Quantum scrambling with classical shadows

Garcia, Roy J.; Zhou, Y.; Jaffe, Arthur

doi:10.1103/physrevresearch.3.033155

Cited by 44 publications

(27 citation statements)

References 75 publications

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“…A related approach to diagnosing scrambling in experiments is to measure the decay of OTOCs [30][31][32][33][34]67]. However, present day quantum simulators are inevitably noisy, and dissipative effects can mimic this decay [35], as can mismatch between forward and backward time evolution.…”

Section: Discussion and Outlookmentioning

confidence: 99%

Quantifying information scrambling via Classical Shadow Tomography on Programmable Quantum Simulators

McGinley¹,

Leontica²,

Garratt³

et al. 2022

Preprint

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We develop techniques to probe the dynamics of quantum information, and implement them experimentally on an IBM superconducting quantum processor. Our protocols adapt shadow tomography for the study of time evolution channels rather than of quantum states, and rely only on single-qubit operations and measurements. We identify two unambiguous signatures of quantum information scrambling, neither of which can be mimicked by dissipative processes, and relate these to many-body teleportation. By realizing quantum chaotic dynamics in experiment, we measure both signatures, and support our results with numerical simulations of the quantum system. We additionally investigate operator growth under this dynamics, and observe behaviour characteristic of quantum chaos. As our methods require only a single quantum state at a time, they can be readily applied on a wide variety of quantum simulators.

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Section: Discussion and Outlookmentioning

confidence: 99%

Quantifying information scrambling via Classical Shadow Tomography on Programmable Quantum Simulators

McGinley¹,

Leontica²,

Garratt³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…( 1) is an out-oftime-ordered correlator. Although troublesome to measure, protocols to do this have been constructed [37][38][39][40][41].…”

Section: A Background On Scramblingmentioning

confidence: 99%

“…Chaos in QNNs has been explored through the fidelity OTOC [20], which has the general form ψ| U † M U |ψ 2 [23,44,45]. However, it was recently proposed that higher-point correlators can reveal the finer-grained dynamics of chaos [41,[46][47][48]. Since the fidelity OTOC carries the same information as the 2-point correlator ψ| U † M U |ψ , it may not reveal the finer scrambling dynamics available to the 4-point OTOC in Eq.…”

Section: D=1mentioning

confidence: 99%

Quantifying scrambling in quantum neural networks

Garcia,

Bu,

Jaffe

2021

Preprint

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We characterize a quantum neural network's error in terms of the network's scrambling properties via the out-of-time-ordered correlator. A network can be trained by optimizing either a loss function or a cost function. We show that, with some probability, both functions can be bounded by outof-time-ordered correlators. The gradients of these functions can be bounded by the gradient of the out-of-time-ordered correlator, demonstrating that the network's scrambling ability governs its trainability. Our results pave the way for the exploration of quantum chaos in quantum neural networks.

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“…Related work-The classical shadow paradigm, with the sample efficiency it touts, has attracted considerable attention over the last couple of years [10]. Several applications have been proposed, including applying the classical shadow framework to estimate expectation values of molecular Hamiltonians [11,12], detecting or estimating the degree of entanglement in quantum systems [1,[13][14][15], classifying quantum data [16], measuring out-of-time-ordered correlators [17], approximating wave function overlaps [18], solving quantum many-body problems [1,19,20], estimating gate-set properties [21], and avoiding barren plateaus [22]. Noise analyses of the classical shadow protocol have been performed, with noise-resilient versions developed [23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Classical shadows with Pauli-invariant unitary ensembles

Bu¹,

Koh²,

Garcia³

et al. 2022

Preprint

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The classical shadow estimation protocol is a noise-resilient and sample-efficient quantum algorithm for learning the properties of quantum systems. Its performance depends on the choice of a unitary ensemble, which must be chosen by a user in advance. What is the weakest assumption that can be made on the chosen unitary ensemble that would still yield meaningful and interesting results? To address this question, we consider the class of Pauli-invariant unitary ensembles, i.e. unitary ensembles that are invariant under multiplication by a Pauli operator. This class includes many previously studied ensembles like the local and global Clifford ensembles as well as locally scrambled unitary ensembles. For this class of ensembles, we provide an explicit formula for the reconstruction map corresponding to the shadow channel and give explicit sample complexity bounds. In addition, we provide two applications of our results. Our first application is to locally scrambled unitary ensembles, where we give explicit formulas for the reconstruction map and sample complexity bounds that circumvent the need to solve an exponential-sized linear system. Our second application is to the classical shadow tomography of quantum channels with Pauli-invariant unitary ensembles. Our results pave the way for more efficient or robust protocols for predicting important properties of quantum states, such as their fidelity, entanglement entropy, and quantum Fisher information.

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Quantum scrambling with classical shadows

Cited by 44 publications

References 75 publications

Quantifying information scrambling via Classical Shadow Tomography on Programmable Quantum Simulators

Quantifying information scrambling via Classical Shadow Tomography on Programmable Quantum Simulators

Quantifying scrambling in quantum neural networks

Classical shadows with Pauli-invariant unitary ensembles

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