Shadow process tomography of quantum channels

Kunjummen, Jonathan; Trân, Minh; Carney, Daniel; Taylor, J. Madison

doi:10.48550/arxiv.2110.03629

Cited by 7 publications

(12 citation statements)

References 22 publications

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“…Refs. [59,60] appeared, where similar proposals to generalize shadow tomography to channels were given.…”

Section: Note Added-during Completion Of This Workmentioning

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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“…Refs. [59,60] appeared, where similar proposals to generalize shadow tomography to channels were given.…”

Section: Note Added-during Completion Of This Workmentioning

confidence: 99%

Quantifying information scrambling via Classical Shadow Tomography on Programmable Quantum Simulators

McGinley¹,

Leontica²,

Garratt³

et al. 2022

Preprint

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“…A more recent development towards the limits of quantum tomography is based on classical shadow of states [33,34] and processes [5,6]. Shadow tomography aims to extract key information about a state/process with only polynomially many measurements.…”

Section: Quantum Tomographymentioning

confidence: 99%

“…The scalability is bounded by the exponential classical simulation overhead. This computation cost can be considerably frugal for pragmatic approximation thresholds of classical shadows [5,6] of quantum information. The proposed Quantum Knowledge Seeking Agent (QKSA) is an AGI framework based on resourcebounded EVO-URL.…”

Section: Introductionmentioning

confidence: 99%

QKSA: Quantum Knowledge Seeking Agent -- resource-optimized reinforcement learning using quantum process tomography

Sarkar¹,

Al-Ars²,

Gandhi³

et al. 2021

Preprint

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In this research, we extend the universal reinforcement learning (URL) agent models of artificial general intelligence to quantum environments. The utility function of a classical exploratory stochastic Knowledge Seeking Agent, KL-KSA, is generalized to distance measures from quantum information theory on density matrices. Quantum process tomography (QPT) algorithms form the tractable subset of programs for modeling environmental dynamics. The optimal QPT policy is selected based on a mutable cost function based on algorithmic complexity as well as computational resource complexity. Instead of Turing machines, we estimate the cost metrics on a high-level language to allow realistic experimentation. The entire agent design is encapsulated in a self-replicating quine which mutates the cost function based on the predictive value of the optimal policy choosing scheme. Thus, multiple agents with pareto-optimal QPT policies evolve using genetic programming, mimicking the development of physical theories each with different resource trade-offs. This formal framework is termed Quantum Knowledge Seeking Agent (QKSA). A proof-of-concept is implemented and available as an open-sourced software.Despite its importance, few quantum reinforcement learning models exist in contrast to the current thrust in quantum machine learning. QKSA is the first proposal for a framework that resembles the classical URL models. Similar to how AIXI-tl is a resource-bounded active version of Solomonoff universal induction, QKSA is a resource-bounded participatory observer framework to the recently proposed algorithmic information-based reconstruction of quantum mechanics. Besides its theoretical impact, QKSA can be applied for simulating and studying aspects of quantum information theory like control automation, multiple observers, course-graining, distance measures, resource complexity trade-offs, etc. Specifically, we demonstrate that it can be used to accelerate quantum variational algorithms which include tomographic reconstruction as its integral subroutine.

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“…Unlike the approach taken in [7], our study circumvents the need to solve an exponential-sized system of linear equations. Second, we apply our results to the shadow process tomography of quantum channels, where we generalize the results of [8,9] to allow for any Pauli-invariant unitary ensemble. Related work-The classical shadow paradigm, with the sample efficiency it touts, has attracted considerable attention over the last couple of years [10].…”

Section: Introductionmentioning

confidence: 99%

“…Authors have proposed variants and generalizations of the protocol, including locally-biased classical shadows [11], derandomization techniques [26], decision diagram techniques [27], grouping strategies [28], POVM-based classical shadows [29], classical shadows with locally-scrambled unitary ensembles [7], and classical shadows with unitary ensembles generated by a Hamiltonian [6]. Extensions have been found to fermions [5] and to quantum channels [8,9]. With respect to certain figures-of-merit, the protocol has been shown to give an advantage over alternative approaches [11,30] and has been analyzed theoretically from a Bayesian point of view [31].…”

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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Shadow process tomography of quantum channels

Cited by 7 publications

References 22 publications

Quantifying information scrambling via Classical Shadow Tomography on Programmable Quantum Simulators

Quantifying information scrambling via Classical Shadow Tomography on Programmable Quantum Simulators

QKSA: Quantum Knowledge Seeking Agent -- resource-optimized reinforcement learning using quantum process tomography

Classical shadows with Pauli-invariant unitary ensembles

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