Quadratic Speed-Up for Simulating Gaussian Boson Sampling
Open accessAbstract
We introduce an algorithm for the classical simulation of Gaussian boson sampling that is quadratically faster than previously known methods.The complexity of the algorithm is exponential in the number of photon pairs detected, not the number of photons, and is directly proportional to the time required to calculate a probability amplitude for a pure Gaussian state.The main innovation is to use auxiliary conditioning variables to reduce the problem of sampling to the computation of the pure-state probability amplitudes, for which the most computationally expensive step is the calculation of a loop hafnian.We implement and benchmark an improved loop-hafnian algorithm and show that it can be used to compute pure-state probabilities, the dominant step in the sampling algorithm, of events involving up to 50 photons in a single workstation, i.e., without the need of a supercomputer.
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On average, it would take more than 9,000 years for the best available algorithms and supercomputers to produce, using exact methods, a single sample from the programmed distribution.
“On average, it would take more than 9,000 years for the best available algorithms and supercomputers to produce, using exact methods, a single sample from the programmed distribution”
From Quantum computational advantage with a programmable photonic processor (2022) · cites this paper as [34]
The best-known algorithm to simulate GBS scales with the total number of modes and the time it takes to calculate a probability amplitude of a pure-state GBS instance.
“The best-known algorithm to simulate GBS30,34 scales with the total number of modes and the time it takes to calculate a probability amplitude of a pure-state GBS instance.”
From Quantum computational advantage with a programmable photonic processor (2022) · cites this paper as [34]
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- Authors
- Quesada, N., Chadwick, R. S., Bell, B. A., Arrazola, J. M., Vincent, T., Qi, H., & García−Patrón, R.
- Affiliations
- Xanadu Quantum Technologies (Canada) (CA)
- University of Bristol (GB)
- Imperial College London (GB)
- University of Edinburgh (GB)
- Venue
- PRX Quantum
- Publisher
- American Physical Society (APS)
- Published
- 2022-01-11
- Volume
- 3
- Issue
- 1
- ISSN
- 2691-3399 (ISSN-L)
- OpenAlex
- W3095883505
- Cited by
- 48
- References
- 38
- Citations by year
- 2026: 5 · 2025: 10 · 2024: 10 · 2023: 9 · 2022: 11 · 2021: 3
- FWCI
- 3.29
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- PRX Quantum (publishedVersion, cc-by)
- arXiv (Cornell University) (submittedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- PolyPublie (École Polytechnique de Montréal) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Engineering and Physical Sciences Research Council (EP/LO15730/1)
- FrEQuMP (846073)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Keywords
- Gaussian boson sampling, classical simulation, computational complexity
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