Probabilistic Interpolation of Quantum Rotation Angles Article Swipe

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Bálint Koczor , John J. L. Morton , Simon C. Benjamin · YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2305.19881

Quantum computing requires a universal set of gate operations; regarding gates as rotations, any rotation angle must be possible. However a real device may only be capable of $B$ bits of resolution, i.e. it might support only $2^B$ possible variants of a given physical gate. Naive discretization of an algorithm's gates to the nearest available options causes coherent errors, while decomposing an impermissible gate into several allowed operations increases circuit depth. Conversely, demanding higher $B$ can greatly complexify hardware. Here we explore an alternative: Probabilistic Angle Interpolation (PAI). This effectively implements any desired, continuously parametrised rotation by randomly choosing one of three discretised gate settings and postprocessing individual circuit outputs. The approach is particularly relevant for near-term applications where one would in any case average over many runs of circuit executions to estimate expected values. While PAI increases that sampling cost, we prove that a) the approach is optimal in the sense that PAI achieves the least possible overhead and c) the overhead is remarkably modest even with thousands of parametrised gates and only $7$ bits of resolution available. This is a profound relaxation of engineering requirements for first generation quantum computers where even $5-6$ bits of resolution may suffice and, as we demonstrate, the approach is many orders of magnitude more efficient than prior techniques. Moreover we conclude that, even for more mature late-NISQ hardware, no more than $9$ bits will be necessary.

Type

preprint

Language

en

Landing Page

http://arxiv.org/abs/2305.19881

PDF

https://arxiv.org/pdf/2305.19881

OA Status

green

Related Works

10

OpenAlex ID

https://openalex.org/W4379089486

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OpenAlex ID

https://openalex.org/W4379089486

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DOI

https://doi.org/10.48550/arxiv.2305.19881

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Title

Probabilistic Interpolation of Quantum Rotation Angles

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Type

preprint

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Language

en

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Publication year

2023

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Publication date

2023-05-31

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Authors

Bálint Koczor, John J. L. Morton, Simon C. Benjamin

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Landing page

https://arxiv.org/abs/2305.19881

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https://arxiv.org/pdf/2305.19881

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Open access

Yes

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OA status

green

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https://arxiv.org/pdf/2305.19881

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Concepts

Overhead (engineering), Probabilistic logic, Computer science, Rotation (mathematics), Interpolation (computer graphics), Algorithm, Quantum gate, Quantum circuit, Set (abstract data type), Quantum computer, Gate count, AND gate, Quantum, Computer engineering, Logic gate, Quantum error correction, Computer hardware, Artificial intelligence, Physics, Image (mathematics), Quantum mechanics, Operating system, Programming language

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Related works (count)

10

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