Related papers: Quantum algorithm for doubling the amplitude of th…
This work presents Quantum Adaptive Search (QAGS), a hybrid quantum-classical algorithm for the global optimization of multivariate functions. The method employs an adaptive mechanism that dynamically narrows the search space based on a…
We give a dimension independent formulation of the quantum search algorithm introduced in [L. K. Grover, Phys. Rev. Lett. {\bf 79}, 325 (1997)]. This algorithm provides a quadratic gain when compared to its classical counterpart by…
Fundamental matrix operations and solving linear systems of equations are ubiquitous in scientific investigations. Using the "Sender-Receiver" model, we propose quantum algorithms for matrix operations such as matrix-vector product,…
In general, a quantum algorithm wants to avoid decoherence or perturbation, since such factors may cause errors in the algorithm. In this letter, we will supply the answer to the interesting question: can the factors seemingly harmful to a…
Quantum computation appears to offer significant advantages over classical computation and this has generated a tremendous interest in the field. In this thesis we consider the application of quantum computers to scientific computing and…
We prove that the generic quantum speedups for brute-force search and counting only hold when the process we apply them to can be efficiently inverted. The algorithms speeding up these problems, amplitude amplification and amplitude…
Quantum algorithms offer significant speedups over their classical counterparts for a variety of problems. The strongest arguments for this advantage are borne by algorithms for quantum search, quantum phase estimation, and Hamiltonian…
Solving linear systems of equations is a common problem that arises both on its own and as a subroutine in more complex problems: given a matrix A and a vector b, find a vector x such that Ax=b. We consider the case where one doesn't need…
We present a continuous time quantum search algorithm analogous to Grover's. In particular, the optimal search time for this algorithm is proportional to $\sqrt{N}$, where $N$ is the database size. This search algorithm can be implemented…
This paper focuses on the quantum amplitude estimation algorithm, which is a core subroutine in quantum computation for various applications. The conventional approach for amplitude estimation is to use the phase estimation algorithm, which…
The field of quantum algorithms aims to find ways to speed up the solution of computational problems by using a quantum computer. A key milestone in this field will be when a universal quantum computer performs a computational task that is…
We study quantum algorithms working on classical probability distributions. We formulate four different models for accessing a classical probability distribution on a quantum computer, which are derived from previous work on the topic, and…
The advantages of quantum information processing are in many cases obtained as consequences of quantum interactions, especially for computational tasks where two-qubit interactions are essential. In this work, we establish the framework of…
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…
This extended abstract reports on on-going research on quantum algorithmic approaches to the problem of generalised tree search that may exhibit effective quantum speedup, even in the presence of non-constant branching factors. Two…
It is suggested that the individual outcomes of a measurement process can be understood within standard quantum mechanics in terms of the measuring apparatus, treated as a quantum computer, executing Grover's search algorithm.
We theoretically and experimentally investigate conditional enhancement of overall coherence of quantum states by probabilistic quantum operations that apply to the input state a quantum filter diagonal in the basis of incoherent states. We…
We present an algorithm to compute the number of solutions of the (constrained) number partitioning problem. A concrete implementation of the algorithm on an Ising-type quantum computer is given.
The structure of satisfiability problems is used to improve search algorithms for quantum computers and reduce their required coherence times by using only a single coherent evaluation of problem properties. The structure of random k-SAT…
We recast Grover's generalised search algorithm in a geometric language even when the states are not approximately orthogonal. We provide a possible search algorithm based on an arbitrary unitary transformation which can speed up the steps…