Related papers: Adiabatic based Algorithm for SAT: a comprehensive…
The system undergoes adiabatic evolution when its population in the instantaneous eigenbasis of its time-dependent Hamiltonian changes only negligibly. Realization of such dynamics requires slow-enough changes of the parameters of the…
Adiabatic quantum computation is a paradigmatic model aiming to solve a computational problem by finding the many-body ground state encapsulating the solution. However, its use of an adiabatic evolution depending on the spectral gap of an…
We analyze the performance of adiabatic quantum computation (AQC) under the effect of decoherence. To this end, we introduce an inherently open-systems approach, based on a recent generalization of the adiabatic approximation. In contrast…
The consistency of quantum adiabatic theorem has been doubted recently. It is shown in the present paper that the difference between the adiabatic solution and the exact solution to the Schrodinger equation with a slowly changing driving…
Fixed-point quantum search algorithms succeed at finding one of $M$ target items among $N$ total items even when the run time of the algorithm is longer than necessary. While the famous Grover's algorithm can search quadratically faster…
We present an analog version of the quantum approximate optimization algorithm suitable for current quantum annealers. The central idea of this algorithm is to optimize the schedule function, which defines the adiabatic evolution. It is…
In this work we present a quantum algorithm for multiobjective combinatorial optimization. We show how to map a convex combination of objective functions onto a Hamiltonian and then use that Hamiltonian to prove that the quantum adiabatic…
We review the quantum adiabatic approximation for closed systems, and its recently introduced generalization to open systems (M.S. Sarandy and D.A. Lidar, e-print quant-ph/0404147). We also critically examine a recent argument claiming that…
The viability of adiabatic quantum computation depends on the slow evolution of the Hamiltonian. The adiabatic switching theorem provides an asymptotic series for error estimates in $1/T$, based on the lowest non-zero derivative of the…
The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a…
Quantum optimization is the most mature quantum computing technology to date, providing a promising approach towards efficiently solving complex combinatorial problems. Methods such as adiabatic quantum computing (AQC) have been employed in…
Analog models of quantum information processing, such as adiabatic quantum computation and analog quantum simulation, require the ability to subject a system to precisely specified Hamiltonians. Unfortunately, the hardware used to implement…
We investigate the performance of a quantum algorithm for solving classical 3-SAT problems. A cycle of post-selected measurements drives the computer's register monotonically toward a steady state which is correlated to the classical…
We present a new adiabatic quantum algorithm for searching over structured databases. The new algorithm is optimized using a simplified complexity analysis.
We derive a version of the adiabatic theorem that is especially suited for applications in adiabatic quantum computation, where it is reasonable to assume that the adiabatic interpolation between the initial and final Hamiltonians is…
We discuss in this chapter the basics of adiabatic computation, as well as some physical implementations. After a short introduction of the quantum circuit model, we describe quantum adiabatic computation, quantum annealing, and the strong…
In this work, we attempt to solve the integer-weight knapsack problem using the D-Wave 2000Q adiabatic quantum computer. The knapsack problem is a well-known NP-complete problem in computer science, with applications in economics, business,…
A pivotal task for quantum computing is to speed up solving problems that are both classically intractable and practically valuable. Among these, combinatorial optimization problems have attracted tremendous attention due to their broad…
Adiabatic reverse annealing (ARA) has been proposed as an improvement to conventional quantum annealing for solving optimization problems, in which one takes advantage of an initial guess at the solution to suppress problematic phase…
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…