False signals of chaos from quantum probes

Kirkby, W.; O’Dell, D. H. J.; Mumford, J.

doi:10.1103/physreva.104.043308

Cited by 8 publications

(4 citation statements)

References 84 publications

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“…To the best of our knowledge, this is the first example of a genuine many-body setup in which such discrepancy is observed. Previous studies dealt only with single-body examples with classical counterparts [34][35][36][37][38][39][40].…”

Section: Discussion and Outlookmentioning

confidence: 99%

Quantum chaos and circuit parameter optimization

Kim

Oz²,

Rosa³

2023

J. Stat. Mech.

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We consider quantum chaos diagnostics of the variational circuit states at random parameters and explore their connection to the circuit expressibility and optimizability. By measuring the operator spreading coefficient and the eigenvalue spectrum of the modular Hamiltonian of the reduced density matrix, we identify the emergence of universal random matrix ensembles in high-depth circuit states. The diagnostics that use the eigenvalue spectrum, e.g. operator spreading and entanglement entropy, turn out to be more accurate measures of the variational quantum algorithm optimization efficiency than those that use the level spacing distribution of the entanglement spectrum, such as r-statistics or spectral form factors.

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Section: Discussion and Outlookmentioning

confidence: 99%

Quantum chaos and circuit parameter optimization

Kim

Oz²,

Rosa³

2023

J. Stat. Mech.

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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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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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“…301,299,302,303,304,305 Note, however, that the exponential increase may not always be attributed to classical chaos. 301,306,307,308 We also note that the exponential growth of C(t) comes from the exponential behavior of either F (t) or I(t), which depends on the initial state. 299…”

Section: Out-of-time-order Correlatormentioning

confidence: 91%

Bounds in Nonequilibrium Quantum Dynamics

Gong¹,

Hamazaki²

2022

Preprint

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We review various bounds concerning out-of-equilibrium dynamics in few-level and manybody quantum systems. We primarily focus on closed quantum systems but will also mention some related results for open quantum systems and classical stochastic systems. We start from the speed limits, the universal bounds on the speeds of (either quantum or classical) dynamical evolutions. We then turn to review the bounds that address how good and how long would a quantum system equilibrate or thermalize. Afterward, we focus on the stringent constraint set by locality in many-body systems, rigorously formalized as the Lieb-Robinson bound. We also review the bounds related to the dynamics of entanglement, a genuine quantum property. Apart from some other miscellaneous topics, several notable error bounds for approximated quantum dynamics are discussed. While far from comprehensive, this topical review covers a considerable amount of recent progress and thus could hopefully serve as a convenient starting point and up-to-date guidance for interested readers.

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False signals of chaos from quantum probes

Cited by 8 publications

References 84 publications

Quantum chaos and circuit parameter optimization

Quantum chaos and circuit parameter optimization

Quantum Chaos and Circuit Parameter Optimization

Bounds in Nonequilibrium Quantum Dynamics

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