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Probing entanglement on quantum platforms using randomized measurements

Aniket Rath

Published Nov 14, 2023• 0 citations
Publisher

Abstract

There have been recently significant progress in quantum technologies to realize physically diverse quantum computation and simulation platforms.The aim of this thesis is to develop theoretical approaches based on measurement protocols to experimentally characterize entanglement generated in these state-of-art quantum technological platforms. In the past few years, protocols belonging to the "randomized measurements toolbox" (RM toolbox) have shown to have the ability to measure bipartite entanglement (entanglement between two parts of a quantum system). These protocols have been implemented in several experimental platforms consisting of quantum simulators and quantum computers beyond the regime of full state tomography.The aim of this manuscript is principally dedicated to the development of new approaches based on the RM toolbox to provide experimental groups with advanced tools and methods to probe new fundamental quantities of interest related to entanglement prepared in large quantum platforms.The first objective of this thesis is to provide a new protocol to optimize the existing RM protocol by reducing the statistical errors in the estimation of the quantities. This is done with two approaches: (i) via importance sampling of local random unitaries and (ii) by implementing common randomized measurements. These techniques automatically enable us to implement the RM toolbox to estimate properties associated to entanglement on larger experimental platforms. Then, a central part of this work proposes an alternate effective protocol to measure a fundamental quantity in quantum metrology known as the "quantum Fisher information" that enables us to characterize the multipartite entanglement content of the underlying quantum state. This novel protocol is based on estimating the QFI via the RM toolbox, as a converging series of lower bound polynomials of the density matrix.Additionally, the manuscript also focuses on solving a practical bottleneck of the current RM toolbox caused by the over-burdening classical cost to post-process experimental RM data to evaluate unbiased estimations of relevant quantities.This motivates the introduction of the "batch shadow formalism" that circumvents this problem and provides an efficient data treatment technique with rigorous performance guarantees to get estimates of quantities accessible from the experimental RM data. Lastly, owing to these developments of the RM toolbox, the manuscript reports estimation of some quantities that were accessed for the first time by experimental implementation of this toolbox on two different architectures of quantum platform consisting of superconducting qubits and trapped ions.

DOI
10.70675/eb1a11c9z5fb1z4213z962bzf7ad46ed28ed

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Probing entanglement on quantum platforms using randomized measurements

Aniket Rath

Sonder l'intrication sur des plateformes quantiques à l'aide de mesures aléatoires La technologie quantique a fait des progrès significatifs dans la réalisation de diverses plateformes de calcul et de simulation quantiques. L'objectif de cette thèse est de développer des approches théoriques pour comprendre le rôle de l'intrication dans les systèmes quantiques, et de proposer des protocoles de mesure pour sonder expérimentalement ces concepts dans ces plateformes technologiques quantiques courantes. Ces dernières années, des protocoles appartenant aux "mesures aléatoires" (randomized measurement toolbox ou RM toolbox) ont montré leur capacité à mesurer l'intrication bipartite (intrication entre deux parties d'un système quantique). Ces protocoles ont été mis en œuvre dans plusieurs plateformes expérimentales composées de simulateurs et d'ordinateurs quantiques.Ce manuscrit rapporte principalement le développement de nouvelles approches basées sur cette toolbox afin de fournir aux groupes expérimentaux des outils avancés de mesure de l'intrication en mesurant des nouvelles quantités fondamentales d'intérêt liées à l'intrication préparée dans les platformes quantiques.Le premier objectif de cette thèse est de fournir un nouveau protocole pour optimiser le protocole RM existant en réduisant les erreurs statistiques dans l'estimation des quantités. Ceci est fait avec deux approches : (i) via l'échantillonnage préférentiel des unitaires aléatoires locales et (ii) en mettant en œuvre des mesures aléatoires communes (common randomized measurements). Ces techniques nous permettent d'implémenter automatiquement la boîte à outils RM (RM toolbox) pour estimer les propriétés associées à l'intrication sur de plus grandes plateformes expérimentales.Ensuite, une partie centrale de ce travail propose un protocole alternatif efficace pour mesurer une quantité fondamentale en métrologie quantique connue comme "information quantique de Fisher" (quantum Fisher information) qui nous permet de caractériser le contenu de l'intrication multipartite de l'état quantique.Ce protocole est basé sur l'estimation de l'information quantique de Fisher via la boîte à outils RM, en tant qu'une série convergente de polynômes de la matrice de densité.En outre, le manuscrit se concentre également sur la résolution d'un problème pratique de la boîte à outils RM actuelle, causé par le coût classique excessif du post-traitement des données RM expérimentales afin d'évaluer des estimations non biaisées des quantités d'intérêt. Cela motive l'introduction du "formalisme de batch shadows" et fournit une technique de traitement des données efficace avec des garanties de performance rigoureuses pour obtenir des estimations des quantités accessibles à partir des données RM expérimentales. Enfin, en raison de ces développements de la boîte à outils RM, le manuscrit discute également des quantités qui ont été accessibles pour la première fois par la mise en œuvre expérimentale de cette boîte à outils sur deux architectures différentes de plateforme quantique composée de qubits supraconducteurs et d'ions piégés.

