Compressed quantum metrology for the Ising Hamiltonian

Boyajian, W. L.; Skotiniotis, Michael; Dür, W.; Kraus, Barbara

doi:10.1103/physreva.94.062326

Cited by 13 publications

(14 citation statements)

References 35 publications

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“…While in the GHZ-based quantum sensing, the interaction between particles should be avoided, in a fundamen-tally different route, one can harness the interaction in strongly correlated many-body quantum systems in [50][51][52][53][54][55][56] and out [57][58][59][60][61][62] of equilibrium for sensing. In fact, thanks to the emergent of multipartite entanglement [63][64][65][66][67][68], many-body systems near criticality provide enhanced quantum precision of η = 2/ν [50][51][52][53][54][55], where ν is the critical exponent in charge of the divergence of correlation length [69,70]. In addition, the evolution of many-body systems has also been used for sensing local [62] and global [71] DC fields as well as extracting information about the spectral structure of time-varying fields [72][73][74].…”

Section: Introductionmentioning

confidence: 99%

Integrable quantum many-body sensors for AC field sensing

Mishra,

Bayat

2021

Preprint

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Quantum sensing is inevitably an elegant example of supremacy of quantum technologies over their classical counterparts. One of the desired endeavor of quantum metrology is AC field sensing. Here, by means of analytical and numerical analysis, we show that integrable many-body systems can be exploited efficiently for detecting the amplitude of an AC field. Unlike the conventional strategies in using the ground states in critical many-body probes for parameter estimation, we only consider partial access to a subsystem. Due to the periodicity of the dynamics, any local block of the system saturates to a steady state which allows achieving sensing precision well beyond the classical limit, almost reaching the Heisenberg bound. We associate the enhanced quantum precision to closing of the Floquet gap, resembling the features of quantum sensing in the ground state of critical systems. We show that the proposed protocol can also be realized in near-term quantum simulators, e.g. ion-traps, with limited number of qubits. We show that in such systems a simple block magnetization measurement and a Bayesian inference estimator can achieve very high precision AC field sensing.

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Section: Introductionmentioning

confidence: 99%

Integrable quantum many-body sensors for AC field sensing

Mishra,

Bayat

2021

Preprint

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“…Having all the above in mind, one immediately recalls the second approach that connects the estimation problem to the concept of criticality [37][38][39][40][41][42][43][44][45]. In that approach one focuses on the situation where the dependence of the state on λ has a completely different origin.…”

Section: Introductionmentioning

confidence: 99%

At the Limits of Criticality-Based Quantum Metrology: Apparent Super-Heisenberg Scaling Revisited

et al. 2018

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We address the question of whether the super-Heisenberg scaling for quantum estimation is indeed realizable. We unify the results of two approaches. In the first one, the original system is compared with its copy rotated by the parameter-dependent dynamics. If the parameter is coupled to the one-body part of the Hamiltonian, the precision of its estimation is known to scale at most as N −1 (Heisenberg scaling) in terms of the number of elementary subsystems used N. The second approach compares the overlap between the ground states of the parameter-dependent Hamiltonian in critical systems, often leading to an apparent super-Heisenberg scaling. However, we point out that if one takes into account the scaling of time needed to perform the necessary operations, i.e., ensuring adiabaticity of the evolution, the Heisenberg limit given by the rotation scenario is recovered. We illustrate the general theory on a ferromagnetic Heisenberg spin chain example and show that it exhibits such super-Heisenberg scaling of ground-state fidelity around the critical value of the parameter (magnetic field) governing the one-body part of the Hamiltonian. Even an elementary estimator represented by a single-site magnetization already outperforms the Heisenberg behavior providing the N −1.5 scaling. In this case, Fisher information sets the ultimate scaling as N −1.75 , which can be saturated by measuring magnetization on all sites simultaneously. We discuss universal scaling predictions of the estimation precision offered by such observables, both at zero and finite temperatures, and support them with numerical simulations in the model. We provide an experimental proposal of realization of the considered model via mapping the system to ultracold bosons in a periodically shaken optical lattice. We explicitly derive that the Heisenberg limit is recovered when the time needed for preparation of quantum states involved is taken into account.

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“…For sufficiently small λ, in a finite system, one hasFidelity susceptibility is directly related to the quantum Fisher information (QFI), G, being directly proportional to the Bures distance between density matrices at slightly differing values of λ [26,27], with G(λ) = 4χ. Fidelity susceptibility emerged as a useful tool to study quantum phase transitions as at the transition point the ground state changes rapidly leading to the enhancement of χ [27][28][29][30][31][32][33][34]. All of these studies were restricted to ground state properties while MBL considers the bulk of excited states (for a discussion of thermal states see [35][36][37][38]).…”

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confidence: 99%

Fidelity susceptibility in Gaussian random ensembles

et al. 2019

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The fidelity susceptibility measures sensitivity of eigenstates to a change of an external parameter. It has been fruitfully used to pin down quantum phase transitions when applied to ground states (with extensions to thermal states). Here we propose to use the fidelity susceptibility as a useful dimensionless measure for complex quantum systems. We find analytically the fidelity susceptibility distributions for Gaussian orthogonal and unitary universality classes for arbitrary system size. The results are verified by a comparison with numerical data.The discovery of many body localization (MBL) phenomenon resulting in non-ergodicity of the dynamics in many body systems [1] restored also the interest in purely ergodic phenomena modeled by Gaussian random ensembles (GRE) [2] and in possible measures to characterize them. The gap ratio between adjacent level spacings [3] was introduced precisely for that purpose as it does not involve the so called unfolding [4] necessary for meaningful studies of level spacing distributions and yet often leading to spurious results [5]. Still, the level spacing distribution belongs to the most popular statistical measures used for single particle quantum chaos studies [6][7][8][9] and also in the transition to MBL [10-13]. A particular place among different measures was taken by those characterizing level dynamics for a Hamiltonian H(λ) dependent on some parameter λ. In Pechukas-Yukawa formulation [14,15] energy levels are positions of a fictitious gas particles, derivatives with respect to the fictitious time λ are velocities (level slopes), the second derivatives describe curvatures of the levels (accelerations). Simons and Altschuler [16] put forward a proposition that the variance of velocities distribution is an important parameter characterizing universality of level dynamics. This led to predictions for distributions of avoided crossings [17] and, importantly, curvature distributions postulated first on the basis of numerical data for GRE [18] and then derived analytically via supersymmetric method by von Oppen [19,20] (for alternative techniques see [21,22]). Curvature distributions were recently addressed in MBL studies [23,24].Apart from quantum chaos studies in the eighties and nineties of the last millennium, another "level dynamics" tool has been introduced in the quantum information area, i.e. the fidelity [25]. It compares two close (possibly mixed) quantum states. If these states are dependent on a parameter λ it is customary to introduce a fidelity susceptibility χ. For sufficiently small λ, in a finite system, one hasFidelity susceptibility is directly related to the quantum Fisher information (QFI), G, being directly proportional to the Bures distance between density matrices at slightly differing values of λ [26,27], with G(λ) = 4χ. Fidelity susceptibility emerged as a useful tool to study quantum phase transitions as at the transition point the ground state changes rapidly leading to the enhancement of χ [27][28][29][30][31][32][33][34]. All of these studies w...

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Compressed quantum metrology for the Ising Hamiltonian

Cited by 13 publications

References 35 publications

Integrable quantum many-body sensors for AC field sensing

Integrable quantum many-body sensors for AC field sensing

At the Limits of Criticality-Based Quantum Metrology: Apparent Super-Heisenberg Scaling Revisited

Fidelity susceptibility in Gaussian random ensembles

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