# Leverage our Quantum Expertise

Quantum Computing holds tremendous potential for a vast variety of industries. To master its complexity our team supports you with its knowledge and experience. We support you from the first step of assessing quantum computing’s impact on your value chain up to the development of specific quantum applications for your needs.

## Quick recognition of application potentials for quantum computing

We provide you with a quick identification of quantum computing potential within your company.

## Quick recognition of application potentials for quantum computing

We provide you with a quick identification of quantum computing potential within your company.

## Leveraging quantum computing as a strategic asset

We help you to sustainably introduce quantum computing to your organization, taking into account enterprise architecture, business processes and strategic challenges.

## Leveraging quantum computing as a strategic asset

We help you to sustainably introduce quantum computing to your organization, taking into account enterprise architecture, business processes and strategic challenges.

## Tailored quantum computing proofs of concept and applications

We develop quantum services and integrate them into your existing IT environment.

## Tailored quantum computing proofs of concept and applications

We develop quantum services and integrate them into your existing IT environment.

## Understanding the relevant facets of quantum computing

We provide individual training courses for your leadership team, experts and IT users to acquire necessary skills in quantum computing.

## Understanding the relevant facets of quantum computing

We provide individual training courses for your leadership team, experts and IT users to acquire necessary skills in quantum computing.

# Use Cases

## Routing

Optimizing routes holds tremendous potential for the improvement of delivery fleet vehicle operation costs, emissions and customer satisfaction. To find an optimal route is based on one of the most prominent problems in computer science: The Travelling Salesperson Problem (TSP). With our Anaqor Quantum Fleet Planning Service we show how quantum computers can be used in the future to solve these complex challenges.

The complexity is particularly driven by the number of variables to consider: Given a graph of nodes (e.g. parcel drop-offs) and edges (e.g. distances) between nodes describing the cost to travel from one node to another (distance, traffic, street type), what is the shortest route (with the lowest cost) traversing all nodes and finishing at the starting node?

In order to tackle the problem with a quantum computer (or a quantum annealer), the latter formulation is suited for expressing the cost via a so-called Hamiltonian, which is an object often encountered when dealing with optimization problems in the quantum realm. The Hamiltonian has different energy levels, which, in this scenario, encode different routes and finding the so-called ground state of the Hamiltonian corresponds to finding the optimal route through the graph.

Finding the ground state with a quantum computer can be achieved by various means, e.g. the Quantum Approximate Optimization Algorithm (QAOA), the Variational Quantum Eigensolver (VQE) or Quantum Annealing (QA). These methods, as well as variations, build the core of the Anaqor Fleet Routing service, whichÂ also incorporates Machine Learning techniques for the pre-processing of the considered graph data.

## Routing

Optimizing routes holds tremendous potential for the improvement of delivery fleet vehicle operation costs, emissions and customer satisfaction. To find an optimal route is based on one of the most prominent problems in computer science: The Travelling Salesperson Problem (TSP). With our Anaqor Quantum Fleet Planning Service we show how quantum computers can be used in the future to solve these complex challenges.

The complexity is particularly driven by the number of variables to consider: Given a graph of nodes (e.g. parcel drop-offs) and edges (e.g. distances) between nodes describing the cost to travel from one node to another (distance, traffic, street type), what is the shortest route (with the lowest cost) traversing all nodes and finishing at the starting node?

In order to tackle the problem with a quantum computer (or a quantum annealer), the latter formulation is suited for expressing the cost via a so-called Hamiltonian, which is an object often encountered when dealing with optimization problems in the quantum realm. The Hamiltonian has different energy levels, which, in this scenario, encode different routes and finding the so-called ground state of the Hamiltonian corresponds to finding the optimal route through the graph.

Finding the ground state with a quantum computer can be achieved by various means, e.g. the Quantum Approximate Optimization Algorithm (QAOA), the Variational Quantum Eigensolver (VQE) or Quantum Annealing (QA). These methods, as well as variations, build the core of the Anaqor Fleet Routing service, whichÂ also incorporates Machine Learning techniques for the pre-processing of the considered graph data.

## Chemistry

Describing chemical and thermodynamical properties of molecules in detail has always been of huge interest for sectors like pharmacy or the chemical industry. The main issue when attempting to describe a molecule in more detail is the limited capability of classical methods to describe the interaction of the molecular building blocks: The atoms. When forming a molecule, the participating atomic orbitals (possible electron configuration for an atom) combine to molecular orbitals. In general, the molecular orbitals are described as a superposition of atomic orbitals, which, even for small molecules, becomes quickly hard to simulate. In fact, when looking at a suitable representation, the number of contributing states to the superposition grows exponentially as \((2^n)\) in the number of orbitals \(n\)

All the information about a molecule is contained in its Hamiltonian, which dominantly takes into account the electrostatic potential between the different building blocks. The second quantized version of this HamiltonianÂ is ideally suited to be transformed into a qubit-compatible form (e.g. via the Jordan-Wigner or Parity-Transformation), which serves as Input for the quantum algorithm of choice. Here, most approaches utilize the variational principle which states, that the minimum of the expectation of the Hamiltonian corresponds to the ground state energy. Finding this ground state is at the heart of the electronic structure problem and can be approached via different hybrid methods, e.g. the Variational Quantum Eigensolver (VQE) or a quantum version of a restricted Boltzmann Machine (QBM).

## Chemistry

Describing chemical and thermodynamical properties of molecules in detail has always been of huge interest for sectors like pharmacy or the chemical industry. The main issue when attempting to describe a molecule in more detail is the limited capability of classical methods to describe the interaction of the molecular building blocks: The atoms. When forming a molecule, the participating atomic orbitals (possible electron configuration for an atom) combine to molecular orbitals. In general, the molecular orbitals are described as a superposition of atomic orbitals, which, even for small molecules, becomes quickly hard to simulate. In fact, when looking at a suitable representation, the number of contributing states to the superposition grows exponentially as \((2^n)\) in the number of orbitals \(n\)

All the information about a molecule is contained in its Hamiltonian, which dominantly takes into account the electrostatic potential between the different building blocks. The second quantized version of this HamiltonianÂ is ideally suited to be transformed into a qubit-compatible form (e.g. via the Jordan-Wigner or Parity-Transformation), which serves as Input for the quantum algorithm of choice. Here, most approaches utilize the variational principle which states, that the minimum of the expectation of the Hamiltonian corresponds to the ground state energy. Finding this ground state is at the heart of the electronic structure problem and can be approached via different hybrid methods, e.g. the Variational Quantum Eigensolver (VQE) or a quantum version of a restricted Boltzmann Machine (QBM).