A Quantum Hamiltonian Identification Algorithm: Computational Complexity and Error Analysis

Wang, Yuanlong; Dong, Daoyi; Qi, Bo; Zhang, Jun; Petersen, Ian R.; Yonezawa, Hidehiro

doi:10.1109/tac.2017.2747507

Cited by 100 publications

(73 citation statements)

References 53 publications

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“…Now (50), (51) and (52) have the same structures as (38), (39) and (40), respectively, while with the dimension decreased by 1. If θ 2 = −θ ′ 2 , we have −Ỹ 1σ = (1, 0, ..., 0) = (−X σ 1 ) T and we can rewrite (50) and (51) as (−X)Ã =Ã ′ (−Ỹ ) and (−Ỹ )Ã = A ′ (−X).…”

Section: B Measuring Ymentioning

confidence: 84%

“…Then {H m } can be chosen as an orthonormal basis of su(d), where the inner product is defined as iH m , iH n = Tr(H † m H n ). The traceless assumption is reasonable because H has an intrinsic degree of freedom (see [38] for details).…”

Section: B Problem Formulation Of Hamiltonian Identifiability and Idmentioning

confidence: 99%

“…We have D ≈ LΨ (q) . We use a least-squares method to obtain an estimateΨ (q) = (L T L) −1 L T D, [38]. For another example of such economic Hamiltonian identification algorithms, please refer to [44].…”

Section: B An Economic Hamiltonian Identification Algorithmmentioning

confidence: 99%

See 2 more Smart Citations

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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Section: B Measuring Ymentioning

confidence: 84%

Section: B Problem Formulation Of Hamiltonian Identifiability and Idmentioning

confidence: 99%

See 1 more Smart Citation

Quantum Hamiltonian Identifiability via a Similarity Transformation Approach and Beyond

Wang¹,

Dong²,

Sone³

et al. 2020

IEEE Trans. Automat. Contr.

Self Cite

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show abstract

“…An isolated quantum system can be characterized by learning its underlying Hamiltonian. This can be achieved by monitoring the dynamics that the Hamiltonian generates [18][19][20][21][22][23][24][25][26][27][28][29][30][31], or by measuring local observables in one of its eigenstates or thermal states [32][33][34][35][36][37][38][39][40]. However, realistic quantum systems are never fully isolated.…”

Section: Introductionmentioning

confidence: 99%

Learning the dynamics of open quantum systems from their steady states

et al. 2020

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Recent works have shown that generic local Hamiltonians can be efficiently inferred from local measurements performed on their eigenstates or thermal states. Realistic quantum systems are often affected by dissipation and decoherence due to coupling to an external environment. This raises the question whether the steady states of such open quantum systems contain sufficient information allowing for full and efficient reconstruction of the system's dynamics. We find that such a reconstruction is possible for generic local Markovian dynamics. We propose a recovery method that uses only local measurements; for systems with finite-range interactions, the method recovers the Lindbladian acting on each spatial domain using only observables within that domain. We numerically study the accuracy of the reconstruction as a function of the number of measurements, type of opensystem dynamics and system size. Interestingly, we show that couplings to external environments can in fact facilitate the reconstruction of Hamiltonians composed of commuting terms.

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“…Various methodologies have been developed for this task, including quantum process tomography [8][9][10][11], Bayesian analysis [12][13][14], compressive sensing [15][16][17], and eigensystem realization algorithm [18][19][20]. Not only are many of these techniques quite complex, but they also often assume complete access to the system to be identified: full controllability and observability via the coupling of the target quantum system with a classical apparatus.…”

Section: Introductionmentioning

confidence: 99%

Hamiltonian identifiability assisted by a single-probe measurement

Sone

Cappellaro

2017

Phys. Rev. A

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We study the Hamiltonian identifiability of a many-body spin-1/2 system assisted by the measurement on a single quantum probe based on the eigensystem realization algorithm approach employed in Zhang and Sarovar, Phys. Rev. Lett. 113, 080401 (2014). We demonstrate a potential application of Gröbner basis to the identifiability test of the Hamiltonian, and provide the necessary experimental resources, such as the lower bound in the number of the required sampling points, the upper bound in total required evolution time, and thus the total measurement time. Focusing on the examples of the identifiability in the spin-chain model with nearest-neighbor interaction, we classify the spin-chain Hamiltonian based on its identifiability, and provide the control protocols to engineer the nonidentifiable Hamiltonian to be an identifiable Hamiltonian.

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A Quantum Hamiltonian Identification Algorithm: Computational Complexity and Error Analysis

Cited by 100 publications

References 53 publications

Quantum Hamiltonian Identifiability via a Similarity Transformation Approach and Beyond

Quantum Hamiltonian Identifiability via a Similarity Transformation Approach and Beyond

Learning the dynamics of open quantum systems from their steady states

Hamiltonian identifiability assisted by a single-probe measurement

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