M.Sc. Arianne Meijer-van de Griend defends her doctoral thesis "*Advances in Quantum Compilation in the NISQ Era*" on Friday the 26th of January 2024 at 13 o'clock in the University of Helsinki Exactum building, Auditorium CK112 (Pietari Kalmin katu 5, basement). Her opponent is Assistant Professor Alexandru Paler (Aalto University) and custos Professor Jukka K. Nurminen (University of Helsinki). The defence will be held in English. It is possible to follow the defence as a live stream at https://video.helsinki.fi/unitube/live-stream.html?room=l16.

The thesis of Arianne Meijer-van de Griend is a part of research done in the Department of Computer Science and in the Empirical Software Engineering group at the University of Helsinki. Her supervisors have been Professor Jukka K. Nurminen and Professor Sabrina Maniscalco (University of Helsinki).

### Advances in Quantum Compilation in the NISQ Era

We live in a time when the first quantum computers are available for researchers and enthusiasts. These quantum computers are still very limited. They have very few quantum bits (qubits) to store information, and calculation with those few qubits can introduce errors. These errors go undetected because we cannot look at the qubits directly without changing them. Some strategies for detecting and correcting errors in quantum computers do exist, but they require many more qubits than we have available right now. Thus, we call this time the Noisy Intermediate-Scale Quantum (NISQ) era.

In this Ph.D. thesis, we focus on mediating the problems in quantum computing in the NISQ era. Particularly, the problem of rewriting a quantum program to be suitable for NISQ computers. The erroneous nature of NISQ computing requires quantum programs to be well-optimized such that no unnecessary calculations are done. Additionally, we need to deal with the problem of qubit connectivity on the quantum hardware. For example, the qubits in superconducting quantum computers are not connected to all other qubits, but only a few, and the quantum program needs to be adjusted such that the calculations that need to be done between two qubits fit the qubit connectivity of the quantum computer.

This connectivity problem is also called the “qubit routing problem”, originally named after the solution: moving (routing) the qubits from one register to another in the quantum computer. This thesis introduces a new strategy for solving this problem, namely changing the calculations in the quantum program to different ones that do the same thing. It shifts the thinking that the qubits are in the wrong place in the quantum computer to that the given program uses the wrong operations. Thus, we need to completely rewrite the given quantum program such that it is suitable for the quantum computer, this is called quantum compilation.

The difficulty of rewriting quantum programs is that we need to understand what the program is doing in enough detail that we can recreate it, but not so much that we are accidentally executing the quantum program. Otherwise, we could have simply executed the quantum program on a classical computer, but that would generally take too long. To this end, we represent the quantum program as a sequence of large computational constructs, called intermediate representations, from which a new program can be generated. We propose a series of algorithms for generating a new quantum program from these intermediate representations such that all operations are immediately allowed by the connectivity of a target quantum computer. We show that this new strategy of quantum compilation results in smaller quantum programs when used for near-term devices and algorithms. Additionally, these algorithms have since been implemented in popular quantum software packages, such as Quantinuum’s TKET (as part of this thesis) and IBM’s Qiskit (independently).

### Availability of the dissertation

An electronic version of the doctoral dissertation will be available on the e-thesis site of the University of Helsinki at http://urn.fi/URN:ISBN:978-952-84-0077-6.

Printed copies will be available on request from Arianne Meijer-van de Griend: arianne.vandegriend@helsinki.fi.