•Nov 14, 2023•0 citations
There have been recently significant progress in quantum technologies to realize physically diverse quantum computation and simulation platforms.The aim of this thesis is to develop theoretical approaches based on measurement protocols to experimentally characterize entanglement generated in these state-of-art quantum technological platforms. In the past few years, protocols belonging to the "randomized measurements toolbox" (RM toolbox) have shown to have the ability to measure bipartite entanglement (entanglement between two parts of a quantum system). These protocols have been implemented in several experimental platforms consisting of quantum simulators and quantum computers beyond the regime of full state tomography.The aim of this manuscript is principally dedicated to the development of new approaches based on the RM toolbox to provide experimental groups with advanced tools and methods to probe new fundamental quantities of interest related to entanglement prepared in large quantum platforms.The first objective of this thesis is to provide a new protocol to optimize the existing RM protocol by reducing the statistical errors in the estimation of the quantities. This is done with two approaches: (i) via importance sampling of local random unitaries and (ii) by implementing common randomized measurements. These techniques automatically enable us to implement the RM toolbox to estimate properties associated to entanglement on larger experimental platforms. Then, a central part of this work proposes an alternate effective protocol to measure a fundamental quantity in quantum metrology known as the "quantum Fisher information" that enables us to characterize the multipartite entanglement content of the underlying quantum state. This novel protocol is based on estimating the QFI via the RM toolbox, as a converging series of lower bound polynomials of the density matrix.Additionally, the manuscript also focuses on solving a practical bottleneck of the current RM toolbox caused by the over-burdening classical cost to post-process experimental RM data to evaluate unbiased estimations of relevant quantities.This motivates the introduction of the "batch shadow formalism" that circumvents this problem and provides an efficient data treatment technique with rigorous performance guarantees to get estimates of quantities accessible from the experimental RM data. Lastly, owing to these developments of the RM toolbox, the manuscript reports estimation of some quantities that were accessed for the first time by experimental implementation of this toolbox on two different architectures of quantum platform consisting of superconducting qubits and trapped ions.
We present the experimental measurement, on a quantum processor, of a series of polynomial lower bounds that to the quantum Fisher information (QFI), a fundamental quantity for certifying multipartite entanglement that is useful for metrological applications. We combine advanced methods of the randomized measurement toolbox to obtain estimators that are robust regarding drifting errors caused uniquely during the randomized measurement protocol. We estimate the QFI for Greenberger-Horne-Zeilinger states, observing genuine multipartite entanglement. Then we prepare the ground state of the transverse-field Ising model at the critical point using a variational circuit. We estimate its QFI and investigate the interplay between state optimization and noise induced by our increasing the circuit depth. Published by the American Physical Society 2024
The quantum Fisher information (QFI) is a fundamental quantity of interest in many areas from quantum metrology to quantum information theory. It can in particular be used as a witness to establish the degree of multiparticle entanglement in quantum many-body systems. In this work, we use polynomials of the density matrix to construct monotonically increasing lower bounds that converge to the QFI. Using randomized measurements we propose a protocol to accurately estimate these lower bounds in state-of-the-art quantum technological platforms. We estimate the number of measurements needed to achieve a given accuracy and confidence level in the bounds, and present two examples of applications of the method in quantum systems made of coupled qubits and collective spins.
We develop a general theoretical framework for measurement protocols employing statistical correlations of randomized measurements. We focus on locally randomized measurements implemented with local random unitaries in quantum lattice models. In particular, we discuss the theoretical details underlying the recent measurement of the second R\'enyi entropy of highly mixed quantum states consisting of up to ten qubits in a trapped-ion quantum simulator [Brydges et al., Science 364, 260 (2019)]. We generalize the protocol to access the overlap of quantum states, prepared sequentially in one experiment. Furthermore, we discuss proposals for quantum state tomography based on randomized measurements within our framework and the respective scaling of statistical errors with system size.
