Related papers: Classical-Quantum Mixing in the Random 2-Satisfiab…
Quantum data access and quantum processing can make certain classically intractable learning tasks feasible. However, quantum capabilities will only be available to a select few in the near future. Thus, reliable schemes that allow…
Using powerful Multicanonical Ensemble Monte Carlo methods from statistical physics we explore the realization space of random K satisfiability (KSAT) in search for computational hard problems, most likely the 'hardest problems'. We search…
Scientists have demonstrated that quantum computing has presented novel approaches to address computational challenges, each varying in complexity. Adapting problem-solving strategies is crucial to harness the full potential of quantum…
Random constraint satisfaction problems (CSP) have been studied extensively using statistical physics techniques. They provide a benchmark to study average case scenarios instead of the worst case one. The interplay between statistical…
Going as far as possible at SAT problem solving is the main aim of our work. For this sake we have made use of quantum computing from its two, on practice, main models of computation. They have required some reformulations over the former…
The solution space of many classical optimization problems breaks up into clusters which are extensively distant from one another in the Hamming metric. Here, we show that an analogous quantum clustering phenomenon takes place in the ground…
In this note we study the power of so called query-limited computers. We compare the strength of a classical computer that is allowed to ask two questions to an NP-oracle with the strength of a quantum computer that is allowed only one such…
We give a general method of construting quantum circuit for random \QTR{it}{satisfiability} (SAT) problems with the basic logic gates such as multi-qubit controlled-NOT and NOT gates. The sizes of these circuits are almost the same as the…
Propositional satisfiability (SAT) is one of the most fundamental problems in computer science. The worst-case hardness of SAT lies at the core of computational complexity theory. The average-case analysis of SAT has triggered the…
We investigate geometrical properties of the random K-satisfiability problem using the notion of x-satisfiability: a formula is x-satisfiable if there exist two SAT assignments differing in Nx variables. We show the existence of a sharp…
We consider classical and quantum algorithms which have a duality property: roughly, either the algorithm provides some nontrivial improvement over random or there exist many solutions which are significantly worse than random. This enables…
The computational problem of distinguishing two quantum channels is central to quantum computing. It is a generalization of the well-known satisfiability problem from classical to quantum computation. This problem is shown to be…
Quantum Approximate Optimization algorithm (QAOA) aims to search for approximate solutions to discrete optimization problems with near-term quantum computers. As there are no algorithmic guarantee possible for QAOA to outperform classical…
The Path Integral Monte Carlo simulated Quantum Annealing algorithm is applied to the optimization of a large hard instance of the Random 3-SAT Problem (N=10000). The dynamical behavior of the quantum and the classical annealing are…
We perform a mathematical analysis of the classical computational complexity of two genuine quantum-mechanical problems, which are inspired in the calculation of the expected magnetizations and the entanglement between subsystems for a…
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"…
There has been much recent interest in the satisfiability of random Boolean formulas. A random k-SAT formula is the conjunction of m random clauses, each of which is the disjunction of k literals (a variable or its negation). It is known…
We introduce the fermionic satisfiability problem, Fermionic $k$-SAT: this is the problem of deciding whether there is a fermionic state in the null-space of a collection of fermionic, parity-conserving, projectors on $n$ fermionic modes,…
Boolean satisfiability (SAT) is a propositional logic problem of determining whether an assignment of variables satisfies a Boolean formula. Many combinatorial optimization problems can be formulated in Boolean SAT logic -- either as k-SAT…
The basic random $k$-SAT problem is: Given a set of $n$ Boolean variables, and $m$ clauses of size $k$ picked uniformly at random from the set of all such clauses on our variables, is the conjunction of these clauses satisfiable? Here we…