**Techpally descry Quantum Computer Applications**

In the foreseeable future, quantum computers will probably only be used for particularly computationally intensive problems, but their solutions can be particularly valuable.

For example, foreseeable applications include

- Simulations for natural and engineering sciences (physics, materials research, quantum chemistry, quantum biology)
- Optimization (logistics, financial management
- Artificial Intelligence and Machine Learning
- IT Consulting
- Cryptography
- Energy saving

## Quantum Computer Application “Simulations for Natural Sciences”

In 1982 the brilliant Richard Feynman finished a famous essay with the equally famous words: “Nature isn’t classical, dammit, and if you want to make a simulation of nature, you’d better make it quantum mechanical, and by golly it’s a wonderful problem, because it doesn’t look so easy” v.

## Quantum Computer Application “Hamiltonian Simulation”

In 1996, Seth Lloyd proved that any such simulation can in principle and efficiently be performed with a quantum computer vi.

This type of calculation is called “Hamiltonian simulations”. They calculate the dynamics, i.e. the time course, of arbitrary quantum systems, which are generally characterized by the so-called Hamiltonian operator (hence the name).

Hamiltonian simulations are among the most difficult calculations that a quantum computer can efficiently perform.

Conventional supercomputers have been proven to be unable to do this exactly, according to Techpally.

Behind many possible applications for quantum computers are still open question marks as to the extent to which known limitations and constraints can be overcome in practice.

However, there is general agreement that the legendary promises of salvation of quantum computers will definitely apply to Hamiltonian simulation.

## Quantum computer application “Synthesis of ammonia”

An exciting application for the Hamiltonian simulation, which has already been examined in detail for its applicability, is the “synthesis of ammonia”:

In 1913 the Haber-Bosch process for the synthesis of ammonia was first introduced on a large industrial scale.

Since then it has been the world’s dominant process for the production of fertilizers.

However, it requires a heat of 400° Celsius and a pressure of 200 bar.

Approximately 1-2% of the worldwide energy demand is annually only put into the Haber-Bosch process.

Plants and fungi, on the other hand, synthesize ammonia at 20° Celsius and a pressure of 1 bar, the atmospheric pressure, according to farmpally.

Researchers have been able to localise the central reactions for this but have not been able to understand them in detail.

The necessary quantum simulations are simply too complex to be calculated by a conventional supercomputer.

However, quantum computers would be able to do this using Hamiltonian simulation vii. Unfortunately, however, not in the NISQ era.

## Quantum computer application “VQE” – Variational Quantum Self Solver

So the application “Hamiltonian simulation” probably exceeds the possibilities for quantum computers of the NISQ era.

Are there other possible applications for quantum simulations that can be implemented on current hardware?

An important question for quantum systems is the question of the binding energies of the system and the atomic or molecular orbitals.

In 2014 the new quantum algorithm “Variational Quantum Self Solver” was presented by Peruzzo and McClean viii ix.

It was designed especially for the quantum computers of the NISQ array.

VQE is basically an optimization algorithm and especially a quantum classical hybrid algorithm:

The qubits are adjusted to represent an orbital candidate.

With this candidate, the quantum computer determines the binding energy of the molecule. With a quantum computer this should be efficiently feasible.

Since this measurement is always a matter of probabilities, it is performed several times and the smallest value is used.

Using a conventional computer, a new orbital candidate is calculated based on the previous optimization process x.

Now the algorithm starts at step 1 again, this time with the new orbital candidate. The algorithm ends when, for example, the lowest binding energy is found.

The basic idea of the Variational Quantum Eigensolver is that a quantum computer is able to create and calculate complicated entangled quantum states.

And just such orbitals are present in molecules. For a conventional computer, this usually quickly becomes exponentially too complex.

Since the Variational Quantum Self-Solver constantly readjusts itself via optimization anyway, the algorithm is also reasonably immune to circuit and qubit errors.

The Variational Quantum Eigensolver sounds very promising in theory.

In fact, however, no one can currently say with certainty whether the VQE actually brings about an acceleration, let alone that it can be quantified.

A great deal of experience still needs to be gathered here. For example, it has been shown that not every classical optimization algorithm in step 3 is equally suitable for the Variational Quantum Self-Solver xi

Around the VQE algorithm, Google has created the open source framework “OpenFermion” for quantum chemistry.

Jarrod McClean, one of the developers of the Variational Quantum Eigensolver, has meanwhile been recruited by Google.

It turns out that the tech giants are increasingly collaborating closely with precisely those scientists who have made a name for themselves for applications of NISQ quantum computers.

## Quantum computer application: The Grover Algorithm

The Grover algorithm is a universal search algorithm that tries out all solution candidates and tests whether they solve the problem.

You can see from this that the Grover algorithm has an incredibly wide range of applications, including optimization problems.

The Grover algorithm has a quadratic acceleration compared to conventional search algorithms.

However, it probably requires too many quantum gates in the application, which is why it cannot be used for quantum computers of the NISQ array.