Polynomial speedup in Torontonian calculation by a scalable recursive algorithm

• URL: http://arxiv.org/abs/2109.04528v3
• Date: Tue, 15 Nov 2022 11:47:56 GMT
• Title: Polynomial speedup in Torontonian calculation by a scalable recursive algorithm
• Authors: \'Agoston Kaposi, Zolt\'an Kolarovszki, Tam\'as Kozsik, Zolt\'an Zimbor\'as, P\'eter Rakyta
• Abstract summary: The Torontonian function is a central computational challenge in the simulation of Gaussian Boson Sampling (GBS) with threshold detection. We propose a recursive algorithm providing a speedup in the exact calculation of the Torontonian compared to state-of-the-art algorithms. We show that the algorithm can be scaled up to use cases making feasible the simulation of threshold GBS up to $35-40$ photon without the needs of large-scale computational capacities.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: 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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