Related papers: Decomposition of unitary matrices and quantum gate…
Conventional ways to solve optimization problems on low-rank matrix sets which appear in great number of applications ignore its underlying structure of an algebraic variety and existence of singular points. This leads to appearance of…
In this paper we define a kind of decomposition for a quantum access structure. We propose a conception of minimal maximal quantum access structure and obtain a sufficient and necessary condition for minimal maximal quantum access…
Efficient decomposition of permutation unitaries is vital as they frequently appear in quantum computing. In this paper, we identify the key properties that impact the decomposition process of permutation unitaries. Then, we classify these…
We introduce a scheme for realizing arbitrary controlled-unitary operations in a two qubit system. If the 2 \times 2 unitary matrix is special unitary (has unit determinant), the controlled-unitary gate operation can be realized in a single…
We propose a scheme for scalable and universal quantum computation using diatomic bits with conditional dipole-dipole interaction, trapped within an optical lattice. The qubit states are encoded by the scattering state and the bound…
We require decomposition methods for the ABCD-matrix formulation in rotationally symmetric paraxial geometric optics when designing a multi-component optical system from a given single paraxial specification (represented by an ABCD matrix)…
Any single-qubit unitary operation or quantum gate can be considered a rotation. Typical experimental implementations of single-qubit gates involve two or three fixed rotation axes, and up to three rotation steps. Here we show that, if the…
We present a general scheme that allows for construction of scalar separability criteria from positive but not completely positive maps. The concept is based on a decomposition of every positive map $\Lambda$ into a difference of two…
Similar to classical programming, high-level quantum programming languages generate code that cannot be executed directly by quantum hardware and must be compiled. However, unlike classical code, quantum programs must be compiled before…
We demonstrate how structured decompositions of unitary operators can be employed to derive control schemes for finite-level quantum systems that require only sequences of simple control pulses such as square wave pulses with finite rise…
Bilevel optimization has been widely used in decision-making process. However, there still lacks an efficient algorithm to determine an optimal solution of a bilevel optimization problem, especially for a large-size problem. To bridge the…
A quantum compiler is a software program for decomposing ("compiling") an arbitrary unitary matrix into a sequence of elementary operations (SEO). The author of this paper is also the author of a quantum compiler called Qubiter. Qubiter…
We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these…
Columns of d^2 x N matrices are shown to create different sets of N operators acting on $d$-dimensional Hilbert space. This construction corresponds to a formalism of the star-product of operator symbols. The known bases are shown to be…
Electron transport in realistic physical and chemical systems often involves the non-trivial exchange of energy with a large environment, requiring the definition and treatment of open quantum systems. Because the time evolution of an open…
In this paper, we propose an iterative algorithm using polar decomposition to approximate a channel characterized by a single unitary matrix based on input-output quantum state pairs. In limited data, we state and prove that the optimal…
A series of hybrid quantum-classical generalized Benders decomposition (GBD) algorithms are proposed to address unit commitment (UC) problems under centralized, distributed, and partially distributed frameworks. In the centralized approach,…
A dynamical decoupling method is presented which is based on embedding a deterministic decoupling scheme into a stochastic one. This way it is possible to combine the advantages of both methods and to increase the suppression of undesired…
Qubits, which are quantum counterparts of classical bits, are used as basic information units for quantum information processing, whereas underlying physical information carriers, e.g. (artificial) atoms or ions, admit encoding of more…
In this paper we propose an approach to approximate a truncated singular value decomposition of a large structured matrix. By first decomposing the matrix into a sum of Kronecker products, our approach can be used to approximate a large…