Related papers: A technical note for the 91-clauses SAT resolution…
The Quantum Approximate Optimization Algorithm (QAOA) is a quantum-classical hybrid algorithm intending to find the ground state of a target Hamiltonian. Theoretically, QAOA can obtain the approximate solution if the quantum circuit is deep…
This paper proposes a quasi-binary encoding based algorithm for solving a specific quadratic optimization models with discrete variables, in the quantum approximate optimization algorithm (QAOA) framework. The quadratic optimization model…
Optimization is often cited as a promising application of quantum computers. However, the low degree of provable quantum speedups has led prior rigorous end-to-end resource analyses to conclude that a quantum computer is unlikely to surpass…
Executing quantum algorithms on a quantum computer requires compilation to representations that conform to all restrictions imposed by the device. Due to devices' limited coherence times and gate fidelities, the compilation process has to…
Noisy Intermediate-Scale Quantum (NISQ) devices are restricted by their limited number of qubits and their short decoherence times. An approach addressing these problems is quantum circuit cutting. It decomposes the execution of a large…
Quantum Approximate Optimization Algorithm (QAOA) enables solving combinatorial optimization problems on quantum computers by optimizing variational parameters for quantum circuits. We investigate a simplified approach that combines linear…
We propose a novel approach for the development, analysis, and verification of reductions between NP-complete problems. This method uses the URSA system, a SAT-based constraint solver and incorporates features that distinguish it from…
Ohya and Volovich have been proposed a new quantum computation model with chaos amplification to solve the SAT problem, which went beyond usual quantum algorithm. In this paper we study the complexity of the SAT algorithm by counting the…
Recent hardware demonstrations and advances in circuit compilation have made quantum computing with higher-dimensional systems (qudits) on near-term devices an attractive possibility. Some problems have more natural or optimal encodings…
We show through numerical simulation that the Quantum Approximate Optimization Algorithm (QAOA) for higher-order, random-coefficient, heavy-hex compatible spin glass Ising models has strong parameter concentration across problem sizes from…
In this manuscript, I present an analysis on the performance of OpenAI O1-preview model in solving random K-SAT instances for K$\in {2,3,4}$ as a function of $\alpha=M/N$ where $M$ is the number of clauses and $N$ is the number of variables…
This paper presents a numerical simulation investigation of the Warm-Start Quantum Approximate Optimization Algorithm (QAOA) as proposed by Tate et al. [1], focusing on its application to 3-regular Max-Cut problems. Our study demonstrates…
A new quantum algorithm is proposed to solve Satisfiability(SAT) problems by taking advantage of non-unitary transformation in ground state quantum computer. The energy gap scale of the ground state quantum computer is analyzed for 3-bit…
Previously, all known variants of the Quantum Satisfiability (QSAT) problem, i.e. deciding whether a $k$-local ($k$-body) Hamiltonian is frustration-free, could be classified as being either in $\mathsf{P}$; or complete for $\mathsf{NP}$,…
The Quantum Approximate Optimization Algorithm (QAOA) is a general purpose quantum algorithm designed for combinatorial optimization. We analyze its expected performance and prove concentration properties at any constant level (number of…
We prove that a random 3-SAT instance with clause-to-variable density less than 3.52 is satisfiable with high probability. The proof comes through an algorithm which selects (and sets) a variable depending on its degree and that of its…
3SAT instances need to be transformed into instances of Quadratic Unconstrained Binary Optimization (QUBO) to be solved on a quantum annealer. Although it has been shown that the choice of the 3SAT-to-QUBO transformation can impact the…
Quantum Approximate Optimization Algorithm (QAOA) provides a way to solve combinatorial optimization problems using quantum computers. QAOA circuits consist of time evolution operators by the cost Hamiltonian and of state mixing operators,…
Boolean satisfiability (SAT) solving is a fundamental problem in computer science. Finding efficient algorithms for SAT solving has broad implications in many areas of computer science and beyond. Quantum SAT solvers have been proposed in…
Despite its popularity, several empirical and theoretical studies suggest that the quantum approximate optimization algorithm (QAOA) has persistent issues in providing a substantial practical advantage. Numerical results for few qubits and…