Quantum CORDIC -- Arcsine on a Budget
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913066371776512 |
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| author | Burge, Iain Barbeau, Michel Garcia-Alfaro, Joaquin |
| author_facet | Burge, Iain Barbeau, Michel Garcia-Alfaro, Joaquin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_14434 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum CORDIC -- Arcsine on a Budget Burge, Iain Barbeau, Michel Garcia-Alfaro, Joaquin Quantum Physics Cryptography and Security 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. |
| title | Quantum CORDIC -- Arcsine on a Budget |
| topic | Quantum Physics Cryptography and Security |
| url | https://arxiv.org/abs/2411.14434 |