Matrix Phase-Space Representations for Gaussian Boson Sampling.

Area of Science:

• Quantum information science
• Quantum computing
• Computational physics

Background:

• Quantum phase-space representations are crucial for analyzing quantum systems.
• Validating quantum computational advantage experiments, such as Gaussian boson sampling (GBS), faces significant computational challenges.
• Existing methods for GBS validation struggle with scalability and accuracy.

Purpose of the Study:

• To introduce a novel method for quantum phase-space representations called coherent matrix phase-space distributions.
• To leverage conservation laws and symmetries for improved accuracy and computational speed.
• To apply this new method to validate low-loss Gaussian boson sampling experiments.

Main Methods:

• Development of coherent matrix phase-space distributions.
• Incorporation of conservation laws and symmetries into the phase-space representation.
• Application to the validation of low-loss Gaussian boson sampling (GBS) quantum computational advantage experiments.
• Comparison of sampling errors and numerical speed with previous methods.

Main Results:

• Demonstrated significant improvements in sampling errors compared to existing methods.
• Achieved a large numerical speedup due to the quadratic scaling of matrix phase-space representations.
• Successfully applied the method to validate GBS experiments where classical simulation is exponentially hard.

Conclusions:

• Coherent matrix phase-space distributions offer a more accurate and efficient approach to quantum phase-space representation.
• The method provides a practical solution for validating large-scale, low-loss GBS networks.
• This advancement accelerates the verification of quantum computational advantage claims.