Related papers: (Sub)Exponential Quantum Speedup for Optimization
We propose a method to speed up the quantum adiabatic algorithm using catalysis by many-body delocalization. This is applied to random-field antiferromagnetic Ising spin models. The algorithm is catalyzed in such a way that the evolution…
Grover's algorithm is one of the most important quantum algorithms, which performs the task of searching an unsorted database without a priori probability. Recently the adiabatic evolution has been used to design and reproduce quantum…
Topological quantum information processing relies on adiabatic braiding of nonabelian quasiparticles. Performing the braiding operations in finite time introduces transitions out of the ground-state manifold and deviations from the…
We provide and analyze examples that counter the widely made claim that tunneling is needed for a quantum speedup in optimization problems. The examples belong to the class of perturbed Hamming-weight optimization problems. In one case,…
Optimization problems in disciplines such as machine learning are commonly solved with iterative methods. Gradient descent algorithms find local minima by moving along the direction of steepest descent while Newton's method takes into…
Adiabatic quantum computation has recently attracted attention in the physics and computer science communities, but its computational power was unknown. We describe an efficient adiabatic simulation of any given quantum algorithm, which…
We study to what extent quantum algorithms can speed up solving convex optimization problems. Following the classical literature we assume access to a convex set via various oracles, and we examine the efficiency of reductions between the…
Recent work has shown that quantum annealing for machine learning, referred to as QAML, can perform comparably to state-of-the-art machine learning methods with a specific application to Higgs boson classification. We propose QAML-Z, a…
We introduce an approach for quantum computing in continuous time based on the Lewis-Riesenfeld dynamic invariants. This approach allows, under certain conditions, for the design of quantum algorithms running on a nonadiabatic regime. We…
In this paper, we identify a family of nonconvex continuous optimization instances, each $d$-dimensional instance with $2^d$ local minima, to demonstrate a quantum-classical performance separation. Specifically, we prove that the recently…
Grover's unstructured search algorithm is one of the best examples to date for the superiority of quantum algorithms over classical ones. Its applicability, however, has been questioned by many due to its oracular nature. We propose a…
Variational quantum algorithms dominate contemporary gate-based quantum enhanced optimisation, eigenvalue estimation and machine learning. Here we establish the quantum computational universality of variational quantum computation by…
The Quantum Approximate Optimization Algorithm (QAOA) is designed to run on a gate model quantum computer and has shallow depth. It takes as input a combinatorial optimization problem and outputs a string that satisfies a high fraction of…
We show that, during adiabatic evolution, any changes in entanglement can be attributed to a succession of avoided energy level crossings at which eigenvalues swap their eigenvectors. These swaps mediate the generation and redistribution of…
One of the main aims in the field of quantum simulation is to achieve a quantum speedup, often referred to as "quantum computational supremacy", referring to the experimental realization of a quantum device that computationally outperforms…
We analyze the performance of quantum annealing as a heuristic optimization method to find the absolute minimum of various continuous models, including landscapes with only two wells and also models with many competing minima and with…
Stochastic Gradient Descent (SGD) and its variants underpin modern machine learning by enabling efficient optimization of large-scale models. However, their local search nature limits exploration in complex landscapes. In this paper, we…
Among various algorithms designed to exploit the specific properties of quantum computers with respect to classical ones, the quantum adiabatic algorithm is a versatile proposition to find the minimal value of an arbitrary cost function…
Quantum adiabatic algorithm is a method of solving computational problems by evolving the ground state of a slowly varying Hamiltonian. The technique uses evolution of the ground state of a slowly varying Hamiltonian to reach the required…
Genetic algorithms have unique properties which are useful when applied to black box optimization. Using selection, crossover, and mutation operators, candidate solutions may be obtained without the need to calculate a gradient. In this…