L. A. Markovich
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View article: Nonparametric Learning Non-Gaussian Quantum States of Continuous Variable Systems
Nonparametric Learning Non-Gaussian Quantum States of Continuous Variable Systems Open
Continuous-variable quantum systems are foundational to quantum computation, communication, and sensing. While traditional representations using wave functions or density matrices are often impractical, the tomographic picture of quantum m…
View article: Efficient High-Dimensional Entangled State Analyzer with Linear Optics
Efficient High-Dimensional Entangled State Analyzer with Linear Optics Open
The use of higher-dimensional photonic encodings (qudits) instead of two-dimensional encodings (qubits) can improve the loss tolerance and reduce the computational resources of photonic-based quantum information processing. To harness this…
View article: Quantum memory assisted observable estimation
Quantum memory assisted observable estimation Open
The estimation of many-qubit observables is an essential task of quantum information processing. The generally applicable approach is to decompose the observables into weighted sums of multi-qubit Pauli strings, i.e., tensor products of si…
View article: Error and Resource Estimates of Variational Quantum Algorithms for Solving Differential Equations Based on Runge-Kutta Methods
Error and Resource Estimates of Variational Quantum Algorithms for Solving Differential Equations Based on Runge-Kutta Methods Open
A focus of recent research in quantum computing has been on developing quantum algorithms for differential equations solving using variational methods on near-term quantum devices. A promising approach involves variational algorithms, whic…
View article: Error correlations in photonic qudit-mediated entanglement generation
Error correlations in photonic qudit-mediated entanglement generation Open
Generating entanglement between distributed network nodes is a prerequisite for the quantum internet. Entanglement distribution protocols based on high-dimensional photonic qudits enable the simultaneous generation of multiple entangled pa…
View article: Not All Probability Density Functions Are Tomograms
Not All Probability Density Functions Are Tomograms Open
This paper delves into the significance of the tomographic probability density function (pdf) representation of quantum states, shedding light on the special classes of pdfs that can be tomograms. Instead of using wave functions or density…
View article: Efficient High-Dimensional Entangled State Analyzer with Linear Optics
Efficient High-Dimensional Entangled State Analyzer with Linear Optics Open
The use of higher-dimensional photonic encodings (qudits) instead of two-dimensional encodings (qubits) can improve the loss tolerance and reduce the computational resources of photonic-based quantum information processing. To harness this…
View article: Not all Probability Density Functions are Tomograms
Not all Probability Density Functions are Tomograms Open
This paper delves into the significance of the tomographic probability density function (pdf) representation of quantum states, shedding light on the special classes of pdfs that can be tomograms. Instead of using wave functions or density…
View article: Efficient and robust estimation of many-qubit Hamiltonians
Efficient and robust estimation of many-qubit Hamiltonians Open
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 u…
View article: Error Correlations in Photonic Qudit-Mediated Entanglement Generation
Error Correlations in Photonic Qudit-Mediated Entanglement Generation Open
Generating entanglement between distributed network nodes is a prerequisite for the quantum internet. Entanglement distribution protocols based on high-dimensional photonic qudits enable the simultaneous generation of multiple entangled pa…
View article: Phase shift rule with the optimal parameter selection
Phase shift rule with the optimal parameter selection Open
The phase shift rules enable the estimation of the derivative of a quantum state with respect to phase parameters, providing valuable insights into the behavior and dynamics of quantum systems. This capability is essential in quantum simul…
View article: High-Precision Observable Estimation with Single Qubit Quantum Memory
High-Precision Observable Estimation with Single Qubit Quantum Memory Open
The estimation of multi-qubit observables is a key task in quantum information science. The standard approach is to decompose a multi-qubit observable into a weighted sum of Pauli strings. The observable can then be estimated from projecti…
View article: Hermitian and Unitary Almost-Companion Matrices of Polynomials on Demand
Hermitian and Unitary Almost-Companion Matrices of Polynomials on Demand Open
We introduce the concept of the almost-companion matrix (ACM) by relaxing the non-derogatory property of the standard companion matrix (CM). That is, we define an ACM as a matrix whose characteristic polynomial coincides with a given monic…
View article: Hermitian and unitary almost-companion matrices of polynomials on demand
Hermitian and unitary almost-companion matrices of polynomials on demand Open
We introduce the concept of Almost-Companion Matrix (ACM) by relaxing the non-derogatory property of the standard Companion Matrix (CM). That is, we define an ACM as a matrix whose characteristic polynomial coincides with a given monic and…
View article: Quantum memory assisted observable estimation
Quantum memory assisted observable estimation Open
The estimation of many-qubit observables is an essential task of quantum information processing. The generally applicable approach is to decompose the observables into weighted sums of multi-qubit Pauli strings, i.e., tensor products of si…
View article: Efficient and robust estimation of many-qubit Hamiltonians
Efficient and robust estimation of many-qubit Hamiltonians Open
Characterizing the interactions and dynamics of quantum mechanical systems is an essential task in the development of quantum technologies. We propose an efficient protocol based on the estimation of the time derivatives of few qubit obser…
View article: Gamma Kernel Estimation of the Density Derivative on the Positive Semi-Axis by Dependent Data
Gamma Kernel Estimation of the Density Derivative on the Positive Semi-Axis by Dependent Data Open
We estimate the derivative of a probability density function defined on [0,∞). For this purpose, we choose the class of kernel estimators with asymmetric gamma kernel functions. The use of gamma kernels is fruitful due to the fact that the…
View article: New Gabor quasi-probability based on the integral transform
New Gabor quasi-probability based on the integral transform Open
New quasi-probability function based on the Gabor integral transform is introduced. Using a quantizer-dequantizer method as a unifying description for representations of states in quantum mechanics the integral connection between this quas…
View article: Malevich’s Suprematist Composition Picture for Spin States
Malevich’s Suprematist Composition Picture for Spin States Open
This paper proposes an alternative geometric representation of single qudit states based on probability simplexes to describe the quantum properties of noncomposite systems. In contrast to the known high dimension pictures, we present the …
View article: Highly parallel algorithm for the Ising ground state searching problem
Highly parallel algorithm for the Ising ground state searching problem Open
Finding an energy minimum in the Ising model is an exemplar objective, associated with many combinatorial optimization problems, that is computationally hard in general, but occurs in all areas of modern science. There are several numerica…
View article: Entopy-energy inequality for superconducting qutrit
Entopy-energy inequality for superconducting qutrit Open
We compare the entropy-energy inequality and the von Neumann entropic inequality for three level atom implemented on superconducting circuits with Josephson junction. The positivity of entropy and energy relations for the qutrit system are…
View article: Gamma-weibull kernel estimation of the heavy tailed densities
Gamma-weibull kernel estimation of the heavy tailed densities Open
We consider the nonparametric estimation of the univariate heavy tailed probability density function (pdf) with a support on $[0,\infty)$ by independent data. To this end we construct the new kernel estimator as a combination of the asymme…
View article: Photon distributions and information nonnegativity versus quadrature uncertainty relation
Photon distributions and information nonnegativity versus quadrature uncertainty relation Open
Using entropic inequalities for Shannon entropies new inequalities for some classical polynomials are obtained. To this end, photon distribution functions for one-, two- and multi-mode squeezed states in terms of Hermite, Laguerre, Legendr…