Probing many-body quantum chaos with quantum simulators

Joshi, Lata Kh; Elben, Andreas; Vikram, Amit; Vermersch, Benoît; Galitski, Victor; Zoller, Peter

doi:10.48550/arxiv.2106.15530

Cited by 3 publications

(3 citation statements)

References 107 publications

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“…We can construct a clock from a quantum field or many-body system in its ground state (zero temperature) by a local quench (or excitation) followed by continuous measurement. Recent work on the energy eigenstate thermalisation hypothesis [20] in many-body systems uses quenches like this. It does however require the right kind of interactions.…”

Section: D[a] and H[a]mentioning

confidence: 99%

Quantum clocks driven by measurement

Gangat¹,

Milburn²

2021

Preprint

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In classical physics, clocks are open dissipative systems driven from thermal equilibrium and necessarily subject to thermal noise. We describe a quantum clock driven by entropy reduction through measurement. The mechanism consists of a superconducting transmon qubit coupled to an open co-planar resonator. The cavity and qubit are driven by coherent fields and the cavity output is monitored with homodyne detection. We show that the measurement itself induces coherent oscillations, with fluctuating period, in the conditional moments. The clock signal can be extracted from the observed measurement currents and analysed to determine the noise performance. The model demonstrates a fundamental principle of clocks at zero temperature: good clocks require high rates of energy dissipation and consequently entropy generation.

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Section: D[a] and H[a]mentioning

confidence: 99%

Quantum clocks driven by measurement

Gangat¹,

Milburn²

2021

Preprint

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“…Second, we point out that while the PR and level spacing ratio studied in section 2 are standard ways of probing the notion of quantum chaos, their measurement in the context of general quantum many-body systems is non-trivial. In this context, we would like to mention recent advances in this direction [70] based on the use of randomized measurements [71][72][73]. Conversely, although the behavior of λ 1 is only an indicator of the onset of chaos, it is measurable with costs that in general scale polynomially in the system size.…”

Section: Discussionmentioning

confidence: 99%

Digital quantum simulation, learning of the Floquet Hamiltonian, and quantum chaos of the kicked top

Olsacher

Pastori

Kokail

et al. 2022

J. Phys. A: Math. Theor.

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The kicked top is one of the paradigmatic models in the study of quantum chaos (Haake et al 2018 Quantum Signatures of Chaos (Springer Series in Synergetics vol 54)). Recently it has been shown that the onset of quantum chaos in the kicked top can be related to the proliferation of Trotter errors in digital quantum simulation (DQS) of collective spin systems. Specifically, the proliferation of Trotter errors becomes manifest in expectation values of few-body observables strongly deviating from the target dynamics above a critical Trotter step, where the spectral statistics of the Floquet operator of the kicked top can be predicted by random matrix theory. In this work, we study these phenomena in the framework of Hamiltonian learning (HL). We show how a recently developed HL protocol can be employed to reconstruct the generator of the stroboscopic dynamics, i.e., the Floquet Hamiltonian, of the kicked top. We further show how the proliferation of Trotter errors is revealed by HL as the transition to a regime in which the dynamics cannot be approximately described by a low-order truncation of the Floquet–Magnus expansion. This opens up new experimental possibilities for the analysis of Trotter errors on the level of the generator of the implemented dynamics, that can be generalized to the DQS of quantum many-body systems in a scalable way. This paper is in memory of our colleague and friend Fritz Haake.

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“…FRUC have given access to the study of non-trivial spectral properties in extended many-body systems. In particular, for the spectral form factor (SFF) [29,30,[32][33][34][35][36][37][38][39][40][41][42][43][44][45][46],…”

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confidence: 99%

Many-Body Quantum Chaos and Space-time Translational Invariance

Chan,

Shivam,

Huse

et al. 2021

Preprint

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We study the consequences of having translational invariance in space and in time in many-body quantum chaotic systems. We consider an ensemble of random quantum circuits, composed of single-site random unitaries and nearest neighbour couplings, as a minimal model of translational invariant many-body quantum chaotic systems. We evaluate the spectral form factor (SFF) as a sum over many-body Feynman diagrams, which simplifies in the limit of large local Hilbert space dimension q. At sufficiently large t, diagrams corresponding to rigid translations dominate, reproducing the random matrix theory (RMT) prediction. At finite t, we show that translational invariance introduces an additional mechanism which delays the emergence of RMT. Specifically, we identify two universality classes characterising the approach to RMT: in d = 1, corrections to RMT are generated by different translations applied to extended domains, known as the crossed diagrams; in d > 1, corrections are the consequence of deranged defects diagrams, where excitations are dilute and localized due to confinement. We introduce a scaling limit of SFF where these universality classes reduce to simple scaling functions. Lastly, we demonstrate universality of the scaling forms with numerical simulations of two circuit models and discuss the validity of the large q limit in the different cases.

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Probing many-body quantum chaos with quantum simulators

Cited by 3 publications

References 107 publications

Quantum clocks driven by measurement

Quantum clocks driven by measurement

Digital quantum simulation, learning of the Floquet Hamiltonian, and quantum chaos of the kicked top

Many-Body Quantum Chaos and Space-time Translational Invariance

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