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arXiv · 2411.14434

Quantum CORDIC -- Arcsine on a Budget

Iain Burge·Michel Barbeau·Joaquin Garcia-Alfaro
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Abstract

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 an approach 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.

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Iain Burge, Michel Barbeau, Joaquin Garcia-Alfaro. 2026-08-04. Quantum CORDIC -- Arcsine on a Budget. https://arxiv.org/abs/2411.14434

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