### Quantum Annealing with examples

Created by Valter Uotila

## Unified Database Management Systems

Problem: modern database management systems do not have a solid theoretical foundation.

Oracle started promoting category theory as a theoretical foundation for various database concepts.

Category theory is very applicable: we published some results in VLDB'21 and its workshops.

Applied category theory for multi-model databases

## Motivation

Quantum computing does not yet outperform classical computers in real-life applications but...

...it might be more sustainable to operate and ...

... we can avoid making ethical mistakes. For example, see Gender BIAS in AI: Perspectives of AI Practitioners.

## Implementation by Initial paper in Nature: Quantum annealing with manufactured spins

## Motivation for quantum annealing

D-wave has many examples of use cases:

## General idea

Goal: finding the global minimum of a given objective function

## Annealing process: bias ## Annealing process: couplers ## Studies about performance of quantum annealing

Google studied that quantum annealing outperforms simulated annealing

General study: Performance of quantum annealing hardware

## Important paper

by Andrew Lucas

Example: Steiner trees

\begin{aligned} H_{A} & = A\left( 1 - \sum_{v}x_{v,0} \right)^2 + A \sum_{v \in U} \left( 1 - \sum_{i}x_{v,i} \right)^2 \\ & + A \sum_{v \notin U} \left( y_v - \sum_{i} x_{v,i} \right)^2 \\ & + A\sum_{v}\sum_{i = 1}^{N/2}\left(x_{v,i} - \sum_{(uv) \in E}x_{uv,i} \right)^2 \\ & + A \sum_{uv \in E}\left( y_{uv} - \sum_{i}(x_{uv,i} - x_{vu, i}) \right)^2 \\ & + A\sum_{uv, vu \in E}\sum_{i = 1}^{N/2}x_{uv,i}(2 - x_{u,i-1} - x_{v,i}) \end{aligned}

## Relationship to gate-model

Quantum computing companies with different paradigms and hardware

## Problem

Cars, especially self-driving cars, require multiple sensors to monitor the car's environment. Positioning the sensors is a combinatorically difficult problem and testing different combinations is slow.

In this challenge BMW wanted to research possibilities of quantum computing in the sensor positioning process.

## New Angles from Right Range:

#### Optimizing Car Sensor Positioning with D-Wave Hybrid Quantum Computers Valter Uotila & Sardana Ivanova

## Core idea of solution

We utilized Quadratic Unconstrained Binary Optimization model and followed the standard approach in D-wave's examples and in the paper Ising formulations of many NP problems.

## Core idea of solution

• Formalizing problem
• Defining suitable binary variables
• Identifying and creating suitable constraints
• Implementing variables and constraints with Ocean software framework

## "Easy" level

Solving classical database optimization and modeling problems with quantum computing

Problem: quantum computing might not scale and bring any benefits

## Join order optimization

Problem: for a given subset of vertices, select a subset of vertices and edges so that they all together form a tree and the total weight is minimized.

Possible solution: Express the problem using Steiner trees and implement using the idea in the paper Ising formulations of many NP problems.

## "Hard" level

Will we be able to store and query quantum data from quantum databases?

What does it mean?

How would it work?

Why do we need it?

Category theory & quantum computing:

## Conclusion

### Thank you for your interest and the opportunity to give a presentation! 