Related papers: Quantum search by partial adiabatic evolution
We introduce an algorithm for combinatorial search on quantum computers that is capable of significantly concentrating amplitude into solutions for some NP search problems, on average. This is done by exploiting the same aspects of problem…
In classical computing, analog approaches have sometimes appeared to be more powerful than they really are. This occurs when resources, particularly precision, are not appropriately taken into account. While the same should also hold for…
Quantum computation has emerged as a powerful computational medium of our time, having demonstrated the remarkable efficiency in factoring a positive integer and searching databases faster than any currently known classical computing…
Advances in quantum algorithms suggest a tentative scaling advantage on certain combinatorial optimization problems. Recent work, however, has also reinforced the idea that barren plateaus render variational algorithms ineffective on large…
In this paper, we will define a quantum operator that performs the inversion about the mean only on a subspace of the system (Partial Diffusion Operator). This operator is used in a quantum search algorithm that runs in O(sqrt{N/M}) for…
We introduce an iterative method to search for time-optimal Hamiltonians that drive a quantum system between two arbitrary, and in general mixed, quantum states. The method is based on the idea of progressively improving the efficiency of…
A proof of the adiabatic theorem for quantum systems whose time evolution proceeds along discrete time, e.g., quantum maps and quantum circuits, is shown.
We design an adiabatic quantum algorithm for the counting problem, i.e., approximating the proportion, $\alpha$, of the marked items in a given database. As the quantum system undergoes a designed cyclic adiabatic evolution, it acquires a…
We solve a problem, which while not fitting into the usual paradigm, can be viewed as a quantum computation. Suppose we are given a quantum system described by an N dimensional Hilbert space with a Hamiltonian of the form $E |w >< w|$ where…
Quantum annealing is guaranteed to find the ground state of optimization problems in the adiabatic limit. Recent work [Phys. Rev. X 6, 031010 (2016)] has found that for some barrier tunneling problems, quantum annealing can be run much…
We present an adiabatic quantum algorithm for the abstract problem of searching marked vertices in a graph, or spatial search. Given a random walk (or Markov chain) $P$ on a graph with a set of unknown marked vertices, one can define a…
A quantum algorithm for combinatorial search is presented that provides a simple framework for utilizing search heuristics. The algorithm is evaluated in a new case that is an unstructured version of the graph coloring problem. It performs…
It has recently been shown that starting with a classical query algorithm (decision tree) and a guessing algorithm that tries to predict the query answers, we can design a quantum algorithm with query complexity $O(\sqrt{GT})$ where $T$ is…
Quantum annealing (QA) is one of the ways to search the ground state of the problem Hamiltonian. Here, we propose the QA scheme to search arbitrary excited states of the problem Hamiltonian. In our scheme, an $n$-th excited state of the…
In the typical model, a discrete-time coined quantum walk searching the 2D grid for a marked vertex achieves a success probability of $O(1/\log N)$ in $O(\sqrt{N \log N})$ steps, which with amplitude amplification yields an overall runtime…
The two main approaches to quantum computing are gate-based computation and analog computation, which are polynomially equivalent in terms of complexity, and they are often seen as alternatives to each other. In this work, we present a…
In this paper we show that the performance of the quantum adiabatic algorithm is determined by phase transitions in underlying problem in the presence of transverse magnetic field $\Gamma$. We show that the quantum version of random…
We have developed a non-unitary extension of Grover's search algorithm by changing the hidden geometry of Hilbert space carried by diffusion operator. Our algorithm finds the solution for search problem by performing a unique bigger…
In this work we propose an approach for implementing time-evolution of a quantum system using product formulas. The quantum algorithms we develop have provably better scaling (in terms of gate complexity and circuit depth) than a naive…
This article introduces quantum computation by analogy with probabilistic computation. A basic description of the quantum search algorithm is given by representing the algorithm as a C program in a novel way.