The quantum Fisher information (QFI) represents a fundamental concept in quantum physics. It quantifies the metrological potential of quantum states in quantum parameter estimation measurements, and is intrinsically related to quantum geometry and multipartite entanglement of many-body systems. Using a nitrogen-vacancy center spin in diamond, we experimentally demonstrate a randomized-measurement method to extract the QFI of the qubit, for both pure and mixed states. We then apply this scheme to a 4-qubit state, using a superconducting quantum computer, and show that it provides access to the sub-QFI, which sets a lower bound on the QFI for general mixed states. We numerically study the scaling of statistical error, considering NNN-qubit states, to illustrate the advantage of our randomized-measurement approach in estimating the QFI and multipartite entanglement. Our results highlight the general applicability of our method to different quantum platforms, including solid-state spin systems, superconducting quantum computers, and trapped ions.
We present the experimental measurement, on a quantum processor, of a series of polynomial lower bounds that converge to the quantum Fisher information (QFI), a fundamental quantity for certifying multipartite entanglement that is useful for metrological applications. We combine advanced methods of the randomized measurement toolbox to obtain estimators that are robust against drifting errors caused uniquely during the randomized measurement protocol. We estimate the QFI for Greenberg-Horne-Zeilinger states, observing genuine multipartite entanglement. Then, we prepare the ground state of the transverse field Ising model at the critical point using a variational circuit. We estimate its QFI and investigate the interplay between state optimization and noise induced by increasing the circuit depth.
Sonder l'intrication sur des plateformes quantiques à l'aide de mesures aléatoires La technologie quantique a fait des progrès significatifs dans la réalisation de diverses plateformes de calcul et de simulation quantiques. L'objectif de cette thèse est de développer des approches théoriques pour comprendre le rôle de l'intrication dans les systèmes quantiques, et de proposer des protocoles de mesure pour sonder expérimentalement ces concepts dans ces plateformes technologiques quantiques courantes. Ces dernières années, des protocoles appartenant aux "mesures aléatoires" (randomized measurement toolbox ou RM toolbox) ont montré leur capacité à mesurer l'intrication bipartite (intrication entre deux parties d'un système quantique). Ces protocoles ont été mis en œuvre dans plusieurs plateformes expérimentales composées de simulateurs et d'ordinateurs quantiques.Ce manuscrit rapporte principalement le développement de nouvelles approches basées sur cette toolbox afin de fournir aux groupes expérimentaux des outils avancés de mesure de l'intrication en mesurant des nouvelles quantités fondamentales d'intérêt liées à l'intrication préparée dans les platformes quantiques.Le premier objectif de cette thèse est de fournir un nouveau protocole pour optimiser le protocole RM existant en réduisant les erreurs statistiques dans l'estimation des quantités. Ceci est fait avec deux approches : (i) via l'échantillonnage préférentiel des unitaires aléatoires locales et (ii) en mettant en œuvre des mesures aléatoires communes (common randomized measurements). Ces techniques nous permettent d'implémenter automatiquement la boîte à outils RM (RM toolbox) pour estimer les propriétés associées à l'intrication sur de plus grandes plateformes expérimentales.Ensuite, une partie centrale de ce travail propose un protocole alternatif efficace pour mesurer une quantité fondamentale en métrologie quantique connue comme "information quantique de Fisher" (quantum Fisher information) qui nous permet de caractériser le contenu de l'intrication multipartite de l'état quantique.Ce protocole est basé sur l'estimation de l'information quantique de Fisher via la boîte à outils RM, en tant qu'une série convergente de polynômes de la matrice de densité.En outre, le manuscrit se concentre également sur la résolution d'un problème pratique de la boîte à outils RM actuelle, causé par le coût classique excessif du post-traitement des données RM expérimentales afin d'évaluer des estimations non biaisées des quantités d'intérêt. Cela motive l'introduction du "formalisme de batch shadows" et fournit une technique de traitement des données efficace avec des garanties de performance rigoureuses pour obtenir des estimations des quantités accessibles à partir des données RM expérimentales. Enfin, en raison de ces développements de la boîte à outils RM, le manuscrit discute également des quantités qui ont été accessibles pour la première fois par la mise en œuvre expérimentale de cette boîte à outils sur deux architectures différentes de plateforme quantique composée de qubits supraconducteurs et d'ions piégés.