Quantum Chaos is Quantum

Leone, Lorenzo; Oliviero, Salvatore F. E.; Zhou, Y.; Hamma, Alioscia

doi:10.22331/q-2021-05-04-453

Cited by 53 publications

(63 citation statements)

References 21 publications

(23 reference statements)

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“…An explicit measure of magic was recently proposed in [45]. Its relations with quantum chaos was studied in [46]. It would be interesting to better investigate the role of magic in the VQA problems, following [47].…”

Section: Discussion and Outlookmentioning

confidence: 99%

Quantum Chaos and Circuit Parameter Optimization

Kim¹,

Oz²,

Rosa³

2022

Preprint

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We explore quantum chaos diagnostics of variational circuit states at random parameters and study their correlation with the circuit expressibility and the optimization of control parameters. By measuring the operator spreading coefficient and the eigenvalue spectrum of the modular Hamiltonian of the reduced density matrix, we identify the universal structure of random matrix models in high-depth circuit states. We construct different layer unitaries corresponding to the GOE and GUE distributions and quantify their VQA performance. Our study also highlights a potential tension between the OTOC and BGS-type diagnostics of quantum chaos.

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Section: Discussion and Outlookmentioning

confidence: 99%

Quantum Chaos and Circuit Parameter Optimization

Kim¹,

Oz²,

Rosa³

2022

Preprint

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“…First and foremost, we want to extend the results of the crossover to more structural aspects of the dynamics with the goal of obtaining a quantum KAM theorem. Second, one could systematically study how different spectra behave together with different ensembles of eigenvectors, for instance, interpolating between Clifford and universal resources in a random quantum circuit [79], by doping a stabilizer Hamiltonian with non-Clifford resources such as the T−gates [66]. Another important aspect is that of the locality of the interactions.…”

Section: Discussionmentioning

confidence: 99%

“…Now we consider l−doped Hamiltonians by doping with T−gates, without loss of generality. Using the technique in [66], a lengthy but straightforward calculation gives the following theorem. Theorem 1.…”

Section: Otocsmentioning

confidence: 99%

Isospectral Twirling and Quantum Chaos

Leone

Oliviero

Hamma

2021

Entropy

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We show that the most important measures of quantum chaos, such as frame potentials, scrambling, Loschmidt echo and out-of-time-order correlators (OTOCs), can be described by the unified framework of the isospectral twirling, namely the Haar average of a k-fold unitary channel. We show that such measures can then always be cast in the form of an expectation value of the isospectral twirling. In literature, quantum chaos is investigated sometimes through the spectrum and some other times through the eigenvectors of the Hamiltonian generating the dynamics. We show that thanks to this technique, we can interpolate smoothly between integrable Hamiltonians and quantum chaotic Hamiltonians. The isospectral twirling of Hamiltonians with eigenvector stabilizer states does not possess chaotic features, unlike those Hamiltonians whose eigenvectors are taken from the Haar measure. As an example, OTOCs obtained with Clifford resources decay to higher values compared with universal resources. By doping Hamiltonians with non-Clifford resources, we show a crossover in the OTOC behavior between a class of integrable models and quantum chaos. Moreover, exploiting random matrix theory, we show that these measures of quantum chaos clearly distinguish the finite time behavior of probes to quantum chaos corresponding to chaotic spectra given by the Gaussian Unitary Ensemble (GUE) from the integrable spectra given by Poisson distribution and the Gaussian Diagonal Ensemble (GDE).

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“…Clifford gates represent an interesting subgroup of the unitary group because they can be efficiently simulated by a classical computer, and yet are still very effective in attaining maximum levels of entanglement [10,[33][34][35]. However, while these gates are easily simulated on classical machines, they are not sufficient for true chaotic behavior in quantum systems [10,33,[35][36][37][38][39]. Including gates outside the Clifford group provides a set that is universal for quantum computation and induces chaotic behavior [24,25,34,40,41].…”

Section: Introductionmentioning

confidence: 99%