arXiv subjects

Yu. I. Bogdanov

Publications and source records attributed to Yu. I. Bogdanov.

At least 37 records · Page 2Linked to original sources

arXiv2019

Theoretical and experimental study of multi-mode thermal states with subtraction of a random number of photons

The work is devoted to the theoretical and experimental study of quantum states of light conditionally prepared by subtraction of a random number of photons from the initial multimode thermal state. A fixed number of photons is subtracted from a multimode quantum state, but only a subsystem of a lower number of modes is registered, in which the number of subtracted photons turns out to be a non-fixed random variable. It is shown that the investigation of multiphoton subtracted multimode thermal states provides a direct study of the fundamental quantum-statistical properties of bosons using a simple experimental implementation. The developed experimental setup plays a role of a specific boson lototron, which is based on the fundamental link between the statistics of boson systems and the Polya distribution. It is shown that the calculation of the photon number distribution based on the Polya urn scheme is equivalent to a calculation using statistical weights for boson systems. A mathematical model based on the composition of the Polya distribution and thermal state is developed and verified. The experimental results are in a good agreement with the developed theory.

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arXiv2019

Representation of Boolean functions in terms of quantum computation

The relationship between quantum physics and discrete mathematics is reviewed in this article. The Boolean functions unitary representation is considered. The relationship between Zhegalkin polynomial, which defines the algebraic normal form of Boolean function, and quantum logic circuits is described. It is shown that quantum information approach provides simple algorithm to construct Zhegalkin polynomial using truth table. Developed methods and algorithms have arbitrary Boolean function generalization with multibit input and multibit output. Such generalization allows us to use many-valued logic (k-valued logic, where k is a prime number). Developed methods and algorithms can significantly improve quantum technology realization. The presented approach is the baseline for transition from classical machine logic to quantum hardware.

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arXiv2019

Quantum approach to the dynamical systems modeling

We present a general approach to the classical dynamical systems simulation. This approach is based on classical systems extension to quantum states. The proposed theory can be applied to analysis of multiple (including non-Hamiltonian) dissipative dynamical systems. As examples, we consider the logistic model, the Van der Pol oscillator, dynamical systems of Lorenz, Rössler (including Rössler hyperchaos) and Rabinovich-Fabrikant. Developed methods and algorithms integrated in quantum simulators will allow us to solve a wide range of problems with scientific and practical significance.

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arXiv2019

Quantum tomography based on principles of completeness, adequacy and fidelity

In this report we present a general approach for estimating quantum circuits by means of measurements. We apply the developed general approach for estimating the quality of superconducting and optical quantum chips. Using the methods of quantum states and processes tomography developed in our previous works, we have defined the adequate models of the states and processes under consideration.

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arXiv2019

High-fidelity quantum tomography with imperfect measurements

In the current work we address the problem of quantum process tomography (QPT) in the case of imperfect preparation and measurement of the states which are used for QPT. The fuzzy measurements approach which helps us to efficiently take these imperfections into account is considered. However, to implement such a procedure one should have a detailed information about the errors. An approach for obtaining the partial information about them is proposed. It is based on the tomography of the ideal identity gate. This gate could be implemented by performing the measurement right after the initial state preparation. By using the result of the identity gate tomography we were able to significantly improve further QPT procedures. The proposed approach has been tested experimentally on the IBM superconducting quantum processor. As a result, we have obtained an increase in fidelity from 89% to 98% for Hadamard transformation and from 77% to 95% for CNOT gate.

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arXiv2018

Non-Gaussianity of multiple photon subtracted thermal states in terms of compound-Poisson photon number distribution parameters: theory and experiment

The multiphoton-subtracted thermal states are an interesting example of quantum states of light which are both classical and non-Gaussian. All the properties of such states can be described by just two parameters of compound-Poisson photon number distribution. The non-Gaussianity dependency on these parameters has been calculated numerically and analytically. The loss of non-Gaussianity during the optical damping has been also studied experimentally.

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arXiv2017

The influence of quantum noise on the Grover algorithm and quantum Fourier transform: quantum operations theory approach

The method of noisy multiqubit quantum circuits modeling is proposed. The analytical formulas for the dependence of quantum algorithms accuracy on qubits count and noise level are obtained for Grover algorithm and quantum Fourier transform. It is shown that the proposed approach is very much in line with results obtained by Monte Carlo statistical modeling method. The developed theory makes it possible to predict the influence of quantum noise on the accuracy of the forward-looking multiqubit quantum systems under development.

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arXiv2017

Tomography of multi-photon polarization states in conditions of non-unit quantum efficiency of detectors

The polarizing multi-photon quantum states tomography with non-unit quantum efficiency of detectors is considered. A new quantum tomography protocol is proposed. This protocol considers events of losing photons of multi-photon quantum state in one or more channels among with n-fold coincidence events. The advantage of the proposed protocol compared with the standard n-fold coincidence protocol is demonstrated using the methods of statistical analysis.

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arXiv2017

Multi-photon subtracted thermal states: description, preparation and reconstruction

We present a study of optical quantum states generated by subtraction of photons from the thermal state. Some aspects of their photon number and quadrature distributions are discussed and checked experimentally. We demonstrate an original method of up to ten photon subtracted state preparation with use of just one single-photon detector. All the states where measured with use of balanced homodyne technique, and the corresponding density matrices where reconstructed. The fidelity between desired and reconstructed states exceeds 99%

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arXiv2017

Study of higher-order correlation functions and photon statistics using multiphoton-subtracted states and quadrature measurements

The estimation of high order correlation function values is an important problem in the field of quantum computation. We show that the problem can be reduced to preparation and measurement of optical quantum states resulting after annihilation of a set number of quanta from the original beam. We apply this approach to explore various photon bunching regimes in optical states with gamma-compounded Poisson photon number statistics. We prepare and perform measurement of the thermal quantum state as well as states produced by subtracting one to ten photons from it. Maximum likelihood estimation is employed for parameter estimation. The goal of this research is the development of highly accurate procedures for generation and quality control of optical quantum states.

