Visualizing operators of coupled spin systems

Garon, Ariane; Zeier, Robert; Glaser, Steffen J.

doi:10.1103/physreva.91.042122

Cited by 41 publications

(133 citation statements)

References 121 publications

(185 reference statements)

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“…These can be understood based on geometrical concepts [341]. In addition, useful tools have been developed to analyze complex pulses [409] and the resulting dynamics in coupled spin systems [405,410,411].…”

Section: State Of the Artmentioning

confidence: 99%

Training Schrödinger’s cat: quantum optimal control

et al. 2015

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Abstract. It is control that turns scientific knowledge into useful technology: in physics and engineering it provides a systematic way for driving a dynamical system from a given initial state into a desired target state with minimized expenditure of energy and resources. As one of the cornerstones for enabling quantum technologies, optimal quantum control keeps evolving and expanding into areas as diverse as quantumenhanced sensing, manipulation of single spins, photons, or atoms, optical spectroscopy, photochemistry, magnetic resonance (spectroscopy as well as medical imaging), quantum information processing and quantum simulation. In this communication, state-of-the-art quantum control techniques are reviewed and put into perspective by a consortium of experts in optimal control theory and applications to spectroscopy, imaging, as well as quantum dynamics of closed and open systems. We address key challenges and sketch a roadmap for future developments. ForewordThe authors of this paper represent the QUAINT consortium, a European Coordination Action on Optimal Control of Quantum Systems, funded by the European Commission Framework Programme 7, Future Emerging Technologies FET-OPEN programme and the Virtual Facility for Quantum Control (VF-QC). This consortium has considerable expertise in optimal control theory and its applications to quantum systems, both in existing areas, such as spectroscopy and imaging, and in emerging quantum technologies, such as quantum information processing, quantum communication, quantum simulation a e-mail: fwm@lusi.uni-sb.de and quantum sensing. The list of challenges for quantum control has been gathered by a broad poll of leading researchers across the communities of general and mathematical control theory, atomic, molecular-, and chemical physics, electron and nuclear magnetic resonance spectroscopy, as well as medical imaging, quantum information, communication and simulation. 144 experts in these fields have provided feedback and specific input on the state of the art, mid-term and long-term goals. Those have been summarized in this document, which can be viewed as a perspectives paper, providing a roadmap for the future development of quantum control. Because such an endeavour can hardly ever be complete (there are many additional areas of quantum control applications, such as spintronics, nano-optomechanical technologies etc.), this roadmap

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Section: State Of the Artmentioning

confidence: 99%

Training Schrödinger’s cat: quantum optimal control

et al. 2015

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“…The phase-space formulation of quantum mechanics is still in the focus of research interst, as it has numerous important applications [1][2][3][4]. Quasi-probability distributions such as the Wigner function [5], the Husimi Q-function [6,7] and Glauber-Sudarshan P-function [8,9] describe completely the states of a quantum system and they are widely used for calculations in various physical problems [10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Minimal sets of dequantizers and quantizers for finite-dimensional quantum systems

et al. 2017

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Abstract. The problem of finding and characterizing minimal sets of dequantizers and quantizers applied in the mapping of operators onto functions is considered, for finite-dimensional quantum systems. The general properties of such sets are determined. An explicit description of all the minimum self-dual sets of dequantizers and quantizers for a qubit system is derived. The connection between some known sets of dequantizers and quantizers and the derived formulae is presented.

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“…Understanding the nature of the correlations between systems is central to harnessing quantum effects for information processing; the methods presented here reveal the nature of these correlations, allowing a clear visualization of the quantum information present in these hybrid discrete-continuous variable quantum systems. The methods presented here could be viewed as a form of quantum state spectroscopy.Bloch sphere [20][21][22][23][24][25][26]. For example, there have been various proposals put forward that use a continuous Wigner function to reveal correlations between DV systems [26][27][28].…”

mentioning

confidence: 99%

“…The methods presented here could be viewed as a form of quantum state spectroscopy.Bloch sphere [20][21][22][23][24][25][26]. For example, there have been various proposals put forward that use a continuous Wigner function to reveal correlations between DV systems [26][27][28]. These methods have further been validated through the direct measurement of phase-space to reveal quantum correlations [28][29][30][31].…”

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confidence: 99%

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Visualization of correlations in hybrid discrete—continuous variable quantum systems

et al. 2020

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In this work we construct Wigner functions for hybrid continuous and discrete variable quantum systems. We demonstrate new capabilities in the visualization of the interactions and correlations between discrete and continuous variable quantum systems, where visualizing the full phase space has proven difficult in the past due to the high number of degrees of freedom. Specifically, we show how to clearly distinguish signatures that arise due to quantum and classical correlations in an entangled Bellcat state. We further show how correlations are manifested in different types of interaction, leading to a deeper understanding of how quantum information is shared between two subsystems. Understanding the nature of the correlations between systems is central to harnessing quantum effects for information processing; the methods presented here reveal the nature of these correlations, allowing a clear visualization of the quantum information present in these hybrid discrete-continuous variable quantum systems. The methods presented here could be viewed as a form of quantum state spectroscopy.Bloch sphere [20][21][22][23][24][25][26]. For example, there have been various proposals put forward that use a continuous Wigner function to reveal correlations between DV systems [26][27][28]. These methods have further been validated through the direct measurement of phase-space to reveal quantum correlations [28][29][30][31]. Recently this has been extended to experiments validating atomic Schrödinger cat states of up to 20 superconducting qubits [32].A case that has not been explored in much detail is the phase-space representation of CV-DV hybridization. This hybridisation is seen in many applications of quantum technologies, including simple gate models for quantum computers, such as hybrid two-qubit gates [33,34], and CV microwave pulse control of DV qubits [35]. The generation of hybrid quantum correlations within CV-DV hybrid 5 systems commonly takes place within the framework of cavity quantum electrodynamics, that describes the interaction between a two-level quantum system and a single mode of a microwave field. These models can be further used to describe the effect of circuit quantum electrodynamics, and to consider the interaction of the microwave field with an artificial atom. Analyzing these interactions within the framework of the Jaynes-Cummings model [36] allows us to display how quantum information is shared between the CV and DV systems.A number of papers [23, 24, 37] have shown the mathematical construction of hybrid states within the phase space, these have been constructed without giving a way to visually display the degrees of freedom of such composite systems. A method for displaying states with heterogeneous degrees of freedom, using the Wigner function, came from the application of composite phase-space methods to quantum chemistry [38]. The technique presented here is based on this approach, however in [38], reduced Wigner functions are used and an envelope is further applied, potentially losing many o...

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Visualizing operators of coupled spin systems

Cited by 41 publications

References 121 publications

Training Schrödinger’s cat: quantum optimal control

Training Schrödinger’s cat: quantum optimal control

Minimal sets of dequantizers and quantizers for finite-dimensional quantum systems

Visualization of correlations in hybrid discrete—continuous variable quantum systems

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