aiqbench takeQuantum Computing

This research investigates how specific probes of chaos in quantum circuits transition from stabilizer bases to random Haar-distributed states using Isospectral Twirling. By analyzing ensembles derived from Random Matrix Theory and the Toric Code Hamiltonian, the study provides a theoretical framework for distinguishing between non-chaotic and chaotic regimes based on expectation values. These findings are significant for understanding fundamental quantum dynamics and characterizing scrambling in complex many-body systems.

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Probes of chaos over the Clifford group and approach to Haar values

arXivJune 17, 20262 min read

arXiv:2603.29695v3 Announce Type: replace 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.

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.

arXiv:2603.29695 [quant-ph]

(or arXiv:2603.29695v3 [quant-ph] for this version)

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