Higher moment theory and learnability of bosonic states

2025/10/02 by Joseph T. Iosue, Iosue, Joseph T., Yuxin Wang +11 · 2 citations
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics

paper · pdf · doi:10.48550/arxiv.2510.01610

Abstract

We present a sample- and time-efficient algorithm to learn any bosonic Fock state acted upon by an arbitrary Gaussian unitary. As a special case, this algorithm efficiently learns states produced in Fock state BosonSampling, thus resolving an open question put forth by Aaronson and Grewal (Aaronson, Grewal 2023). We further study a hierarchy of classes of states beyond Gaussian states that are specified by a finite number of their higher moments. Using the higher moments, we find a full spectrum of invariants under Gaussian unitaries, thereby providing necessary conditions for two states to be related by an arbitrary (including active, e.g. beyond linear optics) Gaussian unitary.

Citations

• Energy-independent tomography of Gaussian states
• The Hardness of Learning Quantum Circuits and its Cryptographic Applications
• Complexity of quantum tomography from genuine non-Gaussian entanglement
• Anti-Concentration for the Unitary Haar Measure and Applications to Random Quantum Circuits
• Learning quantum states of continuous variable systems
• Optimal algorithms for learning quantum phase states
• Learning stabilizer states by Bell sampling

Cited by

• Shedding light on classical shadows: learning photonic quantum states
• Efficient learning of bosonic Gaussian unitaries

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