Related papers: Quantum 3-SAT is QMA1-complete
The quantum approximate optimization algorithm (QAOA) is a promising method for solving certain classical combinatorial optimization problems on near-term quantum devices. When employing the QAOA to 3-SAT and Max-3-SAT problems, the quantum…
We analyse the complexity of the satisfiability problem ssmSAT for State Space Models (SSM), which asks whether an input sequence can lead the model to an accepting configuration. We find that ssmSAT is undecidable in general, reflecting…
In this paper, we provide a deterministic polynomial time algorithm that determines satisfiability of 3-SAT. The complexity analysis for the algorithm takes into account no efficiency and yet provides a low enough bound, that efficient…
Current quantum devices execute specific tasks that are hard for classical computers and have the potential to solve problems such as quantum simulation of material science and chemistry, even without error correction. For practical…
Random $k$-SAT is the single most intensely studied example of a random constraint satisfaction problem. But despite substantial progress over the past decade, the threshold for the existence of satisfying assignments is not known precisely…
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…
The quantified constraint satisfaction problem (QCSP) is the problem of deciding, given a structure and a first-order prenex sentence whose quantifier-free part is the conjunction of atoms, whether or not the sentence holds on the…
The SAT problem is a prototypical NP-complete problem of fundamental importance in computational complexity theory with many applications in science and engineering; as such, it has long served as an essential benchmark for classical and…
The structure of satisfiability problems is used to improve search algorithms for quantum computers and reduce their required coherence times by using only a single coherent evaluation of problem properties. The structure of random k-SAT…
We introduce a novel approach to translate arbitrary 3-SAT instances to Quadratic Unconstrained Binary Optimization (QUBO) as they are used by quantum annealing (QA) or the quantum approximate optimization algorithm (QAOA). Our approach…
One of the most important questions in studying quantum computation is: whether a quantum computer can solve NP-complete problems more efficiently than a classical computer? In 2000, Farhi, et al. (Science, 292(5516):472--476, 2001)…
A detailed Monte Carlo-study of the satisfiability threshold for random 3-SAT has been undertaken. In combination with a monotonicity assumption we find that the threshold for random 3-SAT satisfies $\alpha_3 \leq 4.262$. If the assumption…
The class QMA(k), introduced by Kobayashi et al., consists of all languages that can be verified using k unentangled quantum proofs. Many of the simplest questions about this class have remained embarrassingly open: for example, can we give…
With the growing interest in quantum programs, ensuring their correctness is a fundamental challenge. Although constraint-solving techniques can overcome some limitations of traditional testing and verification, they have not yet been…
Using the cavity equations of \cite{mezard:parisi:zecchina:02,mezard:zecchina:02}, we derive the various threshold values for the number of clauses per variable of the random $K$-satisfiability problem, generalizing the previous results to…
In this work we develop theoretical techniques for analysing the performance of the quantum approximate optimization algorithm (QAOA) when applied to random boolean constraint satisfaction problems (CSPs), and use these techniques to…
In the continuum limit (large number of qubits), adiabatic quantum algorithms display a remarkable similarity to sweeps through quantum phase transitions. We find that transitions of second or higher order are advantageous in comparison to…
The random k-SAT instances undergo a "phase transition" from being generally satisfiable to unsatisfiable as the clause number m passes a critical threshold, $r_k n$. This causes a drastic reduction in the number of satisfying assignments,…
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…
DNA computation could in principle solve the satisfiability (SAT) problem due to the operations in parallel on extremely large numbers of strands. We demonstrate some quantum gates corresponding to the DNA ones, based on which an…