Quantum

Fermionic Porter-Thomas statistics and their emergence in random matchgate circuits

Read full article at source ↗

Based on a feed excerpt; full article content has not been acquired. Source evidence retrieved 05/11/2026, 05:13:24 UTC.

Briefings

Research published in November 2026 on arXiv establishes the Porter-Thomas distribution for random fermionic Gaussian states, showing anticoncentration up to polynomial system-size factors. The study derives exact analogues for states with and without particle-number conservation and analyzes Clifford Gaussian states via an arcs-and-loops model. It demonstrates that random one-dimensional brickwork matchgate circuits exhibit this distribution, with a single-arc approximation capturing the full probability distribution. The paper identifies a diffusive regime followed by slow relaxation on timescales scaling with the square of system size, and proves that quadratic depths are required for collision probability convergence.

Key points

• For Haar-random quantum states, measurement probabilities follow the universal Porter-Thomas distribution, implying anticoncentration where probability spreads over exponentially many outcomes.
• The study derives exact analogues of the Porter-Thomas law for random fermionic Gaussian states, both with and without particle-number conservation, and considers Clifford Gaussian states mapped to an arcs-and-loops model.

Context

This research addresses a fundamental property of random quantum circuits, specifically how fermionic states distribute measurement probabilities. Understanding this distribution is critical for validating random-circuit-sampling experiments and benchmarking quantum hardware, as it reveals the underlying statistical behavior of quantum states in complex computational models.

Limitations

The evidence is a preprint (arXiv:2611.05479v1) from November 2026, so results may be subject to revision. The analysis of Clifford Gaussian states relies on a simplified model of arcs and loops, which may not capture all physical nuances. The study focuses on one-dimensional brickwork matchgate circuits and does not provide data on other circuit architectures or experimental validation results.

Generated by Bittrees-hosted qwen35-2b sha256:aaf42c8b7c3c on 05/11/2026, 06:32:55 UTC. Based on publisher-provided feed evidence; may not cover the full original article. Check the source for details.

View archived briefing on IPFS
bafybeicfxkooebu5q4ngqnvxinxmw4d4t42tx45vn6j57h567ay5cgczfu