High-accuracy Hamiltonian learning via delocalized quantum state evolutions

Rattacaso, Davide; Passarelli, Gianluca; Lucignano, P.

doi:10.22331/q-2023-01-26-905

Cited by 9 publications

(3 citation statements)

References 45 publications

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“…However, continued progress towards this goal requires careful characterization of the underlying Hamiltonians and dissipative dynamics of the hardware to mitigate errors and engineer the desired dynamics. The exponential growth of the dimension of the state space of a quantum device with the number of qubits renders this an outstanding challenge broadly referred to as the Hamiltonian learning problem 7 – 35 .…”

Section: Introductionmentioning

confidence: 99%

Efficient and robust estimation of many-qubit Hamiltonians

Stilck França,

Markovich,

Dobrovitski

et al. 2024

Nat Commun

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Characterizing the interactions and dynamics of quantum mechanical systems is an essential task in developing quantum technologies. We propose an efficient protocol based on the estimation of the time-derivatives of few qubit observables using polynomial interpolation for characterizing the underlying Hamiltonian dynamics and Markovian noise of a multi-qubit device. For finite range dynamics, our protocol exponentially relaxes the necessary time-resolution of the measurements and quadratically reduces the overall sample complexity compared to previous approaches. Furthermore, we show that our protocol can characterize the dynamics of systems with algebraically decaying interactions. The implementation of the protocol requires only the preparation of product states and single-qubit measurements. Furthermore, we improve a shadow tomography method for quantum channels that is of independent interest and discuss the robustness of the protocol to various errors. This protocol can be used to parallelize the learning of the Hamiltonian, rendering it applicable for the characterization of both current and future quantum devices.

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Section: Introductionmentioning

confidence: 99%

Efficient and robust estimation of many-qubit Hamiltonians

Stilck França,

Markovich,

Dobrovitski

et al. 2024

Nat Commun

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“…[21][22][23][24][25][26][27][28] Concerning the characterization of quantum processes, Hamiltonian learning strategies have been extensively investigated in order to provide a reliable solution to this challenge. [29][30][31][32][33][34] Moreover, it is pivotal that the required information is often not directly accessible and must be inferred starting from experimental quantities. 35,36 For parametrized Hamiltonians, this translates in establishing the values of significant Hamiltonian parameters starting from measured quantities.…”

Section: Introductionmentioning

confidence: 99%

Multiparameter estimation of continuous-time quantum walk Hamiltonians through machine learning

Gianani

Benedetti

2023

AVS Quantum Science

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The characterization of the Hamiltonian parameters defining a quantum walk is of paramount importance when performing a variety of tasks, from quantum communication to computation. When dealing with physical implementations of quantum walks, the parameters themselves may not be directly accessible, and, thus, it is necessary to find alternative estimation strategies exploiting other observables. Here, we perform the multiparameter estimation of the Hamiltonian parameters characterizing a continuous-time quantum walk over a line graph with n-neighbor interactions using a deep neural network model fed with experimental probabilities at a given evolution time. We compare our results with the bounds derived from estimation theory and find that the neural network acts as a nearly optimal estimator both when the estimation of two or three parameters is performed.

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“…The knowledge of a parent Hamiltonian is related to Hamiltonian learning [15][16][17] and verification of quantum devices, and can be exploited to experimentally prepare a target ground state. The search for a parent Hamiltonian represents an especially complex instance of the reconstruction of a Hamiltonian from one of its eigenstates [18][19][20][21][22] or time-dependent states [23][24][25][26]. In particular, the space of the Hamiltonians having a given state as an eigenstate can be efficiently reconstructed from correlation functions [14,18,19] or expectation values of local commutators [20].…”

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confidence: 99%

Parent Hamiltonian reconstruction via inverse quantum annealing

Rattacaso¹,

Passarelli²,

Russomanno³

et al. 2023

Preprint

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Finding a local Hamiltonian having a given many-body wavefunction as its ground state is a serious challenge of fundamental importance in quantum technologies. Here we introduce a method, inspired by quantum annealing, that efficiently performs this task through an artificial inverse dynamics: a slow deformation of the state generates an adiabatic evolution of the corresponding Hamiltonian. We name this approach inverse quantum annealing. This method only requires the knowledge of local expectation values. As an example, we apply inverse quantum annealing to find the local Hamiltonian of fermionic Gaussian states.

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High-accuracy Hamiltonian learning via delocalized quantum state evolutions

Cited by 9 publications

References 45 publications

Efficient and robust estimation of many-qubit Hamiltonians

Efficient and robust estimation of many-qubit Hamiltonians

Multiparameter estimation of continuous-time quantum walk Hamiltonians through machine learning

Parent Hamiltonian reconstruction via inverse quantum annealing

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