Quantum state tomography with twostep adaptive strategy. Quantum state tomography qst aims to determine an unknown quantum state from the outcome of mea. In implementations of aqse, half wave plates hwps driven by mechanical rotators are used to change the measurement basis, but these significantly limit the overall speed of the system. Adaptive estimation algorithms iowa state university. Jun 26, 2019 in this paper, a novel quantum genetic algorithm qga is combined with unscented kalman filter ukf for dynamic state estimation of power systems. Quantum tomography is a valuable tool in quantum information processing, being essential for characterisation of quantum states, gates, and measurement equipment. Adaptive measurements have shown more powerful capability than nonadaptive measurements in quantum phase estimation, 26,27,28 phase tracking, 29. The oxford solid state basics steven simon optimal control. Parallel computing has been the enabling technology of highend machines for many years.
This book begins with background formalism in estimation theory to establish the necessary prerequisites. Achieving quantum precision limit in adaptive qubit state. Performing quantum state estimation implies the reconstruction of the density. Quantum state tomography is the process by which a quantum state is reconstructed using measurements on an ensemble of identical quantum states. The oxford solid state basics steven simon optimal. Experimental demonstration of adaptive quantum state estimation ryo okamoto,1,2 minako iefuji,1,2 satoshi oyama,1,2 koichi yamagata,3 hiroshi imai,4 akio fujiwara,3, and shigeki takeuchi1,2, 1research institute for electronic science, hokkaido university, kitaku, sapporo 0010020, japan. Experimental adaptive quantum tomography of twoqubit. However, concerning the problem about the computational complexity as listed in table 3, applying logarithmic search with quantum existence testing to training adaptive support vector regression may cost the least iterations.
Optimal state estimation kalman, h infinity, and nonlinear approaches authors. Computational mechanics is a scientific discipline that marries physics, computers, and mathematics to emulate natural physical phenomena. Spectral estimation, signal modeling, adaptive filtering and array processing authors. The strong consistency and asymptotic efficiency of aqse have been mathematically. Firstly, an innovation matrix is used to improve the estimation accuracy by constructing an adaptive correction factor for correcting the prediction covariance matrix in real time. Quantum state tomography and fidelity estimation via. The approach is based on the quantum phase estimation algorithm qpea proposed by abrams and lloyd, and it relies on projective measurements with an electronic hamiltonian h. Adaptive quantization linear quantization instantaneous companding. In this dissertation, two adaptive estimation algorithms are devised for the case where the signal processes are char acterized as state variables of a known first order, linear. Fisher information and asymptotic normality in system. Belavkin v 20 quantum quasimarkov processes in eventum mechanics dynamics, observation, filtering and control, quantum information processing, 12. Change detection is another kind of adaptive filtering for nonstationary signals, and is the basic tool in fault detection and diagnosis. Quantum states can be used to achieve powerlaw scaling better than 0.
Dan simon file specification extension pdf pages 530 size 37. Adaptive quantum state tomography via linear regression. Recommended citation hariri, ali mohamad, identification, state estimation, and adaptive control of type i diabetic patients 2011. We compared the neural network state reconstruction protocol with a protocol. A generalized circuit for the hamiltonian dynamics through. Pdf experimental demonstration of adaptive quantum state. Adaptive methods for state estimation daniele francesco magnani phd thesis university of pavia printed in pavia, italy, november 2009 isbn 9788895767307 the histogr. The circuit complexity depends on the number of summation terms composing the hamiltonian and requires oln number of quantum gates for the simulation of a molecular hamiltonian. The sp ectr al the or em for a self a dj o in t op erat or a sa y s tha t.
Saki nohara1, ryo okamoto1,2, koichi yamagata3, akio fujiwara4,5 and. Oct 07, 2018 optimal state estimation kalman, h infinity, and nonlinear approaches authors. This book is intended to serve as an instructive and selfcontained medium for advanced undergraduate and postgraduate students to grasp the basics of quantumstate estimation. First, an enhanced battery model is proposed to include the impacts due to different discharge rates and temperatures. Kogon file specification extension pdf pages 814 size 11. This requires that understanding of basic results on diverse topics, and derived from different disciplinary perspectives, is required for appreciating the overall picture. Quantumstate estimation is an important field in quantum information theory that deals with the characterization of states of affairs for quantum sources.
Localmeasurementbased quantum state tomography via neural. Quantum state tomography allows the estimation of an unknown quantum state that is available in many identical copies. Recently, quantum information theory has been developing through a fusion of results from various research fields. In this paper, a novel quantum genetic algorithm qga is combined with unscented kalman filter ukf for dynamic state estimation of power systems.
The first experimental demonstration of an adaptive quantum state estimation aqse is reported. Introduction to quantumstate estimation ebook by yong siah. Applying classical methods of machine learning to the study of quantum systems sometimes called quantum machine learning is the focus of an emergent area of physics research. The joint adaptive kalman filter jakf for vehicle motion. This book is a comprehensive survey of most of the theoretical and experimental achievements in the field of quantum estimation of states and operations. Realization of highspeed adaptive quantum state estimation. Adaptive state of charge estimation for liion batteries. Apr 24, 2017 adaptive measurements have shown more powerful capability than nonadaptive measurements in quantum phase estimation, 26,27,28 phase tracking, 29 quantum state discrimination, 30, 31 and. Measurement projects an initially prepared quantum state onto the eigenstate of a given hamiltonian, and the probability to obtain a particular outcome is proportional to.
