Related papers: Simulated Quantum Computation of Global Minima
We present a quantum algorithm that has rigorous runtime guarantees for several families of binary optimization problems, including Quadratic Unconstrained Binary Optimization (QUBO), Ising spin glasses ($p$-spin model), and $k$-local…
We study the limit computability of finding a global optimum of a continuous function. We give a short proof to show that the problem of checking whether a point is a global minimum is not limit computable. Thereby showing the same for the…
We consider the Grover search algorithm implementation for a quantum register of size $N = 2^k$ using k (or k +1) microwave- and laser-driven Rydberg-blockaded atoms, following the proposal by M{\o}lmer, Isenhower, and Saffman [J. Phys. B…
In the last decade, public and industrial research funding has moved quantum computing from the early promises of Shor's algorithm through experiments to the era of noisy intermediate scale quantum devices (NISQ) for solving real-world…
The quantum basin hopping algorithm for continuous global optimisation combines a local search with Grover's algorithm, and can locate the global optimum using effort proportional to the square root of the number of basins. This article…
We build a quantum algorithm which uses the Grover quantum search procedure in order to sample the exact equilibrium distribution of a wide range of classical statistical mechanics systems. The algorithm is based on recently developed exact…
We propose a simple design of a quantum electron microscope that ``queries'' a beam-sensitive phase object, such as a biological specimen, as part of quantum computation. Lower quantum query complexity, not the time complexity, of a quantum…
Finding a minimum is an essential part of mathematical models, and it plays an important role in some optimization problems. Durr and Hoyer proposed a quantum searching algorithm (DHA), with a certain probability of success, to achieve…
The Grover search algorithm is a pivotal advancement in quantum computing, promising a remarkable speedup over classical algorithms in searching unstructured large databases. Here, we report results for the implementation and…
A new algorithm for one-dimensional minimization is described in detail and the results of some tests on practical cases are reported and illustrated. The method requires only punctual computation of the function, and is suitable to be…
A novel class of hybrid quantum-classical algorithms based on the variational approach have recently emerged from separate proposals addressing, for example, quantum chemistry and combinatorial problems. These algorithms provide an…
We report the experimental implementation of Grover's quantum search algorithm on a quantum computer with three quantum bits. The computer consists of molecules of $^{13}$C-labeled CHFBr$_2$, in which the three weakly coupled spin-1/2…
This paper presents a global optimization approach to quantum mechanics, which describes the most fundamental dynamics of the universe. It suggests that the wave-like behavior of (sub)atomic particles could be the critical characteristic of…
We propose a novel quantum algorithm for solving linear optimization problems by quantum-mechanical simulation of the central path. While interior point methods follow the central path with an iterative algorithm that works with successive…
A construction is given for simulating any deterministic finite state machine (FSM) on a quantum computer in a space-efficient manner. By constructing a superposition of input strings of lengths K or less, questions can be asked about the…
We study the problem of designing worst-case to average-case reductions for quantum algorithms. For all linear problems, we provide an explicit and efficient transformation of quantum algorithms that are only correct on a small (even…
We present a novel use case for quantum computation: the sensitivity analysis for a risk model used at Deutsche B\"orse Group. Such an analysis is computationally too expensive to perform on classical computers. We show in detail how the…
We present a quantum algorithm that additively approximates the value of a tensor network to a certain scale. When combined with existing results, this provides a complete problem for quantum computation. The result is a simple new way of…
Grover's search algorithm is the cornerstone of many applications of quantum computing, providing a quadratic speed-up over classical methods. One limitation of the algorithm is that it requires knowledge of the number of solutions to…
Grover's search algorithm can be applied to a wide range of problems; even problems not generally regarded as searching problems, can be reformulated to take advantage of quantum parallelism and entanglement, and lead to algorithms which…