Driven Quantum Dynamics: Will It Blend?

Banchi, Leonardo; Burgarth, Daniel; Kastoryano, Michael J.

doi:10.1103/physrevx.7.041015

Cited by 61 publications

(65 citation statements)

References 81 publications

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“…The distribution for staggered hopping, Fig. 11-(b) clearly presents level repulsion and suppression at small angles, with − cos θ = 0.2356 (24) and r = 0.7382 (7). Both effects are compatible with the Ginibre universality class (recall that, for 10 4 × 10 4 matrices from the GinUE, we found − cos θ = 0.24051(61) and r = 0.73810 (18)).…”

Section: Numerical Resultsmentioning

confidence: 55%

Complex Spacing Ratios: A Signature of Dissipative Quantum Chaos

2020

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We introduce a complex-plane generalization of the consecutive level-spacing distribution, used to distinguish regular from chaotic quantum spectra. Our approach features the distribution of complex-valued ratios between nearest-and next-to-nearest neighbor spacings. We show that this quantity can successfully detect the chaotic or regular nature of complex-valued spectra. This is done in two steps. First, we show that, if eigenvalues are uncorrelated, the distribution of complex spacing ratios is flat within the unit circle, whereas random matrices show a strong angular dependence in addition to the usual level repulsion. The universal fluctuations of Gaussian Unitary and Ginibre Unitary universality classes in the large-matrix-size limit are shown to be well described by Wigner-like surmises for small-size matrices with eigenvalues on the circle and on the two-torus, respectively. To study the latter case, we introduce the Toric Unitary Ensemble, characterized by a flat joint eigenvalue distribution on the two-torus. Second, we study different physical situations where nonhermitian matrices arise: dissipative quantum systems described by a Lindbladian, non-unitary quantum dynamics described by nonhermitian Hamiltonians, and classical stochastic processes. We show that known integrable models have a flat distribution of complex spacing ratios whereas generic cases, expected to be chaotic, conform to Random Matrix Theory predictions. Specifically, we were able to clearly distinguish chaotic from integrable dynamics in boundary-driven dissipative spin-chain Liouvillians and in the classical asymmetric simple exclusion process and to differentiate localized from delocalized phases in a nonhermitian disordered many-body system.

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Section: Numerical Resultsmentioning

confidence: 55%

Complex Spacing Ratios: A Signature of Dissipative Quantum Chaos

2020

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“…Indeed, while we have used quantum optimal control to reach a desired target Haar-random unitary, such fine-tuned control may not be required. Since a random control waveform should yield a pseudorandom transition matrix after a suitably long mixing time (see [85]), we expect this time might be much shorter than that required to reach a particular target chosen from Haar random unitary matrices. This could lead to a more efficient and scalable approach to Boson Sampling.…”

Section: Discussionmentioning

confidence: 99%

Quantum computational supremacy in the sampling of bosonic random walkers on a one-dimensional lattice

2019

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We study the sampling complexity of a probability distribution associated with an ensemble of identical noninteracting bosons undergoing a quantum random walk on a one-dimensional lattice. With uniform nearest-neighbor hopping we show that one can efficiently sample the distribution for times logarithmic in the size of the system, while for longer times there is no known efficient sampling algorithm. With time-dependent hopping and optimal control, we design the time evolution to approximate an arbitrary Haar-random unitary map analogous to that designed for photons in a linear optical network. This approach highlights a route to generating quantum complexity by optimal control only of a single-body unitary matrix. We study this in the context of two potential experimental realizations: a spinor optical lattice of ultracold atoms and a quantum gas microscope.

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“…We remark here that the N-level system has recently been analyzed in great detail in [47] for the case when one control is present and the control field is chosen randomly. Based on unitary q-designs it was shown that the time to implement a generic goal gate operation scales as ( ) N 3 .…”

Section: N-level Systemmentioning

confidence: 99%

Dependence of the quantum speed limit on system size and control complexity

Lee

Arenz

Rabitz³

et al. 2018

New J. Phys.

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We extend the work in 2017 New J. Phys. 19 103015 by deriving a lower bound for the minimum time necessary to implement a unitary transformation on a generic, closed quantum system with an arbitrary number of classical control fields. This bound is explicitly analyzed for a specific N-level system similar to those used to represent simple models of an atom, or the first excitation sector of a Heisenberg spin chain, both of which are of interest in quantum control for quantum computation. Specifically, it is shown that the resultant bound depends on the dimension of the system, and on the number of controls used to implement a specific target unitary operation. The value of the bound determined numerically, and an estimate of the true minimum gate time are systematically compared for a range of system dimension and number of controls; special attention is drawn to the relationship between these two variables. It is seen that the bound captures the scaling of the minimum time well for the systems studied, and quantitatively is correct in the order of magnitude.

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Driven Quantum Dynamics: Will It Blend?

Cited by 61 publications

References 81 publications

Complex Spacing Ratios: A Signature of Dissipative Quantum Chaos

Complex Spacing Ratios: A Signature of Dissipative Quantum Chaos

Quantum computational supremacy in the sampling of bosonic random walkers on a one-dimensional lattice

Dependence of the quantum speed limit on system size and control complexity

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