Related papers: Classical and Quantum Annealing in the Median of T…
We determine the complexity of several constraint satisfaction problems using the quantum adiabatic algorithm in its simplest implementation. We do so by studying the size dependence of the gap to the first excited state of "typical"…
Classical satisfiability (SAT) and quantum satisfiability (QSAT) are complete problems for the complexity classes NP and QMA which are believed to be intractable for classical and quantum computers, respectively. Statistical ensembles of…
We consider a classical and superadiabatic version of an iterative quantum adiabatic algorithm to solve combinatorial optimization problems. This algorithm is deterministic because it is based on purely classical dynamics, that is, it does…
In this paper we show that the performance of the quantum adiabatic algorithm is determined by phase transitions in underlying problem in the presence of transverse magnetic field $\Gamma$. We show that the quantum version of random…
Adiabatic quantum computers can solve difficult optimization problems (e.g., the quadratic unconstrained binary optimization problem), and they seem well suited to train machine learning models. In this paper, we describe an adiabatic…
An adiabatic quantum algorithm is essentially given by three elements: An initial Hamiltonian with known ground state, a problem Hamiltonian whose ground state corresponds to the solution of the given problem and an evolution schedule such…
We compare classical and quantum query complexities of total Boolean functions. It is known that for worst-case complexity, the gap between quantum and classical can be at most polynomial. We show that for average-case complexity under the…
Quantum annealing is a contender to solve combinatorial optimization problems based on quantum dynamics. While significant efforts have been undertaken to investigate the quality of the solutions and the required runtimes, much less…
Quantum annealing (QA) has the potential to significantly improve solution quality and reduce time complexity in solving combinatorial optimization problems compared to classical optimization methods. However, due to the limited number of…
We give a quantum algorithm for solving instances of the satisfiability problem, based on adiabatic evolution. The evolution of the quantum state is governed by a time-dependent Hamiltonian that interpolates between an initial Hamiltonian,…
Designing quantum algorithms with a speedup over their classical analogs is a central challenge in quantum information science. Motivated by recent experimental observations of a superlinear quantum speedup in solving the Maximum…
Adiabatic quantum optimization offers a new method for solving hard optimization problems. In this paper we calculate median adiabatic times (in seconds) determined by the minimum gap during the adiabatic quantum optimization for an NP-hard…
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…
In a recent study (Ref. [1]), quantum annealing was reported to exhibit a scaling advantage for approximately solving Quadratic Unconstrained Binary Optimization (QUBO). However, this claim critically depends on the choice of classical…
Understanding how classical physics emerges from quantum mechanics remains a central problem in the foundations of physics. Here we derive a classical limit from finite-resolution measurements, modeled by continuous coarse-grained POVMs.…
Using a recently constructed ensemble of hard 2SAT realizations, that has a unique ground-state we calculate for the quantized theory the median gap correlation length values $\xi_{GAP}$ along the direction of the quantum adiabatic control…
The utility of satisfiability (SAT) as an application focused hard computational problem is well established. We explore the potential of quantum annealing to enhance classical SAT solving, especially where sampling from the space of all…
Quantum k-SAT is the problem of deciding whether there is a n-qubit state which is perpendicular to a set of vectors, each of which lies in the Hilbert space of k qubits. Equivalently, the problem is to decide whether a particular type of…
We construct a set of instances of 3SAT which are not solved efficiently using the simplest quantum adiabatic algorithm. These instances are obtained by picking random clauses all consistent with two disparate planted solutions and then…
Quantum computers use quantum resources to carry out computational tasks and may outperform classical computers in solving certain computational problems. Special-purpose quantum computers such as quantum annealers employ quantum adiabatic…