Related papers: Faster than Classical Quantum Algorithm for dense …
The problem Hamiltonian of the adiabatic quantum algorithm for the maximum-weight independent set problem (MIS) that is based on the reduction to the Ising problem (as described in [Choi08]) has flexible parameters. We show that by choosing…
In the past decade quantum algorithms have been found which outperform the best classical solutions known for certain classical problems as well as the best classical methods known for simulation of certain quantum systems. This suggests…
We construct an oracular (i.e., black box) problem that can be solved exponentially faster on a quantum computer than on a classical computer. The quantum algorithm is based on a continuous time quantum walk, and thus employs a different…
A local search algorithm solving an NP-complete optimisation problem can be viewed as a stochastic process moving in an 'energy landscape' towards eventually finding an optimal solution. For the random 3-satisfiability problem, the…
We describe a general method to obtain quantum speedups of classical algorithms which are based on the technique of backtracking, a standard approach for solving constraint satisfaction problems (CSPs). Backtracking algorithms explore a…
Along with the development of quantum technology, finding useful applications of quantum computers has been a central pursuit. Despite various quantum algorithms have been developed, many of them often require strong input assumptions,…
A quantum algorithm is proposed to solve the Satisfiability problems by the ground-state quantum computer. The scale of the energy gap of the ground-state quantum computer is analyzed for the 3-bit Exact Cover problem. The time cost of this…
The Maximum Satisfiability (MaxSAT) problem is the problem of finding a truth assignment that maximizes the number of satisfied clauses of a given Boolean formula in Conjunctive Normal Form (CNF). Many exact solvers for MaxSAT have been…
Recent research has demonstrated that quantum computers can solve certain types of problems substantially faster than the known classical algorithms. These problems include factoring integers and certain physics simulations. Practical…
Constraint satisfiability problems, crucial to several applications, are solved on a quantum computer using Grover's search algorithm, leading to a quadratic improvement over the classical case. The solutions are obtained with high…
We explore the possibility of accelerating the formal verification of classical programs with a quantum computer. A common source of security flaws stems from the existence of common programming errors like use after free, null-pointer…
Many computational problems are subject to a quantum speed-up: one might find that a problem having an O(n^3)-time or O(n^2)-time classic algorithm can be solved by a known O(n^1.5)-time or O(n)-time quantum algorithm. The question…
Simon's problem plays an important role in the history of quantum algorithms, as it inspired Shor to discover the celebrated quantum algorithm solving integer factorization in polynomial time. Besides, the quantum algorithm for Simon's…
A common way of solving satisfiability instances with quantum methods is to transform these instances into instances of QUBO, which in itself is a potentially difficult and expensive task. State-of-the-art transformations from MAX-3SAT to…
Optimization problems in finance, physics and computer science are typically very hard to tackle in classical computing and quantum computing could help speed up computations and provide efficient methods for tackling large problems.…
Recent works have shown that quantum computers can polynomially speed up certain SAT-solving algorithms even when the number of available qubits is significantly smaller than the number of variables. Here we generalise this approach. We…
The remarkable achievements of machine learning techniques in analyzing discrete structures have drawn significant attention towards their integration into combinatorial optimization algorithms. Typically, these methodologies improve…
By introducing the "comparison and replacement" (CNR) operation, we propose a general-purpose pure quantum approximate optimization algorithm and derive its core optimization mechanism quantitatively. The algorithm is constructed to a…
Quantum satisfiability is a constraint satisfaction problem that generalizes classical boolean satisfiability. In the quantum k-SAT problem, each constraint is specified by a k-local projector and is satisfied by any state in its nullspace.…
This paper introduces a new algorithm for solving a sub-class of quantified constraint satisfaction problems (QCSP) where existential quantifiers precede universally quantified inequalities on continuous domains. This class of QCSPs has…