Adaptive quantum state estimation aqse provides the best possible estimation of unknown parameters of quantum states. Adaptive thresholding for sparse covariance matrix estimation tony cai and weidong liu tony cai is dorothy silberberg professor, department of statistics, the wharton school, university of pennsylvania, philadelphia, pa 19104. State tomography of qubit systems using linear regression. Jakf views lidar and radar data as the source of the local filters, which aims to adaptively adjust the measurement noise variancecovariance vc matrix r and the system noise vc matrix q. Proceedings of the 2011 american control conference, 43344339. This page is intended to be useful to a variety of visitors, from experimental research groups setting up quantum tomography systems, to students learning about the theory of characterizing quantum states. As discussed below, this estimator differs from the technique used in. It has been experimentally demonstrated for a variety of physical systems, among them the quantum state of a light mode 75, the vibrational state of a single ion 76, and the wave packets of atoms of an atomic beam 77. In our raqst protocol, no prior assumption is made on the state to be reconstructed. Adaptive estimator estimates the parameter of interest equally well regardless whether the value of the nuisance parameter is known or not. Any reader with a solid foundation in quantum mechanics, linear algebra and calculus would be able to follow the book comfortably. In this paper, we call it recursively adaptive quantum state tomography raqst because the parameter estimation is recursively updated and adaptive measurements are used. The second one is sequential mc smc 7an importance sampling based algorithmrecently used for adaptive quantum state tomography 8. A novel qgaukf algorithm for dynamic state estimation of.
Experimental adaptive quantum tomography of twoqubit states. The strong consistency and asymptotic efficiency of aqse have been mathematically proven a. A basic example of this is quantum state tomography, where a quantum state is learned from measurement. We design an observer, which is an estimation of the quantum systems.
Diversity of quantum optimizations for training adaptive. Statistical and adaptive signal processing dimitris. For a repeated measurement on the chains output we show that. In particular, we consider adaptive quantumenhanced metrology, which performs sequential mea. The update criterion is based on averagevariance optimality aoptimality in classical statistics, and it has low computational cost for onequbit state estimation. Efficient estimation of banach parameters in semiparametric models klaassen, chris a. This type of estimator will be termed an adaptive estimator since it has the ability to adapt to the initially unknown portion of the statistical model. This book is the first comprehensive treatment of modern quantum measurement and measurementbased quantum control, which are vital elements for realizing quantum technology. Stabilizing feedback controls for quantum systems siam. The retrospective cost state estimation rcse technique proposed in the present paper is based on an adaptive lter whose input is the innovations. A book containing tomography articles from groups around the world, including the second book chapter presented above. Obviously, an increase on the photon number for fidelity estimation and quantum state tomography causes a dramatic increase in the elements of the positive operator valued measures povms, which results in a great consumption of time in measurements.
Shigeki takeuchi the first experimental demonstration of an adaptive quantum state estimation aqse is reported. Adaptive thresholding for sparse covariance matrix estimation. The necessary condition for a regular parametric model to have an adaptive estimator is that. Experimental neural network enhanced quantum tomography npj.
We propose a new approach inspired of the bfn method used in geophysical data assimilation 1 to reconstruct the state of the system from the measured data. Adaptive filtering is a branch of digital signal processing which enables the selective enhancement of desired elements of a signal and the reduction of undesired elements. Albeit still quite young, this field has already been recognized as a necessary tool for research in quantum optics and quantum information, beyond being a fascinating subject on its own as it. The retrospective cost state estimation rcse technique proposed in the present paper is based on an adaptive lter whose input is. The experiment in 8 relied on a single adaptive step. In this chapter, we propose an adaptive experimental design whose expected losses are smaller than those of standard quantum state tomography.
The control of individual quantum systems promises a new technology for the 21st century quantum technology. Quantum algorithms by optimal state estimation andrew childs caltech institute for quantum information in collaboration with dave bacon university of washington wim van dam uc santa barbara quantph0501044, quantph0504083, quantph0507190. Now, it has finally become the ubiquitous key to the efficient use of any kind of multiprocessor computer architecture, from smart phones, tablets, embedded systems and cloud computing up to exascale computers. In particular, its asymptotic theory has been developed during this period. This paper proposes an adaptive soc estimation method based on unscented kalman filter algorithms for lithium liion batteries. Even though the performances of three kinds of quantum optimizations in fact are almost very closely one another, in. A seminar on adaptive quantization methods presented by mahesh pawar 2. Quantum statistical inference, a research field with deep roots in the foundations of both quantum physics and mathematical statistics, has made remarkable progress since 1990.
Identification, state estimation, and adaptive control of. Adaptive quantum state estimation for dynamic quantum. Quantum state tomography is a daunting challenge of experimental. This text takes the unique approach that change detection is a natural extension of. Experiments of multiphoton entanglement have been performed by several groups. Weidong liu is faculty member, department of mathematics and institute of natural sciences, shanghai jiao tong. Controlling adaptive quantumphase estimation with scalable. Experimental demonstration of adaptive quantum state estimation. Improvement of estimation precision by adaptive design of. In this paper, we consider a similar setting to the one in 4, 5, 6.
This paper proposes a multisensory joint adaptive kalman filter jakf through extending innovationbased adaptive estimation iae to estimate the motion state of the moving vehicles ahead. This paper further investigates the adaptive linear regression estimation alre. Yu liu, yuzhang lin and junbo zhao, advanced grid operational tools based on state estimation, for book new technologies for power system. Accurate estimation of the state of charge soc of batteries is one of the key problems in a battery management system. Back and forth nudging for quantum state estimation by. Adaptive strategy shows decreased sn and time requirements for a given accuracy.
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