Hamiltonian identifiability assisted by a single-probe measurement

Sone, Akira; Cappellaro, Paola

doi:10.1103/physreva.95.022335

Cited by 70 publications

(76 citation statements)

References 47 publications

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“…However, even with the rapid progress in the coherent manipulation and quantum-state tomography of several quantum systems, such as photons [6,7], electron spins [8][9][10], atomic qubits [11], superconducting circuits [12,13], and mechanical resonators [14,15], many quantum systems still remain difficult to access for a direct observation of their state, systems we will refer to as dark. In order to circumvent the requirement of such a direct access, a promising technique is to employ an auxiliary quantum system as a measurement probe, on which measurements as well as coherent manipulations can be performed [16][17][18][19][20][21][22][23]. Interferometry [24] based on such a measurement probe allows us to extract information on a target system [25][26][27][28][29][30].…”

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confidence: 99%

Pulsed Quantum-State Reconstruction of Dark Systems

et al. 2019

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We propose a novel strategy to reconstruct the quantum state of dark systems, i.e., degrees of freedom that are not directly accessible for measurement or control. Our scheme relies on the quantum control of a two-level probe that exerts a state-dependent potential on the dark system. Using a sequence of control pulses applied to the probe makes it possible to tailor the information one can obtain and, for example, allows us to reconstruct the density operator of a dark spin as well as the Wigner characteristic function of a harmonic oscillator. Because of the symmetry of the applied pulse sequence, this scheme is robust against slow noise on the probe. The proof-of-principle experiments are readily feasible in solid-state spins and trapped ions.Introduction.-The measurement of the quantum state of a system is a prerequisite ingredient in most modern quantum experiments, ranging from fundamental tests of quantum mechanics [1, 2] to various quantuminformation-processing tasks [3][4][5]. However, even with the rapid progress in the coherent manipulation and quantum-state tomography of several quantum systems, such as photons [6,7], electron spins [8-10], atomic qubits [11], superconducting circuits [12,13], and mechanical resonators [14,15], many quantum systems still remain difficult to access for a direct observation of their state, systems we will refer to as dark. In order to circumvent the requirement of such a direct access, a promising technique is to employ an auxiliary quantum system as a measurement probe, on which measurements as well as coherent manipulations can be performed [16][17][18][19][20][21][22][23]. Interferometry [24] based on such a measurement probe allows us to extract information on a target system [25][26][27][28][29][30]. Nevertheless, it still remains a key challenge to achieve a full quantum-state tomography of dark systems without requiring any direct control.

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confidence: 99%

Pulsed Quantum-State Reconstruction of Dark Systems

et al. 2019

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“…If for almost any value of θ , the solutions always satisfy θ ′ = θ , then the system is identifiable. In order to investigate identifiability, Sone and Cappellaro [27] employed Gröbner basis to determine the conditions of identifiability. By directly solving (10) where the RHS is replaced by a specific transfer function reconstructed from experimental data, one can develop algorithms like that in [26] to identify the Hamiltonian.…”

Section: The Laplace Transform Approach and Atypical Casesmentioning

confidence: 99%

“…Identifiability test criteria are improved and the analysis method for non-minimal systems based on Structure Preserving Transformation (SPT) is proposed. • Based on the STA method, three physical cases in [27] are analyzed and the identifiability conclusions are proved for the systems with arbitrary dimension. • To analyze general non-minimal systems, an SPT method is developed to present an indicator for the existence of economic Hamiltonian identification algorithms, which have computational complexity directly depending on the number of unknown parameters.…”

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Quantum Hamiltonian Identifiability via a Similarity Transformation Approach and Beyond

Wang¹,

Dong²,

Sone³

et al. 2020

IEEE Trans. Automat. Contr.

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The identifiability of a system is concerned with whether the unknown parameters in the system can be uniquely determined with all the possible data generated by a certain experimental setting. A test of quantum Hamiltonian identifiability is an important tool to save time and cost when exploring the identification capability of quantum probes and experimentally implementing quantum identification schemes. In this paper, we generalize the identifiability test based on the Similarity Transformation Approach (STA) in classical control theory and extend it to the domain of quantum Hamiltonian identification. We employ STA to prove the identifiability of spin-1/2 chain systems with arbitrary dimension assisted by single-qubit probes. We further extend the traditional STA method by proposing a Structure Preserving Transformation (SPT) method for non-minimal systems. We use the SPT method to introduce an indicator for the existence of economic quantum Hamiltonian identification algorithms, whose computational complexity directly depends on the number of unknown parameters (which could be much smaller than the system dimension). Finally, we give an example of such an economic Hamiltonian identification algorithm and perform simulations to demonstrate its effectiveness.

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“…where the nth row element of the column vector F is − 2 N C jkn . By combining (16), (17), (21), and (22), we obtain the gradient of the objective J with respect to γ jk . Therefore, if we update γ jk as…”

Section: B Gradient Algorithm For the Identification Problemmentioning

confidence: 99%

Identification of Non-Markovian Environments for Spin Chains

Xue

Zhang

Petersen

2019

IEEE Trans. Contr. Syst. Technol.

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Correlations of an environment are crucial for the dynamics of non-Markovian quantum systems, which may not be known in advance. In this paper, we propose a gradient algorithm for identifying the correlations in terms of timevarying damping rate functions in a time-convolution-less master equation for spin chains. By measuring time trace observables of the system, the identification procedure can be formulated as an optimization problem. The gradient algorithm is designed based on a calculation of the derivative of an objective function with respect to the damping rate functions, whose effectiveness is shown in a comparison to a differential approach for a two-qubit spin chain. I. INTRODUCTIONTo exactly process quantum information, accurate models, including parameters, structures, and descriptions of dynamics, for quantum information carriers are required. With these models, sophisticated feedback control strategies can be designed, for example, feedback stabilization of a number state in a cavity [1], preservation of quantum coherence and entanglement for qubit systems [2] and linear quantum systems [3], or coherent feedback rejection of quantum colored noise [4], [5].However, in practice, an accurate model may not be obtainable since parts of the parameters, structures or dynamics of the quantum system may not be well understood. This would lead to unexpected experimental results or degraded control performance of a quantum control system. For example, in a recent experiment on quantum dots [6], a calculation based on the theoretical model has a discrepancy from the experimental data on the broadened resonator line-width under suitable parameters, which means that some unknown dynamics of the system are not included in the model. Correspondingly, it is shown that degraded estimation performance can be observed due to ignorance of a noise model for a quantum system [7]. Hence, the problem of how to determine the unknown parameters, structures or dynamics of a "dark" quantum system is an

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Hamiltonian identifiability assisted by a single-probe measurement

Cited by 70 publications

References 47 publications

Pulsed Quantum-State Reconstruction of Dark Systems

Pulsed Quantum-State Reconstruction of Dark Systems

Quantum Hamiltonian Identifiability via a Similarity Transformation Approach and Beyond

Identification of Non-Markovian Environments for Spin Chains

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