相关论文: Quantum State Detection Via Elimination
We focus on determining the separability of an unknown bipartite quantum state $\rho$ by invoking a sufficiently large subset of all possible entanglement witnesses given the expected value of each element of a set of mutually orthogonal…
An important subcase of the hidden subgroup problem is equivalent to the shift problem over abelian groups. An efficient solution to the latter problem would serve as a building block of quantum hidden subgroup algorithms over solvable…
The ultimate objective of this paper is to create a stepping stone to the development of new quantum algorithms. The strategy chosen is to begin by focusing on the class of abelian quantum hidden subgroup algorithms, i.e., the class of…
The quantum hidden subgroup approach is an actively studied approach to solve combinatorial problems in quantum complexity theory. With the success of the Shor's algorithm, it was hoped that similar approach may be useful to solve the other…
We present a method for describing and characterizing the state of N particles that may be distinguishable in principle but not in practice due to experimental limitations. The technique relies upon a careful treatment of the exchange…
There have been several research works on the hidden shift problem, quantum algorithms for the problem, and their applications. However, all the results have focused on discrete groups with discrete oracle functions. In this paper, we…
We propose a probabilistic quantum protocol to realize a nonlinear transformation of qutrit states, which by iterative applications on ensembles can be used to distinguish two types of pure states. The protocol involves single-qutrit and…
Many quantum algorithms, including Shor's celebrated factoring and discrete log algorithms, proceed by reduction to a hidden subgroup problem, in which a subgroup H of a group G must be determined from a quantum state y uniformly supported…
We consider the problem of determining the state of a quantum system given one or more readings of the expectation value of an observable. The system is assumed to be a finite dimensional quantum control system for which we can influence…
We consider a natural generalization of an abelian Hidden Subgroup Problem where the subgroups and their cosets correspond to graphs of linear functions over a finite field F with d elements. The hidden functions of the generalized problem…
A quantum algorithm is a set of instructions for a quantum computer, however, unlike algorithms in classical computer science their results cannot be guaranteed. A quantum system can undergo two types of operation, measurement and quantum…
Extracting information from quantum devices has long been a crucial problem in the field of quantum mechanics. By performing elaborate measurements, quantum state tomography, an important and fundamental tool in quantum science and…
Motivated by the need to uncover some underlying mathematical structure of optimal quantum computation, we carry out a systematic analysis of a wide variety of quantum algorithms from the majorization theory point of view. We conclude that…
To accelerate the algorithms for the dihedral hidden subgroup problem, we present a new algorithm based on algorithm SV(shortest vector). A subroutine is given to get a transition quantum state by constructing a phase filter function, then…
We employ concepts and tools from the theory of finite permutation groups in order to analyse the Hidden Subgroup Problem via Quantum Fourier Sampling (QFS) for the symmetric group. We show that under very general conditions both the weak…
We address the problem of distinguishing among a finite collection of quantum states, when the states are not entirely known. For completely specified states, necessary and sufficient conditions on a quantum measurement minimizing the…
Motivated by a connection, described here for the first time, between the hidden normal subgroup problem (HNSP) and abelian hypergroups (algebraic objects that model collisions of physical particles), we develop a stabilizer formalism using…
A fast quantum search algorithm for continuous variables is presented. The result is the quantum continuous variable analog of Grover's algorithm originally proposed for qubits. A continuous variable analog of the Hadamard (i.e., Fourier…
The arguments given in this paper suggest that Grover's and Shor's algorithms are more closely related than one might at first expect. Specifically, we show that Grover's algorithm can be viewed as a quantum algorithm which solves a…
We present a quantum algorithm for solving the hidden subgroup problem in the general linear group over a finite field where the hidden subgroup is promised to be a conjugate of the group of the invertible lower triangular matrices. The…