Quantum CORDIC -- Arcsin on a Budget

• URL: http://arxiv.org/abs/2411.14434v1
• Date: Sat, 02 Nov 2024 11:00:58 GMT
• Title: Quantum CORDIC -- Arcsin on a Budget
• Authors: Iain Burge, Michel Barbeau, Joaquin Garcia-Alfaro,
• Abstract summary: This work introduces a quantum algorithm for computing the arcsine function to an arbitrary accuracy. We leverage a technique from embedded computing and field-programmable gate array (FPGA), called COordinate Rotation DIgital Computer (CORDIC)
• Score: 0.8739101659113155
• License:
• Abstract: This work introduces a quantum algorithm for computing the arcsine function to an arbitrary accuracy. We leverage a technique from embedded computing and field-programmable gate array (FPGA), 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 which 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.

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