Related papers: Quantum algorithms for systems of linear equations…
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…
In quantum adiabatic algorithm, as the adiabatic parameter $s(t)$ changes slowly from zero to one with finite rate, a transition to excited states inevitably occurs and this induces an intrinsic computational error. We show that this…
Adiabatic quantum computation provides an alternative approach to quantum computation using a time-dependent Hamiltonian. The time evolution of entanglement during the adiabatic quantum search algorithm is studied, and its relevance as a…
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…
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…
The discrete formulation of adiabatic quantum computing is compared with other search methods, classical and quantum, for random satisfiability (SAT) problems. With the number of steps growing only as the cube of the number of variables,…
This thesis investigates quantum algorithms for eigenstate preparation, with a focus on solving eigenvalue problems such as the Schrodinger equation by utilizing near-term quantum computing devices. These problems are ubiquitous in several…
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…
Adiabatic state preparation provides an analytical solution for generating the ground state of a target Hamiltonian, starting from an easily prepared ground state of the initial Hamiltonian. While effective for time-dependent Hamiltonians…
Many quantum algorithms, such as adiabatic algorithms (e.g. AQC) and phase randomisation, require simulating Hamiltonian evolution. In addition, the simulation of physical systems is an important objective in its own right. In many cases,…
In this review we consider the performance of the quantum adiabatic algorithm for the solution of decision problems. We divide the possible failure mechanisms into two sets: small gaps due to quantum phase transitions and small gaps due to…
We present a quantum adiabatic algorithm for a set of quantum 2-satisfiability (Q2SAT) problem, which is a generalization of 2-satisfiability (2SAT) problem. For a Q2SAT problem, we construct the Hamiltonian which is similar to that of a…
We assess the prospects for algorithms within the general framework of quantum annealing (QA) to achieve a quantum speedup relative to classical state of the art methods in combinatorial optimization and related sampling tasks. We argue for…
Exploiting the similarity between adiabatic quantum algorithms and quantum phase transitions, we argue that second-order transitions -- typically associated with broken or restored symmetries -- should be advantageous in comparison to…
We introduce the idea of using adiabatic rotation to generate superpositions of a large class of quantum states. For quantum computing this is an interesting alternative to the well-studied "straight line" adiabatic evolution. In ways that…
Solving linear systems of equations is essential for many problems in science and technology, including problems in machine learning. Existing quantum algorithms have demonstrated the potential for large speedups, but the required quantum…
In this paper, we study two different nonlinear interpolating paths in adiabatic evolution algorithms for solving a particular class of quantum search problems where both the initial and final Hamiltonian are one-dimensional projector…
The propagation of errors severely compromises the reliability of quantum computations. The quantum adiabatic algorithm is a physically motivated method to prepare ground states of classical and quantum Hamiltonians. Here, we analyze the…
We present an adaptive variational quantum algorithm to estimate the Berry phase accumulated by a nondegenerate ground state under cyclic, adiabatic evolution of a time-dependent Hamiltonian. Our method leverages cyclic adiabatic evolution…
Adiabatic quantum programming defines the time-dependent mapping of a quantum algorithm into an underlying hardware or logical fabric. An essential step is embedding problem-specific information into the quantum logical fabric. We present…