First proof that random walks on unitary groups achieve constant spectral gaps independent of system size and representations. Resolves longstanding questions about convergence rates of random quantum circuits to Haar-random distributions.
#QuantumCircuits #SpectralGap #Research
#QuantumCircuits #SpectralGap #Research
Random Unitary Circuits with Constant Spectral Gap
arxiv.org
July 24, 2026 at 5:22 AM
First proof that random walks on unitary groups achieve constant spectral gaps independent of system size and representations. Resolves longstanding questions about convergence rates of random quantum circuits to Haar-random distributions.
#QuantumCircuits #SpectralGap #Research
#QuantumCircuits #SpectralGap #Research
Arbitrarily small classical 1-local perturbations destabilize undecidable spectral gap behavior, rendering previously uncomputable properties decidable through finite-size checking of energy thresholds.
#SpectralGap #QuantumComputation #Research
#SpectralGap #QuantumComputation #Research
Instability of the Undecidable Spectral Gap in 1D Quantum Systems
arxiv.org
July 10, 2026 at 2:09 AM
Arbitrarily small classical 1-local perturbations destabilize undecidable spectral gap behavior, rendering previously uncomputable properties decidable through finite-size checking of energy thresholds.
#SpectralGap #QuantumComputation #Research
#SpectralGap #QuantumComputation #Research
Jiawei Gu, Ziyue Qiao, Zechao Li: SpectralGap: Graph-Level Out-of-Distribution Detection via Laplacian Eigenvalue Gaps https://arxiv.org/abs/2505.15177 https://arxiv.org/pdf/2505.15177 https://arxiv.org/html/2505.15177
May 22, 2025 at 6:09 AM
Jiawei Gu, Ziyue Qiao, Zechao Li: SpectralGap: Graph-Level Out-of-Distribution Detection via Laplacian Eigenvalue Gaps https://arxiv.org/abs/2505.15177 https://arxiv.org/pdf/2505.15177 https://arxiv.org/html/2505.15177