyperbolic, and elementary functions using only bit shifts and additions. Adapting CORDIC to the quantum context is non-trivial, as the algorithm traditionally uses several non-reversible operations. We detail a method for CORDIC that avoids such non-reversible operations. We propose multiple approaches to calculate the arcsine function reversibly with CORDIC. For n bits of precision, our method has space complexity of order n qubits, a layer count in the order of n times log n, and a CNOT count in the order of n squared. This primitive function is a required step for the Harrow-Hassidim-Lloyd (HHL) algorithm, is necessary for quantum digital-to-analog conversion, can simplify a quantum speed-up for Monte-Carlo methods, and has direct applications in the quantum estimation of Shapley values.

Iain Burge, Michel Barbeau, Joaquin Garcia-Alfaro

This work focuses on developing efficient post-hoc explanations for quantum AI algorithms. In classical contexts, the cooperative game theory concept of the Shapley value adapts naturally to post-hoc explanations, where it can be used to identify which factors are important in an AI's decision-making process. An interesting question is how to translate Shapley values to the quantum setting and whether quantum effects could be used to accelerate their calculation. We propose quantum algorithms that can extract Shapley values within some confidence interval. Our method is capable of quadratically outperforming classical Monte Carlo approaches to approximating Shapley values up to polylogarithmic factors in various circumstances. We demonstrate the validity of our approach empirically with specific voting games and provide rigorous proofs of performance for general cooperative games.