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arXiv2017

Analysis of quantum tomography protocol efficiency for triphoton polarization states

Reliable generation and measurement of triphoton states has yet to be achieved in laboratory. We give an overview of the problems in generating and measuring triphoton quantum states and analyze several protocols of quantum measurements, which allow for high precision of reconstruction when sizes of available statistical data samples are limited. The tomography procedure under investigation is based on root approach to state estimation. In particular, we use the generalized Fisher information matrix to assess the accuracy of the quantum state parameters measurement. We use tomographic protocols, based on the symmetry of the Platonic solids. We demonstrate the capability to reconstruct triphoton quantum states with precision close to the maximum achievable value allowed by quantum mechanics

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arXiv2017

Schmidt decomposition and multivariate statistical analysis

The new method of multivariate data analysis based on the complements of classical probability distribution to quantum state and Schmidt decomposition is presented. We considered Schmidt formalism application to problems of statistical correlation analysis. Correlation of photons in the beam splitter output channels, when input photons statistics is given by compound Poisson distribution is examined. The developed formalism allows us to analyze multidimensional systems and we have obtained analytical formulas for Schmidt decomposition of multivariate Gaussian states. It is shown that mathematical tools of quantum mechanics can significantly improve the classical statistical analysis. The presented formalism is the natural approach for the analysis of both classical and quantum multivariate systems and can be applied in various tasks associated with research of dependences.

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arXiv2017

Quantum states tomography with noisy measurement channels

We consider realistic measurement systems, where measurements are accompanied by decoherence processes. The aim of this work is the construction of methods and algorithms for precise quantum measurements with fidelity close to the fundamental limit. In the present work the notions of ideal and non-ideal quantum measurements are strictly formalized. It is shown that non-ideal quantum measurements could be represented as a mixture of ideal measurements. Based on root approach the quantum state reconstruction method is developed. Informational accuracy theory of non-ideal quantum measurements is proposed. The monitoring of the amount of information about the quantum state parameters is examined, including the analysis of the information degradation under the noise influence. The study of achievable fidelity in non-ideal quantum measurements is performed. The results of simulation of fidelity characteristics of a wide class of quantum protocols based on polyhedrons geometry with high level of symmetry are presented. The impact of different decoherence mechanisms, including qubit amplitude and phase relaxation, bit-flip and phase-flip, is considered.

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arXiv2014

The study of Lorenz and Rössler strange attractors by means of quantum theory

We have developed a method for complementing an arbitrary classical dynamical system to a quantum system using the Lorenz and Rössler systems as examples. The Schrödinger equation for the corresponding quantum statistical ensemble is described in terms of the Hamilton-Jacobi formalism. We consider both the original dynamical system in the position space and the conjugate dynamical system corresponding to the momentum space. Such simultaneous consideration of mutually complementary position and momentum frameworks provides a deeper understanding of the nature of chaotic behavior in dynamical systems. We have shown that the new formalism provides a significant simplification of the Lyapunov exponents calculations. From the point of view of quantum optics, the Lorenz and Rössler systems correspond to three modes of a quantized electromagnetic field in a medium with cubic nonlinearity. From the computational point of view, the new formalism provides a basis for the analysis of complex dynamical systems using quantum computers.

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arXiv2014

The study of amplitude and phase relaxation impact on the quality of quantum information technologies

The influence of amplitude and phase relaxation on evolution of quantum states within the formalism of quantum operations is considered. The model of polarizing qubits where noises are determined by the existence of spectral degree of freedom that shows up during the light propagation inside anisotropic mediums with dispersion is studied. Approximate analytic model for calculation of phase plate impact on polarizing state with dispersion influence taken into consideration is suggested.

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arXiv2014

Numerical and analytical research of the impact of decoherence on quantum circuits

Three different levels of noisy quantum schemes modeling are considered: vectors, density matrices and Choi-Jamiolkowski related states. The implementations for personal computers and supercomputers are described, and the corresponding results are shown. For the level of density matrices, we present the technique of the fixed rank approximation and show some analytical estimates of the fidelity level.

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arXiv2014

Root approach for estimation of statistical distributions

Application of root density estimator to problems of statistical data analysis is demonstrated. Four sets of basis functions based on Chebyshev-Hermite, Laguerre, Kravchuk and Charlier polynomials are considered. The sets may be used for numerical analysis in problems of reconstructing statistical distributions by experimental data. Based on the root approach to reconstruction of statistical distributions and quantum states, we study a family of statistical distributions in which the probability density is the product of a Gaussian distribution and an even-degree polynomial. Examples of numerical modeling are given. The results of present paper are of interest for the development of tomography of quantum states and processes.

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arXiv2013

The efficiency of quantum tomography based on photon detection

We propose a general methodology for efficient statistical reconstruction of a quantum state through collection and analysis of photon counting statistics. Our approach includes both strict quantitative criteria for adequacy and completeness of the statistical inverse problem, as well as a simple and reliable method for evaluating errors in the reconstructed state and approximation of a quantum state by means of the reduced finite-dimensional model.

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