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Towards the Simplest Model of Quantum Supremacy: Atomic Boson Sampling in a Box Trap
Vitaly V Kocharovsky1, Vladimir V Kocharovsky1, William D Shannon1
1Department of Physics and Astronomy, Institute for Quantum Science and Engineering, Texas A&M University, College Station, TX 77843, USA.
Entropy (Basel, Switzerland)
|December 23, 2023
Summary
This study introduces a novel platform using interacting atoms in Bose-Einstein-condensed (BEC) gas for quantum supremacy research. It demonstrates that inherent atomic interactions self-generate the necessary conditions for computational ♯P-hardness.
Area of Science:
- Quantum Information Science
- Atomic, Molecular, and Optical Physics
- Computational Complexity Theory
Background:
- Bose-Einstein-condensed (BEC) gas is a quantum state of matter with unique properties.
- Boson sampling is a key task for demonstrating quantum computational advantage.
- Computational ♯P-hardness is a complexity class relevant to counting problems.
Purpose of the Study:
- To present a new platform for studying computational ♯P-hardness and quantum supremacy using interacting atoms from a BEC gas.
- To investigate the role of interatomic interactions in generating quantum computational properties.
Main Methods:
- Utilizing the noncondensed fraction of BEC gas confined in a box trap.
- Calculating characteristic functions and atom number statistics via the Hafnian master theorem.
- Applying Bloch-Messiah reduction to analyze interatomic interactions.
Main Results:
- Interatomic interactions generate two key entities: eigen-squeeze modes and eigen-energy quasiparticles.
- The interplay of these entities with sampling atom states governs the BEC gas behavior.
- Squeezing and interference, essential for ♯P-hardness, are self-generated within the gas.
Conclusions:
- Interacting BEC gas provides a self-sufficient platform for quantum supremacy experiments.
- External sources of squeezed bosons are not required, simplifying experimental setups.
- This work advances the understanding of quantum many-body systems and their computational power.
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