Related papers: A technical note for the 91-clauses SAT resolution…
The Boolean constraint satisfaction problem 3-SAT is arguably the canonical NP-complete problem. In contrast, 2-SAT can not only be decided in polynomial time, but in fact in deterministic linear time. In 2006, Bravyi proposed a physically…
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.…
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…
The ability of the Quantum Approximate Optimization Algorithm (QAOA) to deliver a quantum advantage on combinatorial optimization problems is still unclear. Recently, a scaling advantage over a classical solver was postulated to exist for…
Most quantum circuits require SWAP gate insertion to run on quantum hardware with limited qubit connectivity. A promising SWAP gate insertion method for blocks of commuting two-qubit gates is a predetermined swap strategy which applies…
Quantum optimization solvers typically rely on one-variable-to-one-qubit mapping. However, the low qubit count on current quantum computers is a major obstacle in competing against classical methods. Here, we develop a qubit-efficient…
The Quantum Approximate Optimization Algorithm (QAOA) is a promising approach for programming a near-term gate-based hybrid quantum computer to find good approximate solutions of hard combinatorial problems. However, little is currently…
Boolean Satisfiability (SAT) problems are expressed as mathematical formulas. This paper presents a matrix representation for these SAT problems. It shows how to use this matrix representation to get the full set of valid satisfying…
Quadratic Unconstrained Binary Optimization (QUBO) is recognized as a unifying framework for modeling a wide range of problems. Problems can be solved with commercial solvers customized for solving QUBO and since QUBO have degree two, it is…
The quantum approximate optimisation algorithm (QAOA) is a hybrid quantum-classical algorithm used to approximately solve combinatorial optimisation problems. It involves multiple iterations of a parameterised ansatz comprising a problem…
This short tutorial provides an introduction to the Quantum Approximation Optimization Algorithm (QAOA). Specifically, how to use QAOA with the Simultaneous Perturbation Stochastic Approximation (SPSA) algorithm to solve the Max-Cut…
We comparatively study, through large-scale numerical simulation, the performance across a large set of Quantum Alternating Operator Ansatz (QAOA) implementations for finding approximate and optimum solutions to unconstrained combinatorial…
We consider the following problem. Given a 2-CNF formula, is it possible to remove at most $k$ clauses so that the resulting 2-CNF formula is satisfiable? This problem is known to different research communities in Theoretical Computer…
QAOA is a quantum algorithm for solving combinatorial optimization problems. It is capable of searching for the minimizing solution vector $x$ of a QUBO problem $x^TQx$. The number of two-qubit CNOT gates in the QAOA circuit scales linearly…
We present a quantum alternating operator ansatz (QAOA$^+$) that solves a class of linearly constrained optimization problems by evolving a quantum state within a Hilbert subspace of feasible problem solutions. Our main focus is on a class…
The random 3-satisfiability (3-SAT) problem is in the unsatisfiable (UNSAT) phase when the clause density $\alpha$ exceeds a critical value $\alpha_s \approx 4.267$. However, rigorously proving the unsatisfiability of a given large 3-SAT…
Satisfiability (SAT) is a central problem in computer science, and advances in SAT-solving algorithms have a far-reaching impact across many fields. Recent works have proposed quantum SAT solvers based on Grover's algorithm, a quantum…
The problem of P vs. NP is very serious, and solutions to the problem can help save lives. This article is an attempt at solving the problem using a computer algorithm. It is presented in a fashion that will hopefully allow for easy…
When creating benchmarks for SAT solvers, we need SAT instances that are easy to build but hard to solve. A recent development in the search for such methods has led to the Balanced SAT algorithm, which can create k-SAT instances with m…
The Circuit Satisfiability (CSAT) problem, a variant of the Boolean Satisfiability (SAT) problem, plays a critical role in integrated circuit design and verification. However, existing SAT solvers, optimized for Conjunctive Normal Form…