Quantum non-demolition measurement of a many-body Hamiltonian

Yang, Dayou; Grankin, Andrey; Sieberer, Lukas M.; Vasilyev, Denis V.; Zoller, P.

doi:10.1038/s41467-020-14489-5

Cited by 35 publications

(23 citation statements)

References 74 publications

(123 reference statements)

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“…(3)] where in addition to the unitary evolutionÛ (in our example generated by the Quantum Ising Model) there is a stochastic measurement process on each siteM = L i=1M (r) i . 27,28,29]. Also in this case entanglement phase transitions have been identified [22,30].…”

Section: Introductionmentioning

confidence: 62%

Many-Body Quantum Zeno Effect and Measurement-Induced Subradiance Transition

Biella

Schiró

2021

Quantum

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It is well known that by repeatedly measuring a quantum system it is possible to completely freeze its dynamics into a well defined state, a signature of the quantum Zeno effect. Here we show that for a many-body system evolving under competing unitary evolution and variable-strength measurements the onset of the Zeno effect takes the form of a sharp phase transition. Using the Quantum Ising chain with continuous monitoring of the transverse magnetization as paradigmatic example we show that for weak measurements the entanglement produced by the unitary dynamics remains protected, and actually enhanced by the monitoring, while only above a certain threshold the system is sharply brought into an uncorrelated Zeno state. We show that this transition is invisible to the average dynamics, but encoded in the rare fluctuations of the stochastic measurement process, which we show to be perfectly captured by a non-Hermitian Hamiltonian which takes the form of a Quantum Ising model in an imaginary valued transverse field. We provide analytical results based on the fermionization of the non-Hermitian Hamiltonian in supports of our exact numerical calculations.

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Section: Introductionmentioning

confidence: 62%

Many-Body Quantum Zeno Effect and Measurement-Induced Subradiance Transition

Biella

Schiró

2021

Quantum

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“…More recently, a number of ideas have been developed for tackling classically intractable regimes. These include a self-verifying technique for simulations of the Lattice-Schwinger model [1], a method based on non-demolition measurements of the Hamiltonian [2] and the broader concept of crossplatform verification, i.e. comparing results for the same problem from different quantum hardware or the measurement of compatible correlation functions that can verify specific Hamiltonians even when the quantum dynamics cannot be classically simulated [3,4].…”

Section: Introductionmentioning

confidence: 99%

Randomized benchmarking in the analogue setting

Derbyshire

Malo

Daley

et al. 2020

Quantum Sci. Technol.

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Current development in programmable analogue quantum simulators (AQS), whose physical implementation can be realised in the near-term compared to those of large-scale digital quantum computers, highlights the need for robust testing techniques in analogue platforms. Methods to properly certify or benchmark AQS should be efficiently scalable, and also provide a way to deal with errors from state preparation and measurement (SPAM). Up to now, attempts to address this combination of requirements have generally relied on model-specific properties. We put forward a new approach, applying a well-known digital noise characterisation technique called randomized benchmarking (RB) to the analogue setting. RB is a scalable experimental technique that provides a measure of the average errorrate of a gate-set on a quantum hardware, incorporating SPAM errors. We present the original form of digital RB, the necessary alterations to translate it to the analogue setting and introduce the analogue randomized benchmarking protocol (ARB). In ARB we measure the average error-rate per time evolution of a family of Hamiltonians and we illustrate this protocol with two case-studies of simple analogue models; classically simulating the system by incorporating physically motivated noise. We find that for both case-studies the data fit with the theoretical model and we gain values for the average error rate for differing unitary sets. We compare our protocol with digital RB, where both advantages (more realistic assumptions on noise) and disadvantages (difficulty in reversing the time-evolution) are discussed.

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“…Yet faster transition to the ordered phase can be obtained for the feedback signal containing the derivative of the measured photo-current as in the classical PID-controlled systems. These results demonstrate the advantages one can have with the feedback phase transition in atom-optical systems, which can lead to new types 21 of time crystals [51][52][53] and Floquet engineering, as well as creation of novel quantum bath simulators 21 , in particular, in many-body systems 13,22,[73][74][75] , as well as tuning the universality class of phase transitions 21 . It will be intriguing to study, how more advanced methods than the feedback control can influence quantum systems, for example, applying the digital methods of machine learning and artificial intelligence in real time.…”

Section: Discussionmentioning

confidence: 70%

Cavityless self-organization of ultracold atoms due to the feedback-induced phase transition

Иванов

Ivanova

Caballero-Benítez

et al. 2020

Sci Rep

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feedback is a general idea of modifying system behavior depending on the measurement outcomes. It spreads from natural sciences, engineering, and artificial intelligence to contemporary classical and rock music. Recently, feedback has been suggested as a tool to induce phase transitions beyond the dissipative ones and tune their universality class. Here, we propose and theoretically investigate a system possessing such a feedback-induced phase transition. the system contains a Bose-einstein condensate placed in an optical potential with the depth that is feedback-controlled according to the intensity of the Bragg-reflected probe light. We show that there is a critical value of the feedback gain where the uniform gas distribution loses its stability and the ordered periodic density distribution emerges. Due to the external feedback, the presence of a cavity is not necessary for this type of atomic self-organization. We analyze the dynamics after a sudden change of the feedback control parameter. The feedback time constant is shown to determine the relaxation above the critical point. We show as well that the control algorithm with the derivative of the measured signal dramatically decreases the transient time. Feedback control is known to be a useful tool to modify dynamics of classical 1 as well as quantum systems 2. There were many theoretical proposals 3-13 and several experimental realizations 14-18 of quantum feedback control in optics and atomic physics. The feedback control of quantum systems is fundamentally different from that of classical systems mainly due to the inevitable measurement back-action 19. In most cases this quantum effect does not pose sever limitations on the feasibility of feedback control, but it has to be taken into account designing quantum control algorithms 20. Recently the feedback loop has been suggested as a tool to control phase transitions in quantum systems 21 and, in particular, in many-body settings 13,22. The feedback control of atomic self-organization has been recently demonstrated experimentally in 23. Thus the new class of feedback phase transitions (FPT) has been introduced, which can have properties beyond dissipative phase transitions in open systems. The key advantage of FPT is its extremely high degree of flexibility and controllability, which allows for the manipulation of the critical point and critical exponents and, therefore, enables the tuning and control of the universality class of phase transitions 21. In this report we apply the concept of FPT to a system based on Bragg light scattering from a Bose-Einstein condensate (BEC). Instead of the self-formed standing-wave potential 24,25 , we propose to use an actively controlled optical lattice with the control based on the Bragg-reflected signal of a probe light. The system with active feedback provides much higher degree of control on the distribution of atoms and its evolution around the critical point in comparison to systems without feedback. Such improved controllability can assist in quantum simulations, ...

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Quantum non-demolition measurement of a many-body Hamiltonian

Cited by 35 publications

References 74 publications

Many-Body Quantum Zeno Effect and Measurement-Induced Subradiance Transition

Many-Body Quantum Zeno Effect and Measurement-Induced Subradiance Transition

Randomized benchmarking in the analogue setting

Cavityless self-organization of ultracold atoms due to the feedback-induced phase transition

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