Logarithmic-Depth Fermion Sampling: Anticoncentration and Average-Case Hardness

arXiv:2609.40100 · quant-ph · Submitted 2026-09-30 · Read on arXiv

quant-ph

Submitted: 2026-09-30

Updated: 2026-09-30

Terminology

• Anticoncentration — 38× in this paper · explained in 1 episode
• Benchmark — 14× in this paper · explained in 2 episodes
• Core — 11× in this paper · explained in 2 episodes
• Trace — 11× in this paper · explained in 2 episodes
• Accuracy — 7× in this paper · explained in 1 episode
• Quantum Circuits — 6× in this paper · explained in 2 episodes
• Robustness — 4× in this paper · explained in 5 episodes
• Embeddings — 3× in this paper · explained in 2 episodes
• Verification — 3× in this paper · explained in 2 episodes
• Adam — 2× in this paper · explained in 2 episodes
• Generalization — 2× in this paper · explained in 13 episodes
• Generative Model — 2× in this paper · explained in 2 episodes
• Generative Models — 2× in this paper · explained in 2 episodes
• Quantization — 2× in this paper · explained in 12 episodes
• All-to-All Connectivity — 1× in this paper · explained in 1 episode
• Benchmarking — 1× in this paper · explained in 3 episodes
• Diffusion Model — 1× in this paper · explained in 8 episodes
• Entanglement — 1× in this paper · explained in 3 episodes
• Generative Modeling — 1× in this paper · explained in 3 episodes
• Hilbert Space — 1× in this paper · explained in 2 episodes

Sources

• All pure fermionic non-Gaussian states are magic states for matchgate computations
• Fermion Sampling: a robust quantum computational advantage scheme using fermionic linear optics and magic input states
• Optimal Haar random fermionic linear optics circuits
• The commutant of fermionic Gaussian unitaries
• Classical simulation of free-fermionic dynamics and quantum chemistry with magic input
• Scalable Quantum Machine Learning: Trainability, Expressivity and Efficiency
• The Born Supremacy: Quantum Advantage and Training of an Ising Born Machine
• "Train classical, deploy quantum" requires rethinking generalization
• Quantum Supremacy and the Complexity of Random Circuit Sampling
• Quantum supremacy and hardness of estimating output probabilities of quantum circuits
• Average-case hardness of estimating probabilities of random quantum circuits with a linear scaling in the error exponent
• Quantum advantage from random geometrically-two-local Hamiltonian dynamics
• Universal blind quantum computation
• Random quantum circuits anti-concentrate in log depth
• Average-case complexity versus approximate simulation of commuting quantum computations
• Random regular graph states are complex at almost any depth
• General framework for anticoncentration and linear cross-entropy benchmarking in photonic quantum advantage experiments
• Boson sampling beyond the dilute regime: second moments and anti-concentration
• Anticoncentration of the Permanent in Ginibre Ensembles

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