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2026
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| Online Access: | https://doi.org/10.5281/zenodo.20201526 |
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| author | Ansh Sharma, Ansh Vansh Sharma, Vansh |
| author_facet | Ansh Sharma, Ansh Vansh Sharma, Vansh |
| contents | <p>We present a novel algorithm for computing the von Neumann entropy of single-mode squeezed<br>quantum states - the fundamental quantum state of photonic quantum computers - using Ramanujan's<br>mock theta function f(q) as an optimal stopping criterion. The algorithm replaces standard term-by-term<br>series summation with a short partial sum of K terms, where K is determined by the superexponential<br>decay of the mock theta weight qn2, followed by an exact closed-form analytical tail correction requiring<br>no additional summation. At squeezing parameter r = 3.0 - representative of high-power photonic<br>quantum hardware - the algorithm achieves a 218x reduction in computation steps with 0.0000% error<br>versus the closed-form exact result. The speedup grows monotonically with squeezing, reaching 84x at<br>r = 2.5 and 36x at r = 2.0, precisely in the high-power regime where standard methods are most<br>computationally expensive. The result scales linearly to N-mode systems: for Xanadu Borealis (216<br>modes), the total computation reduces from 472,608 steps to 2,160 steps per entropy calculation. To<br>our knowledge, this constitutes the first algorithmic application of Ramanujan's mock theta functions to<br>photonic quantum computing.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20201526 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Mock Theta Functions as Optimal Stopping Criteria for Photonic Quantum Entropy Computation Ansh Sharma, Ansh Vansh Sharma, Vansh <p>We present a novel algorithm for computing the von Neumann entropy of single-mode squeezed<br>quantum states - the fundamental quantum state of photonic quantum computers - using Ramanujan's<br>mock theta function f(q) as an optimal stopping criterion. The algorithm replaces standard term-by-term<br>series summation with a short partial sum of K terms, where K is determined by the superexponential<br>decay of the mock theta weight qn2, followed by an exact closed-form analytical tail correction requiring<br>no additional summation. At squeezing parameter r = 3.0 - representative of high-power photonic<br>quantum hardware - the algorithm achieves a 218x reduction in computation steps with 0.0000% error<br>versus the closed-form exact result. The speedup grows monotonically with squeezing, reaching 84x at<br>r = 2.5 and 36x at r = 2.0, precisely in the high-power regime where standard methods are most<br>computationally expensive. The result scales linearly to N-mode systems: for Xanadu Borealis (216<br>modes), the total computation reduces from 472,608 steps to 2,160 steps per entropy calculation. To<br>our knowledge, this constitutes the first algorithmic application of Ramanujan's mock theta functions to<br>photonic quantum computing.</p> |
| title | Mock Theta Functions as Optimal Stopping Criteria for Photonic Quantum Entropy Computation |
| url | https://doi.org/10.5281/zenodo.20201526 |