Related papers: A Note on Parallel Distinguishability of two Quant…
In this article we develop a duality principle suitable for a large class of problems in optimization. The main result is obtained through basic tools of convex analysis and duality theory. We establish a correct relation between the…
We consider the following equations: \begin{equation*} \left\{\begin{array}{ll} (-\triangle)^{\alpha/2}u(x)=f(v(x)), \\ (-\triangle)^{\beta/2}v(x)=g(u(x)), &x \in R^{n},\\ u,v\geq 0, &x \in R^{n}, \end{array} \right. \end{equation*} for…
Let $A,B\in \mathbb{B}(\mathscr{H})$ be such that $0<b_{1}I \leq A \leq a_{1}I$ and $0<b_{2}I \leq B \leq a_{2}I$ for some scalars $0<b_{i}< a_{i},\;\; i=1,2$ and $\Phi:\mathbb{B}(\mathscr{H})\rightarrow\mathbb{B}(\mathscr{K})$ be a…
We revisit the adiabatic criterion in stimulated Raman adiabatic passage for the three-level $\Lambda$-system, and compare the situation with and without nonlinearity. In linear systems, the adiabatic condition is derived with the help of…
A pair of quantum observables diagonal in the same "incoherent" basis can be measured jointly, so some coherence is obviously required for measurement incompatibility. Here we first observe that coherence in a single observable is linked to…
We show how the separability problem is dual to that of decomposing any given matrix into a conic combination of rank-one partial isometries, thus offering a duality approach different to the positive maps characterization problem. Several…
We consider numeration systems where digits are integers and the base is an algebraic number $\beta$ such that $|\beta|>1$ and $\beta$ satisfies a polynomial where one coefficient is dominant in a certain sense. For this class of bases…
We develop a non-adiabatic generalization of holonomic quantum computation in which high-speed universal quantum gates can be realized by using non-Abelian geometric phases. We show how a set of non-adiabatic holonomic one- and two-qubit…
We propose quantum algorithms, purely quantum in nature, for calculating the determinant and inverse of an $(N-1)\times (N-1)$ matrix (depth is $O(N^2\log N)$) which is a simple modification of the algorithm for calculating the determinant…
In the task of discriminating between nonorthogonal quantum states from multiple copies, the key parameters are the error probability and the resources (number of copies) used. Previous studies have considered the task of minimizing the…
The formalism of linear response theory can be extended to encompass physical situations where an open quantum system evolves towards a non-equilibrium steady-state. Here, we use the framework put forward by Konopik and Lutz [Phys. Rev.…
Full formal descriptions of algorithms making use of quantum principles must take into account both quantum and classical computing components, as well as communications between these components. Moreover, to model concurrent and…
Generalizing earlier work characterizing the quantum query complexity of computing a function of an unknown classical ``black box'' function drawn from some set of such black box functions, we investigate a more general quantum query model…
The nonlinear supersymmetry of one-dimensional systems is investigated in the context of the quantum anomaly problem. Any classical supersymmetric system characterized by the nonlinear in the Hamiltonian superalgebra is symplectomorphic to…
We study the limitations and fast-forwarding of quantum algorithms for linear ordinary differential equation (ODE) systems with a particular focus on non-quantum dynamics, where the coefficient matrix in the ODE is not anti-Hermitian or the…
The adiabatic theorem refers to a setup where an evolution equation contains a time-dependent parameter whose change is very slow, measured by a vanishing parameter $\epsilon$. Under suitable assumptions the solution of the…
Quantum theory is consistent with a computational model permitting black-box operations to be applied in an indefinite causal order, going beyond the standard circuit model of computation. The quantum switch -- the simplest such example --…
In this paper we consider a linear homogeneous system of $m$ equations in $n$ unknowns with integer coefficients over the reals. Assume that the sum of the absolute values of the coefficients of each equation does not exceed $k+1$ for some…
Quantum computation has revolutionary potential for speeding algorithms and for simulating quantum systems such as molecules. We report here a quantum computer design that performs universal quantum computation within a single…
We present an efficient quantum algorithm for some independent set problems in graph theory, based on non-abelian adiabatic mixing. We illustrate the performance of our algorithm with analysis and numerical calculations for two different…