Probes of chaos over the Clifford group and approach to Haar values
quant-ph
Submitted: 2026-03-31
Updated: 2026-09-21
Comments: 76 pages
License: http://creativecommons.org/licenses/by/4.0/
The gist: Chaotic behavior of quantum systems can be characterized by the adherence of the expectation values of given probes to moments of the Haar distribution.
Terminology
Abstract
Chaotic behavior of quantum systems can be characterized by the adherence of the expectation values of given probes to moments of the Haar distribution. In this work, we analyze the behavior of several probes of chaos using a technique known as Isospectral Twirling [1]. This consists in fixing the spectrum of the Hamiltonian and picking its eigenvectors at random. Here, we study the transition from stabilizer bases to random bases according to the Haar measure by T-doped random quantum circuits. We then compute the average value of the probes over ensembles of random spectra from Random Matrix Theory, the Gaussian Diagonal Ensemble and the Gaussian Unitary Ensemble, associated with non-chaotic and chaotic behavior respectively. We also study the behavior of such probes over the Toric Code Hamiltonian.
Sources
- Simulating quantum chaos without chaos
- Quantum codes on a lattice with boundary
- Integrability and Chaos via fractal analysis of Spectral Form Factors: Gaussian approximations and exact results
- Ergodicity, eigenstate thermalization, and the foundations of statistical mechanics in quantum and classical systems
- The Resource Theory of Stabilizer Computation
- Interplay of entanglement structures and stabilizer entropy in spin models
- Anticoncentration and State Design of Doped Real Clifford Circuits and Tensor Networks
- The Clifford group fails gracefully to be a unitary 4-design
- A complete theory of the Clifford commutant
- Analytic Tools for Harvesting Magic Resource in Curved Spacetime
- Gravitational back-reaction is magical
- Stabilizer Entropy of Subspaces
- Non-stabilizerness and violations of CHSH inequalities
- Witnessing Magic with Bell inequalities
- Efficient witnessing and testing of magic in mixed quantum states
- Quantum State Designs via Magic Teleportation
- How fast do stabilizer Hamiltonians thermalize?
- Scrambling Dynamics and Out-of-Time Ordered Correlators in Quantum Many-Body Systems: a Tutorial
- Free mutual information and higher-point OTOCs
- Efficient decoding for the Hayden-Preskill protocol
Related papers
- Reconquering Bell sampling on qudits: stabilizer learning and testing, quantum pseudorandomness bounds, and more
- Encrypted clones can leak: Classification of informative subsets in Quantum Encrypted Cloning
- Polynomial-time classical and quantum simulation of quantum impurity models
- Theory of quantum-enhanced interferometry with general Markovian light sources
- A convergent hierarchy of spectral gap certificates for qubit Hamiltonians
- Universal Bound and Phase Transition in Many-Body Fermionic Non-Gaussianity