Polynomial speedup in Torontonian calculation by a scalable recursive algorithm

Polynomial speedup in Torontonian calculation by a scalable recursive algorithm

Evaluating the Torontonian function is a central computational challenge in the simulation of Gaussian Boson Sampling (GBS) with threshold detection. In this work, we propose a recursive algorithm providing a polynomial speedup in the exact calculation of the Torontonian compared to state-of-the-art...

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Veröffentlicht in:arXiv.org 2022-11
Hauptverfasser: Ágoston Kaposi, Kolarovszki, Zoltán, Kozsik, Tamás, Zimborás, Zoltán, Rakyta, Péter
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Algorithms
Mathematical analysis
Numerical analysis
Polynomials
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description Evaluating the Torontonian function is a central computational challenge in the simulation of Gaussian Boson Sampling (GBS) with threshold detection. In this work, we propose a recursive algorithm providing a polynomial speedup in the exact calculation of the Torontonian compared to state-of-the-art algorithms. According to our numerical analysis the complexity of the algorithm is proportional to \(N^{1.0691}2^{N/2}\) with \(N\) being the size of the problem. We also show that the recursive algorithm can be scaled up to HPC use cases making feasible the simulation of threshold GBS up to \(35-40\) photon clicks without the needs of large-scale computational capacities.
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subjects Algorithms
Mathematical analysis
Numerical analysis
Polynomials
title Polynomial speedup in Torontonian calculation by a scalable recursive algorithm
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