相关论文: State reconstruction formulas for the s-distributi…
This work is concerned with various aspects of the formulation of the quantum inverse scattering method for the one-dimensional Hubbard model. We first establish the essential tools to solve the eigenvalue problem for the transfer matrix of…
We propose a divide-and-conquer algorithm to find recursively the Scattering matrix of general tight-binding structures. The Scattering matrix allows a direct calculation of transport properties in mesoscopic systems by using the Landauer…
Quantum state tomography, the ability to deduce the density matrix of a quantum system from measured data, is of fundamental importance for the verification of present and future quantum devices. It has been realized in systems with few…
We propose a quantum inverse iteration algorithm which can be used to estimate the ground state properties of a programmable quantum device. The method relies on the inverse power iteration technique, where the sequential application of the…
Our studies concern some aspects of scattering theory of the singular differential systems $ y'-x^{-1}Ay-q(x)y=\rho By, \ x>0 $ with $n\times n$ matrices $A,B, q(x), x\in(0,\infty)$, where $A,B$ are constant and $\rho$ is a spectral…
We show how the rotational quantum state of a linear or symmetric top rotor can be reconstructed from finite time observations of the polar angular distribution under certain conditions. The presented tomographic method can reconstruct the…
We present a novel approach to the regression of quantum mechanical energies based on a scattering transform of an intermediate electron density representation. A scattering transform is a deep convolution network computed with a cascade of…
A general method for solving the so-called quantum inverse scattering problem (namely the reconstruction of local quantum (field) operators in term of the quantum monodromy matrix satisfying a Yang-Baxter quadratic algebra governed by an…
We propose an alternative approach for the construction of the unitary matrix which performs generalized unitary rotations of the system consisting of independent identical subsystems (for example spin system). This matrix, when applied to…
When working with quantum states, analysis of the final quantum state generated through probabilistic measurements is essential. This analysis is typically conducted by constructing the density matrix from either partial or full tomography…
Several problems in computer algebra can be efficiently solved by reducing them to calculations over finite fields. In this paper, we describe an algorithm for the reconstruction of multivariate polynomials and rational functions from their…
We consider quantum walks on a finite graphs to which infinite tails are attached. We explore how the propagating and bound states depend on the structure of the finite graph. The S-matrix for such graphs is defined. Its unitarity is proved…
The subject of this thesis is a novel construction method for interacting relativistic quantum field theories on two-dimensional Minkowski space. The input in this construction is not a classical Lagrangian, but rather a prescribed…
We consider the massive Thirring model in the laboratory coordinates and explain how the inverse scattering transform can be developed with the Riemann-Hilbert approach. The key ingredient of our method is to transform the corresponding…
In this paper we study the state determination for composite systems of two spatial qubits. We show, theoretically, that one can use the technique of quantum tomography to reconstruct the density matrixes of these systems. This tomographic…
A new approach to the construction of interacting quantum field theories on two-dimensional Minkowski space is discussed. In this program, models are obtained from a prescribed factorizing S-matrix in two steps. At first, quantum fields…
Quantum circuits for loading probability distributions into quantum states are essential subroutines in quantum algorithms used in physics, finance engineering, and machine learning. The ability to implement these with high accuracy in…
A major bottleneck in the quest for scalable many-body quantum technologies is the difficulty in benchmarking their preparations, which suffer from an exponential `curse of dimensionality' inherent to their quantum states. We present an…
Recently quantum tomography has been proposed as a fundamental tool for prototyping a few qubit quantum device. It allows the complete reconstruction of the state produced from a given input into the device. From this reconstructed density…
Reconstructing quantum states is an important task for various emerging quantum technologies. The process of reconstructing the density matrix of a quantum state is known as quantum state tomography. Conventionally, tomography of arbitrary…