Related papers: Adiabatic quantum computation: Enthusiast and Scep…
We introduce a simple framework for estimating lower bounds on the runtime of a broad class of adiabatic quantum algorithms. The central formula consists of calculating the variance of the final Hamiltonian with respect to the initial…
Adiabatic quantum computation (AQC) is a promising counterpart of universal quantum computation, based on the key concept of quantum annealing (QA). QA is claimed to be at the basis of commercial quantum computers and benefits from the fact…
The quantum adiabatic theorem ensures that a slowly changing system, initially prepared in its ground state, will evolve to its final ground state with arbitrary precision. As a first result this thesis extends the original theorem to…
We provide rigorous bounds for the error of the adiabatic approximation of quantum mechanics under four sources of experimental error: perturbations in the initial condition, systematic time-dependent perturbations in the Hamiltonian,…
We study quantum annealing for combinatorial optimization with Hamiltonian $H = z H_f + H_0$ where $H_f$ is diagonal, $H_0=-|\phi \rangle \langle \phi|$ is the equal superposition state projector and $z$ the annealing parameter. We…
We present two new continuous time quantum search algorithms similar to the adiabatic search algorithm, but now without an adiabatic evolution. We find that both algorithms work for a wide range of values of the parameters of the…
Application of the adiabatic model of quantum computation requires efficient encoding of the solution to computational problems into the lowest eigenstate of a Hamiltonian that supports universal adiabatic quantum computation. Experimental…
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…
Quantum annealing is a continuous-time heuristic quantum algorithm for solving or approximately solving classical optimization problems. The algorithm uses a schedule to interpolate between a driver Hamiltonian with an easy-to-prepare…
The short-path quantum algorithm introduced by Hastings (Quantum 2018, 2019) is a variant of adiabatic quantum algorithms that enables an easier worst-case analysis by avoiding the need to control the spectral gap along a long adiabatic…
Adiabatic quantum algorithms represent a promising approach to universal quantum computation. Whilst in a closed system these algorithms are limited by avoided level crossings, where the gap becomes exponentially small in the system size,…
The quantum adiabatic unstructured search algorithm is one of only a handful of quantum adiabatic optimization algorithms to exhibit provable speedups over their classical counterparts. With no fault tolerance theorems to guarantee the…
Planning energy production is a challenging task due to its cost-sensitivity, fast-moving energy markets, uncertainties in demand, and technical constraints of power plants. Thus, more complex models of this so-called \emph{unit commitment…
We show how to perform universal Hamiltonian and adiabatic computing using a time-independent Hamiltonian on a 2D grid describing a system of hopping particles which string together and interact to perform the computation. In this…
We report on a detailed analysis of generalization of the local adiabatic search algorithm. Instead of evolving directly from an initial ground state Hamiltonian to a solution Hamiltonian a different evolution path is introduced and is…
Adiabatic quantum optimization is a procedure to solve a vast class of optimization problems by slowly changing the Hamiltonian of a quantum system. The evolution time necessary for the algorithm to be successful scales inversely with the…
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…
Linear system solvers are widely used in scientific computing, with the primary goal of solving linear system problems. Classical iterative algorithms typically rely on the conjugate gradient method. The rise of quantum computing has…
The digital version of adiabatic quantum computing enhanced by counterdiabatic driving, known as digitized counterdiabatic quantum computing, has emerged as a paradigm that opens the door to fast and low-depth algorithms. In this work, we…
Nonadiabatic holonomic quantum computation (NHQC) provides a method to implement error resilient gates and that has attracted considerable attention recently. Since it was proposed, three-level {\Lambda} systems have become the typical…