Related papers: Optimal parametrizations of adiabatic paths
Motivated by the need to uncover some underlying mathematical structure of optimal quantum computation, we carry out a systematic analysis of a wide variety of quantum algorithms from the majorization theory point of view. We conclude that…
Optimization is finding the best solution, which mathematically amounts to locating the global minimum of some cost function. Optimization is traditionally automated with digital or quantum computers, each having their limitations and none…
We introduce an algorithm to perform an optimal adiabatic evolution that operates without an apriori knowledge of the system spectrum. By probing the system gap locally, the algorithm maximizes the evolution speed, thus minimizing the total…
We present a bound on the length of the path defined by the ground states of a continuous family of Hamiltonians in terms of the spectral gap G. We use this bound to obtain a significant improvement over the cost of recently proposed…
Big Data is characterized by Volume, Velocity, Veracity and Complexity. The interaction between this huge data is complex with an associated free will having dynamic and non linear nature. We reduced big data based on its characteristics,…
Numerous problems of both theoretical and practical interest are related to finding shortest (or otherwise optimal) paths in networks, frequently in the presence of some obstacles or constraints. A somewhat related class of problems focuses…
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 decompose the quantum adiabatic evolution as the products of gauge invariant unitary operators and obtain the exact nonadiabatic correction in the adiabatic approximation. A necessary and sufficient condition that leads to adiabatic…
We point out that, when an optimization problem has more than one solution, the quantum adiabatic algorithms (QAA) encounter topological obstructions leading to adiabatic spectral flows where spectral branches unavoidably traverse the…
Environmental noise can enhance transport, an effect known as environmental noise-assisted quantum transport. Most theoretical studies focus on optimizing system parameters under spatially uniform system-environment coupling. Here, instead,…
In this paper the computational challenges of time-optimal path following are addressed. The standard approach is to minimize the travel time, which inevitably leads to singularities at zero path speed, when reformulating the optimization…
One of the significant breakthroughs in quantum computation is Grover's algorithm for unsorted database search. Recently, the applications of Grover's algorithm to solve global optimization problems have been demonstrated, where unknown…
Adiabatic quantum optimization has been proposed as a route to solve NP-complete problems, with a possible quantum speedup compared to classical algorithms. However, the precise role of quantum effects, such as entanglement, in these…
It is believed that the presence of anticrossings with exponentially small gaps between the lowest two energy levels of the system Hamiltonian, can render adiabatic quantum optimization inefficient. Here, we present a simple adiabatic…
A computation in adiabatic quantum computing is implemented by traversing a path of nondegenerate eigenstates of a continuous family of Hamiltonians. We introduce a method that traverses a discretized form of the path: At each step we apply…
Adiabatic quantum computing is a general framework for preparing eigenstates of Hamiltonians on quantum devices. However, its digital implementation requires an efficient Hamiltonian simulation subroutine, which may introduce extra…
Adiabatic quantum optimization has attracted a lot of attention because small scale simulations gave hope that it would allow to solve NP-complete problems efficiently. Later, negative results proved the existence of specifically designed…
For systems in an externally controllable time-dependent potential, the optimal protocol minimizes the mean work spent in a finite-time transition between given initial and final values of a control parameter. For an initially thermalized…
We explore the role of entanglement in adiabatic quantum optimization by performing approximate simulations of the real-time evolution of a quantum system while limiting the amount of entanglement. To classically simulate the time evolution…
A condition on the Hamiltonian of a time-dependent quantum mechanical system is derived which, if satisfied, implies optimal adiabaticity (defined below). The condition is expressed in terms of the Hamiltonian and in terms of the evolution…