## SciPost Submission Page

# Assessment of Quantum Annealing for the Construction of Satisfiability Filters

### by Marlon Azinović, Daniel Herr, Bettina Heim, Ethan Brown, Matthias Troyer

#### - Published as SciPost Phys. 2, 013 (2017)

### Submission summary

As Contributors: | Daniel Herr |

Arxiv Link: | https://arxiv.org/abs/1607.03329v6 |

Date accepted: | 2017-03-17 |

Date submitted: | 2017-03-08 |

Submitted by: | Herr, Daniel |

Submitted to: | SciPost Physics |

Discipline: | Physics |

Subject area: | Quantum Physics |

Approach: | Computational |

### Abstract

Satisfiability filters, introduced by S. A. Weaver et al. in 2014, are a new and promising type of filters to address set membership testing. In order to construct satisfiability filters, it is necessary to find disparate solutions to hard random $k$-SAT problems. This paper compares simulated annealing, simulated quantum annealing and walkSAT, an open-source SAT solver, in terms of their ability to find such solutions. The results indicate that solutions found by simulated quantum annealing are generally less disparate than solutions found by the other solvers and therefore less useful for the construction of satisfiability filters.

### Ontology / Topics

See full Ontology or Topics database.Published as SciPost Phys. 2, 013 (2017)

### List of changes

Dear Editor,

as suggested by the referee we added a paragraph which illustrates what values (FPR, size of the set, storage requirements) a typical SAT-filter has. We explicitly mention the size of the SAT-problem and the size (in bits) that need to be stored for the solutions of these problems.

The paragraph can be found towards the end of section 2.4 Important Quantities:

"""

Since filters are mainly used in big data contexts, their size can be quite large, depending on the size of the set $\left|Y\right|$ and the required FPR. To illustrate this, we give an example for a SAT filter encoding a set $Y$ with $\left|Y\right|=2^{16}$ elements: The $2^{16}$ elements result in $m=2^{16}$ clauses. If the required FPR is $p=\frac{1}{4}$ a 4-SAT filter needs to store $s\approx22$ (independent) solutions~\cite{weaver2014}. If the targeted efficiency is given by $\mathcal{E}=0.75$ each solution involves $n \approx 8136$ literals. The filter therefore stores $\approx 22 \cdot 8136$ bits. A 5-SAT filter achieving the same efficiency and FPR needs to store $s\approx 44$ (independent) solutions with $n \approx 4002$ literals. It should be noted that a physical implementation needs more spins as there are literals, because embedding is needed to accommodate for the restricted connectivity of physical devices. Thus, an implementation with current hardware is not yet possible, but the rapid development in this field might lead to physical implementations, soon.

"""

We again like to thank the referees for their work on our manuscript.

Best wishes,

Daniel Herr