Quantum CORDIC -- Arcsine on a Budget

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.

Quantum Physics (quant-ph); Cryptography and Security (cs.CR)

arXiv:2411.14434 [quant-ph]

(or arXiv:2411.14434v3 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2411.14434 Focus to learn more arXiv-issued DOI via DataCite

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.