Related papers: Hybrid Quantum-Classical Search Algorithms
In this work, we present a multi-layer quantum search method that generates an exponential speedup of the standard Grover's algorithm. As direct applications, any NP problems can be solved efficiently on a quantum circuit with only…
The expectations arising from the latest achievements in the quantum computing field are causing that researchers coming from classical artificial intelligence to be fascinated by this new paradigm. In turn, quantum computing, on the road…
The search for "a quantum needle in a quantum haystack" is a metaphor for the problem of finding out which one of a permissible set of unitary mappings---the oracles---is implemented by a given black box. Grover's algorithm solves this…
Optimizing high-degree of freedom robotic manipulators requires searching complex, high-dimensional configuration spaces, a task that is computationally challenging for classical methods. This paper introduces a quantum native framework…
We consider the problem of search of an unstructured list for a marked element, when one is given advice as to where this element might be located, in the form of a probability distribution. The goal is to minimise the expected number of…
Although quantum computers are predicted to have many commercial applications, less attention has been given to their potential for resolving foundational issues in quantum mechanics. Here we focus on quantum computers' utility for the…
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…
Quantum computing is a winsome field that concerns with the behaviour and nature of energy at the quantum level to improve the efficiency of computations. In recent years, quantum computation is receiving much attention for its capability…
We compare classical and quantum query complexities of total Boolean functions. It is known that for worst-case complexity, the gap between quantum and classical can be at most polynomial. We show that for average-case complexity under the…
This paper presented two general quantum search algorithms. We derived the iterated formulas and the simpler approximate formulas and the precise formula for the amplitude in the desired state. A mathematical proof of Grover's algorithm…
Achieving high-quality solutions faster than classical solvers on computationally hard problems is a challenge for quantum optimization to deliver utility. Using a superconducting quantum computer, we experimentally investigate the…
In this work I describe a classical analog of Grover's quantum searching algorithm, explaining why a quantum algorithm should be able to perform search in O(sqrtN) steps and also acting as a useful pedagogic demonstration.
We consider classical and quantum algorithms which have a duality property: roughly, either the algorithm provides some nontrivial improvement over random or there exist many solutions which are significantly worse than random. This enables…
Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time…
Grover's algorithm is one of the pioneering demonstrations of the advantages of quantum computing over its classical counterpart, providing - at most - a quadratic speed-up over the classical solution for unstructured database search. The…
An essential component of many sophisticated metaheuristics for solving combinatorial optimization problems is some variation of a local search routine that iteratively searches for a better solution within a chosen set of immediate…
The difference between classical and quantum algorithms (QA) is following: problem solved by QA is coded in the structure of the quantum operators. Input to QA in this case is always the same. Output of QA says which problem coded. In some…
We discuss quantum algorithms that calculate numerical integrals and descriptive statistics of stochastic processes. With either of two distinct approaches, one obtains an exponential speed increase in comparison to the fastest known…
Primitive polynomials over finite fields are crucial for various domains of computer science, including classical pseudo-random number generation, coding theory and post-quantum cryptography. Nevertheless, the pursuit of an efficient…
Quantum search algorithms are considered in the context of protein sequence comparison in biocomputing. Given a sample protein sequence of length m (i.e m residues), the problem considered is to find an optimal match in a large database…