Robust online Hamiltonian learning

Granade, Christopher; Ferrie, Christopher; Wiebe, Nathan; Cory, David G.

doi:10.1088/1367-2630/14/10/103013

Cited by 173 publications

(230 citation statements)

References 45 publications

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“…4(c) and 4(d). We find that when |ω r,0 − µ ω | is no larger than few times g 0 , the number of measurement shots is comparable to the one ideally required when ω r is initially known precisely [3,6], indicating the near optimality of our algorithm in this parameter region.…”

Section: Measurement Shot Relative Median Squared Errormentioning

confidence: 82%

“…We use a controlled qubit to characterize the uncertain frequency of another mode ω r that is coupled to the qubit with uncertain coupling strength g. Our algorithm employs modern Bayesian inference techniques to choose informative experimental settings while remaining computationally feasible. We demonstrate that our approach is robust against experimental imperfections [3,4].…”

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confidence: 86%

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Efficient Estimation of Resonant Coupling between Quantum Systems

2014

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We present an efficient method for the characterization of two coupled discrete quantum systems, one of which can be controlled and measured. For two systems with transition frequencies ωq, ωr, and coupling strength g we show how to obtain estimates of g and ωr whose error decreases exponentially in the number of measurement shots rather than as a power law expected in simple approaches. Our algorithm can thereby identify g and ωr simultaneously with high precision in a few hundred measurement shots. This is achieved by adapting measurement settings upon data as it is collected. We also introduce a method to eliminate erroneous estimates with small overhead. Our algorithm is robust against the presence of relaxation and typical noise. Our results are applicable to many candidate technologies for quantum computation, in particular, for the characterization of spurious two-level systems in superconducting qubits or stripline resonators. Parameter estimation in many microscopic and some macroscopic systems inevitably involves quantum measurements. This implies that parameters cannot be identified with a single measurement shot since the outcome of such a measurement is generally random. Instead, the standard approach is to determine ensemble averages for many experiments and fit the parameters of certain quantitative models to those averages. The most common example for this is spectroscopy: it involves direct measurement of the energy splittings between quantum states in the form of resonances to incoming radiation. Typically, a large ensemble average is produced by gathering data from a large number of independent trials, either simultaneously on an ensemble of molecules (in nuclear magnetic resonance [1]) or from many repetitions of a specific experiment (in optical spectroscopy of single molecules, quantum dots, or superconducting qubits [2]).While being reliable in many contexts, this approach is often too resource intensive. Specifically, the error in the estimate of a single expectation value at a fixed measurement setting decreases in proportion to M − 1 2 r after M r measurement shots. Moreover, many choices of measurement settings are usually required for complex measurement tasks. Such slowness of parameter estimation can also turn into imprecision in the estimate if the parameters of interest drift as a function of time, broadening spectroscopic signatures.Imprecision in system characterization is particularly problematic for quantum information processing applications. These require extremely precise logic operations, usually implemented as pulses. The pulse parameters such as length, amplitude, and carrier frequency, depend on the system parameters. In manufactured solid state qubits, this is rather central as they are subject to fabrication uncertainty.In this Letter, we demonstrate that advanced spectroscopy can be performed far more efficiently. Our re-(b) (a) Figure 1: (color online) (a) Theoretically obtained swap spectrum in frequency-waiting time plane.Here, δ = (ωq − ωr,0)/(2g0), with ωq the q...

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Section: Measurement Shot Relative Median Squared Errormentioning

confidence: 82%

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confidence: 86%

Efficient Estimation of Resonant Coupling between Quantum Systems

2014

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“…Researchers have found many novel approaches to quantum metrology using, for example, multipass interferometers [6], machine learning techniques [7], and computational Bayesian statistics [8] as well as new bounds [9,10] in increasingly more general scenarios. Here we supplement these results with one of a different flavor.…”

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confidence: 99%

“…[6] and adaptive measurement techniques of Refs. [22] and [8]. In these phase estimation examples, additional channels are added (quantum data processing) which depend on the unknown parameter.…”

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Data-processing inequalities for quantum metrology

Ferrie

2014

Phys. Rev. A

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We apply the classical data-processing inequality to quantum metrology to show that manipulating the classical information from a quantum measurement cannot aid in the estimation of parameters encoded in quantum states. We further derive a quantum data-processing inequality to show that coherent manipulation of quantum data also cannot improve the precision in estimation. In addition, we comment on the assumptions necessary to arrive at these inequalities and how they might be avoided, providing insights into enhancement procedures which are not provably wrong. Parameter estimation is an integral part of physics. Quantum metrology refers to the study of the ultimate limits in the accuracy of estimates given the structure imposed by quantum theory [1,2]. Estimation at or near this limit is important for practical objectives such as improving time and frequency standards [3,4] as well as fundamental physics, such as the detection of gravitational waves [5].Researchers have found many novel approaches to quantum metrology using, for example, multipass interferometers [6], machine learning techniques [7], and computational Bayesian statistics [8] as well as new bounds [9,10] in increasingly more general scenarios. Here we supplement these results with one of a different flavor. We provide a very general bound on the estimation accuracy in quantum metrology when noise or data processing (either classical or coherent) is present. Precisely, we give a classical and quantum data processing inequality which shows that estimators based on the raw data are optimal. In other words, processing the data cannot improve quantum metrology. We conclude by showing how to avoid the inequalities with more exotic procedures which can be classed into three conceptually intuitive categories: (1) processing data in a way dependent on the parameter; (2) circumventing an imposed operational restriction; or (3) modifying the dynamics which impart the parameter. Consider a statistical model defining a likelihood function Pr(x|θ ; C). In words, there is an experimental context C whose outcomes are labeled by the random variable x and θ is an unknown parameter to be estimated. For quantum metrology, the goal is estimate a parameter which defines a quantum dynamical process:

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Machine Learning Experimental Multipartite Entanglement Structure

et al. 2022

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With the rapid growth of controllable qubits in recent years, experimental multipartite entangled states can be created with high fidelity in various moderate-and large-scale physical systems. However, the characterization of multipartite entanglement structure remains a formidable challenge, as traditionally it requires exponential number of local measurements to realize the identification. Machine learning is demonstrated to be an efficient tool to detect the underlying entanglement structure for ideal states, but it has non-negligible underperformance when tackling imperfect experimental data in reality. Here, a modified classifier based on feed-forward neural network to predict experimental entanglement structure in terms of entanglement intactness and depth is proposed. By preprocessing the input data, the classifier maintains efficiency and reliability against experimental noises, with the accuracy being enhanced from 69.7% to 91.2% for 6-qubit entangled states in spin systems. This method is anticipated to shed light on future studies of entanglement structure, in particular when the number of controlled qubits reaches explosive growth in practice.

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Robust online Hamiltonian learning

Cited by 173 publications

References 45 publications

Efficient Estimation of Resonant Coupling between Quantum Systems

Efficient Estimation of Resonant Coupling between Quantum Systems

Data-processing inequalities for quantum metrology

Machine Learning Experimental Multipartite Entanglement Structure

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