Simulating Nonlinear Dynamics of Collective Spins via Quantum Measurement and Feedback

Muñoz-Arias, Manuel H.; Poggi, Pablo M.; Jessen, Poul; Deutsch, Ivan

doi:10.1103/physrevlett.124.110503

Cited by 33 publications

(14 citation statements)

References 76 publications

(69 reference statements)

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“…Understanding back-action as a control resource leads to further interesting possibilities like feedback-induced quantum phase transitions due to the continuous monitoring process itself [85]. Also, continuous measurement and feedback open up certain simulation abilities, as has recently been shown in an atomic system [86].…”

Section: Discussionmentioning

confidence: 94%

Continuous measurements for control of superconducting quantum circuits

Hacohen-Gourgy

Martin

2020

Advances in Physics: X

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Developments over the last two decades have opened the path towards quantum technologies in many quantum systems, such as cold atoms, trapped ions, cavity-quantum electrodynamics (QED), and circuit-QED. However, the fragility of quantum states to the effects of measurement and decoherence still poses one of the greatest challenges in quantum technology. An imperative capability in this path is quantum feedback, as it enhances the control possibilities and allows for prolonging coherence times through quantum error correction. While changing parameters from shot to shot of an experiment or procedure can be considered feedback, quantum mechanics also allows for the intriguing possibility of performing feedback operations during the measurement process itself. This broader approach to measurements leads to the concepts of weak measurement, quantum trajectories, and numerous types of feedback with no classical analogs. These types of processes are the primary focus of this review. We introduce the concept of quantum feedback in the context of circuit-QED, an experimental platform with significant potential in quantum feedback and technology. We then discuss several experiments and see how they elucidate the concepts of continuous measurements and feedback. We conclude with an overview of coherent feedback, with application to fault-tolerant error correction.

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Section: Discussionmentioning

confidence: 94%

Continuous measurements for control of superconducting quantum circuits

Hacohen-Gourgy

Martin

2020

Advances in Physics: X

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“…As a paradigmatic model for both theoretical [7][8][9][10][11][71][72][73][74][75][76][77][78] and experimental [79][80][81][82] studies of quantum chaos, the kicked top model consists of a larger spin with total angular momentum j whose dynamics is captured by the following Hamiltonian (throughout this work, h = 1) [10,71]:…”

Section: Kicked-top Modelmentioning

confidence: 99%

Multifractality in Quasienergy Space of Coherent States as a Signature of Quantum Chaos

Wang

Robnik

2021

Entropy

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We present the multifractal analysis of coherent states in kicked top model by expanding them in the basis of Floquet operator eigenstates. We demonstrate the manifestation of phase space structures in the multifractal properties of coherent states. In the classical limit, the classical dynamical map can be constructed, allowing us to explore the corresponding phase space portraits and to calculate the Lyapunov exponent. By tuning the kicking strength, the system undergoes a transition from regularity to chaos. We show that the variation of multifractal dimensions of coherent states with kicking strength is able to capture the structural changes of the phase space. The onset of chaos is clearly identified by the phase-space-averaged multifractal dimensions, which are well described by random matrix theory in a strongly chaotic regime. We further investigate the probability distribution of expansion coefficients, and show that the deviation between the numerical results and the prediction of random matrix theory behaves as a reliable detector of quantum chaos.

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“…The framework should be applicable to strongly correlated quantum materials, such as non-Hermitian exciton-polariton condensates [64,65] that are open and operated under extreme conditions. We aim to impose as little structure as possible on the allowed evolution beyond preserving the Hermitian symmetry, positive semi-definiteness, and trace of the density matrix X. Stochastic nonlinearity, [43,44,54] including projective measurement with postselection [66][67][68][69][70][71] and weak continuous measurement, [72][73][74][75] is known to be a useful resource, but is not considered here. [76] Therefore, we restrict ourselves to deterministic nonlinear positive trace-preserving (PTP) channels.…”

Section: Introductionmentioning

confidence: 99%

Fast Quantum State Discrimination with Nonlinear Positive Trace‐Preserving Channels

Geller

2023

Adv Quantum Tech

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Models of nonlinear quantum computation based on deterministic positive trace-preserving (PTP) channels and evolution equations are investigated. The models are defined in any finite Hilbert space, but the main results are for dimension N = 2. For every normalizable linear or nonlinear positive map 𝝓 on bounded linear operators X, there is an associated normalized PTP channel 𝝓(X)∕tr[𝝓(X)]. Normalized PTP channels include unitary mean field theories, such as the Gross-Pitaevskii equation for interacting bosons, as well as models of linear and nonlinear dissipation. They classify into four types, yielding three distinct forms of nonlinearity whose computational power are explored. In the qubit case, these channels support Bloch ball torsion and other distortions studied previously, where it has been shown that such nonlinearity can be used to increase the separation between a pair of close qubit states, suggesting an exponential speedup for state discrimination. Building on this idea, the authors argue that this operation can be made robust to noise by using dissipation to induce a bifurcation to a novel phase where a pair of attracting fixed points create an intrinsically fault-tolerant nonlinear state discriminator.

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Simulating Nonlinear Dynamics of Collective Spins via Quantum Measurement and Feedback

Cited by 33 publications

References 76 publications

Continuous measurements for control of superconducting quantum circuits

Continuous measurements for control of superconducting quantum circuits

Multifractality in Quasienergy Space of Coherent States as a Signature of Quantum Chaos

Fast Quantum State Discrimination with Nonlinear Positive Trace‐Preserving Channels

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