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Paper Abstract and Keywords
Presentation 2023-12-17 17:30
[Poster Presentation] Practical algorithm for optimal Clifford+T approximation of SU(2)
Hayata Morisaki (Osaka Univ.)
Abstract (in Japanese) (See Japanese page) 
(in English) In this paper, we consider the problem of approximating arbitrary single-qubit unitaries with a given precision $epsilon$ by single-qubit Clifford+$T$ circuits.
We reduce this problem to a lattice problem and propose an algorithm to find the Clifford+$T$ circuit with the smallest number of $T$ gates.
Its average runtime for a given precision $epsilon$ is $O(1/epsilon log(1/epsilon))$.
While the runtime grows exponentially with the number of gates, we have successfully achieved an approximation with the precision $epsilon = 10^{−10}$.
There are results indicating that by appropriately mixing several unitaries with $epsilon$-precision, the approximation precision can automatically rise to $epsilon^2$-precision.
Using this result, it is possible to perform an approximation with the precision $epsilon = 10^{−20}$ as probabilistic unitaries.
This level of approximation is considered practically sufficient.
We conduct numerical experiments to investigate the required number of $T$ gates for the approximation.
Our proposed algorithm requires approximately $3log_2(1/epsilon)$ $T$ gates for approximating $mathrm{SU(2)}$ by single-qubit Clifford+$T$ circuits.
In comparison with existing methods, our proposed algorithm reduces the required number of $T$ gates to approximately $1/3$.
Keyword (in Japanese) (See Japanese page) 
(in English) Clifford+$T$ approximation / decomposition of $mathrm{SU(2)}$ / quantum compiler / / / / /  
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Conference Information
Committee QIT  
Conference Date 2023-12-17 - 2023-12-19 
Place (in Japanese) (See Japanese page) 
Place (in English) OIST 
Topics (in Japanese) (See Japanese page) 
Topics (in English) Quantum Information 
Paper Information
Registration To QIT 
Conference Code 2023-12-QIT 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Practical algorithm for optimal Clifford+T approximation of SU(2) 
Sub Title (in English)  
Keyword(1) Clifford+$T$ approximation  
Keyword(2) decomposition of $mathrm{SU(2)}$  
Keyword(3) quantum compiler  
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1st Author's Name Hayata Morisaki  
1st Author's Affiliation Osaka University (Osaka Univ.)
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Speaker Author-1 
Date Time 2023-12-17 17:30:00 
Presentation Time 120 minutes 
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