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Transition of Anticoncentration in Gaussian Boson Sampling
Adam Ehrenberg1,2, Joseph T Iosue1,2, Abhinav Deshpande3
1University of Maryland, College Park, Joint Center for Quantum Information and Computer Science, NIST/, Maryland 20742, USA.
Physical Review Letters
|April 25, 2025
Summary
Gaussian boson sampling
Area of Science:
- Quantum computing
- Quantum information science
Background:
- Gaussian boson sampling is a key method for demonstrating quantum advantage.
- Statistical properties of its output distribution, particularly anticoncentration, are not well understood.
Purpose of the Study:
- To analyze the statistical properties of Gaussian boson sampling output distributions.
- To investigate the anticoncentration of output probabilities.
Main Methods:
- Developed a graph-theoretic framework to analyze moments of the Gaussian boson sampling distribution.
- Examined the relationship between squeezed modes and measured photons.
Main Results:
- Identified a transition in anticoncentration based on the scaling of squeezed modes relative to measured photons.
- Lack of anticoncentration occurs when squeezed modes scale slowly with photons.
- Weak anticoncentration is observed when squeezed modes scale quickly with photons.
Conclusions:
- The anticoncentration of Gaussian boson sampling output is sensitive to the ratio of squeezed modes to measured photons.
- This finding impacts arguments for the complexity-theoretic hardness of Gaussian boson sampling.
- Understanding this transition is crucial for realizing quantum advantage through this scheme.
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