Influence of Different 3SAT-to-QUBO Transformations on the Solution Quality of Quantum Annealing: A Benchmark Study

To solve 3sat instances on quantum annealers they need to be transformed to an instance of Quadratic Unconstrained Binary Optimization (QUBO). When there are multiple transformations available, the question arises whether different transformations lead to differences in the obtained solution quality. Thus, in this paper we conduct an...

Pattern QUBOs: Algorithmic Construction of 3SAT-to-QUBO Transformations

One way of solving 3sat instances on a quantum computer is to transform the 3sat instances into instances of Quadratic Unconstrained Binary Optimizations (QUBOs), which can be used as an input for the QAOA algorithm on quantum gate systems or as an input for quantum annealers. This mapping is performed by a 3sat-to-QUBO transformation....

Algorithmic QUBO formulations for k-SAT and hamiltonian cycles

Quadratic Unconstrained Binary Optimization (QUBO) can be seen as a generic language for optimization problems. QUBOs attract particular attention since they can be solved with quantum hardware, like quantum annealers or quantum gate computers running QAOA. In this paper, we present two novel QUBO formulations for k-SAT and Hamiltonian Cycles...

How to Approximate any Objective Function via Quadratic Unconstrained Binary Optimization

Quadratic unconstrained binary optimization (QUBO) has become the standard format for optimization using quantum computers, i.e., for both the quantum approximate optimization algorithm (QAOA) and quantum annealing (QA). We present a toolkit of methods to transform almost arbitrary problems to QUBO by (i) approximating them as a polynomial and...

A Quantum Annealing Approach for Solving Hard Variants of the Stable Marriage Problem

The Stable Marriage Problem (SMP) describes the problem, of finding a stable matching between two equally sized sets of elements (e.g., males and females) given an ordering of preferences for each element. A matching is stable, when there does not exist any match of a male and female which both prefer each other to their current partner under...