Related papers: Computing scalar products via a two-terminal quant…
In one dimensional transport problems the scattering matrix $S$ is decomposed into a block structure corresponding to reflection and transmission matrices at the two ends. For $S$ a random unitary matrix, the singular value probability…
Quantum computation is based on tensor products and entangled states. We discuss an alternative to the quantum framework where tensor products are replaced by geometric products and entangled states by multivectors. The resulting theory is…
We develop a novel quantum transfer matrix method to study thermodynamic properties of one-dimensional (1D) disordered electronic systems. It is shown that the partition function can be expressed as a product of $2\times2$ local transfer…
Coherent electron transport through a quantum channel in the presence of a general extended scattering potential is investigated using a T-matrix Lippmann-Schwinger approach. The formalism is applied to a quantum wire with Gaussian type…
We propose to encode quantum information in rotational excitations in a molecular ensemble. Using a stripline cavity field for quantum state transfer between the molecular ensemble and a Cooper pair box two-level system, our proposal offers…
Non-classical features of quantum systems have the potential to strengthen the way we currently exchange information. In this paper, we explore this enhancement on the most basic level of single particles. To be more precise, we compare how…
We introduce a systematic way to obtain expressions for computing the amount of fundamental quantities such as helicity and angular momentum contained in static matter, given its charge and magnetization densities. The method is based on a…
This paper introduces a novel approach to implementing non-unitary linear transformations of basis on quantum computational platforms, a significant leap beyond the conventional unitary methods. By integrating Singular Value Decomposition…
We study quantum algorithms that learn properties of a matrix using queries that return its action on an input vector. We show that for various problems, including computing the trace, determinant, or rank of a matrix or solving a linear…
We consider a system of static spin qubits embedded in a one-dimensional spin coherent channel and develop a scheme to readout the state of one and two qubits separately. We use unpolarized flying qubits for this purpose that scatter off…
We develop a scalable architecture for quantum computation using controllable electrons of double-dot molecules coupled to a microwave stripline resonator on a chip, which satisfies all Divincenzo criteria. We analyze the performance and…
Motivated by the existence of bi-Hamiltonian classical systems and the correspondence principle, in this paper we analyze the problem of finding Hermitian scalar products which turn a given flow on a Hilbert space into a unitary one. We…
If the states of spins in solids can be created, manipulated, and measured at the single-quantum level, an entirely new form of information processing, quantum computing, will be possible. We first give an overview of quantum information…
Kronecker products of unitary Fourier matrices play important role in solving multilevel circulant systems by a multidimensional Fast Fourier Transform. They are also special cases of complex Hadamard (Zeilinger) matrices arising in many…
Quantum classifiers are trainable quantum circuits used as machine learning models. The first part of the circuit implements a quantum feature map that encodes classical inputs into quantum states, embedding the data in a high-dimensional…
Quantum computing is powerful because unitary operators describing the time-evolution of a quantum system have exponential size in terms of the number of qubits present in the system. We develop a new "Singular value transformation"…
The problem of scalar multiplication applied to vectors is considered in the Lee metric. Unlike in other metrics, the Lee weight of a vector may be increased or decreased by the product with a nonzero, nontrivial scalar. This problem is of…
We investigate quantum phase transitions in ladders of spin 1/2 particles by engineering suitable matrix product states for these ladders. We take into account both discrete and continuous symmetries and provide general classes of such…
A numerical analysis to the scalar form-factor in the $\pi\pi$ and KK coupled--channel system is made by solving the coupled-channel dispersive integral equations, using the iteration method. The solutions are found not unique. Physical…
The tensor product of two holomorphic discrete series representations of $SU(1,1)$ can be decomposed as a direct sum of infinitely many discrete series. I shall introduce equivariant quantum channels for each component of the direct sum,…