Near-term Quantum Computing

• Lecturer: Dr. Tobias Stollenwerk
• Teaching Assistant: Victoria Wadewitz
• Host institution: RWTH Aachen, Computer Science Department (Prof. Dr. Dominique Unruh)

Overview

This lecture is an interdisciplinary (computer science, physics, mathematics) introduction to modern algorithmic challenges as they occur in the usage of near-term quantum computing hardware. After reviewing the basics of quantum computation and algorithms we will cover the limitation of current quantum computing hardware from a computer scientist’s point of view. Next, we will discuss algorithms for near-term quantum computers, before we turn to quantum compilation, i.e. algorithms for the optimal mapping of quantum algorithms to real quantum computers. Finally, we will cover the basics of quantum error correction and mitigation.

• Target audience: Master and PhD students in physics, computer science, mathematics
• Scope: 3h/week lecture, 1h/week programming exercise
• ETCP: 6
• Requirements:
• Linear algebra
• Quantum information/computing fundamentals

• Time and Place
• Tue, 8:30 - 10:00, Lecture, Room 5056 (E2 Informatikzentrum)
• Thu, 8:30 - 10:00, Lecture and Practice, Room 140 (except at 18.7. in Room 5), Schinkelstr. 1, Templergraben 51
• Exams:
• 20.8.2024, 8:30 - 10:30, Room H03, CARL
• 26.9.2024, 8:30 - 10:30, Room H03, CARL
• Lecture notes (in development)

Lectures

Note: This is a rough plan which will be constantly updated thoughout the semester.

• Lecture 1 - Tue, April 8
• Revision of fundamentals of quantum algorithms: quantum states and their manipulation. Publication of Exercise 1.
• Quantum states
• Quantum unitary transformations
• Lecture 2 - Thu, April 11
• Revision of fundamentals of quantum algorithms: quantum states and their manipulation
• Quantum unitary transformations
• Quantum measurements

• Lecture 3 - Tue, April 16
• Limitations and characteristics of real quantum computing chips from a computer scientist's perspective
• Limited gate operations on real devices
• Mixed quantum states
• Practice 1 - Thu, April 18
• Quantum states and their manipulation

• Lecture 4 - Tue, April 23
• Limitations and characteristics of real quantum computing chips from a computer scientist's perspective
• General quantum operations
• Quantum noise
• Lecture 5 - Tue, April 25
• Algorithms for near-term quantum computers
• NISQ Algorithms and Complexity Class
• Quantum Optimization
• Pseudo-Boolean Functions

• Lecture 6 - Tue, April 30
• Cancelled
• Practice 2 - Tue, May 2
• Limitations and characteristics of real quantum computing chips from a computer scientist's perspective

• Lecture 7 - Tue, May 7
• Algorithms for near-term quantum computers - Combinatorial optimization

Thu, May 9 Public Holiday

• Lecture 8 - Tue, May 14
• Algorithms for near-term quantum computers - Combinatorial optimization
• Practice 3 - Thu, May 16
• Algorithms for near-term quantum computers - Combinatorial optimization

May 20 to May 26 - Week of Pfingsten

• Tue, May 28 - No lecture

Thu, May 30 Public Holiday

• Lecture 9 - Tue, June 4
• Quantum compilation: Circuit synthesis
• Lecture 10 - Thu, June 6
• Quantum compilation: Circuit synthesis and the routing problem

• Lecture 11 - Tue, June 11
• Quantum compilation: The routing problem
• Practice 4 - Thu, June 13
• Quantum compilation

• Lecture 12 - Tue, June 18
• Introduction to diagrammatic methods for quantum computation
• Lecture 13 - Thu, June 20 (Victoria Wadewitz)
• Introduction to diagrammatic methods for quantum computation

• Lecture 14 - Tue, June 25 (Victoria Wadewitz)
• Circuit synthesis with diagrammatic methods
• Practice 5 - Thu, June 27 (Victoria Wadewitz)
• Diagrammatic methods

• Lecture 15 - Tue, July 2
• Quantum error mitigation
• Lecture 16 - Thu, July 4
• Quantum error mitigation 2

• Practice 6 - Tue, July 9
• Quantum error mitigation
• Lecture 17 - Thu, July 11
• Quantum error correction

• Lecture 18 - Tue, July 16
• Quantum error correction with diagrammatic methods
• Practice 7 - Thu, July 18
• Quantum error correction

Literature

Fundamentals

• Phillip Kaye, Raymond Laflamme, and Michele Mosca. An Introduction to Quantum Computing. USA: Oxford University Press, Inc., 2007. isbn: 0198570007.
• Michael A. Nielsen and Isaac L. Chuang. Quantum Computation and Quantum Information: 10th Anniversary Edition. 10th. USA: Cambridge University Press, 2011. isbn: 1107002176.
• Eleanor Rieffel and Wolfgang Polak. Quantum Computing: A Gentle Introduction. 1st. The MIT Press, 2011. isbn: 9780262015066.

Diagrammatic Calculus

• John van de Wetering. “ZX-calculus for the working quantum computer scientist”.
• Coecke, B. and Kissinger, A. (2017) Picturing Quantum Processes: A First Course in Quantum Theory and Diagrammatic Reasoning. Cambridge: Cambridge University Press.

Near-term Algorithms

• Edward Farhi, Jeffrey Goldstone, and Sam Gutmann. “A quantum approximate optimization algorithm”. In: arXiv preprint arXiv:1411.4028 (2014).
• Alberto Peruzzo et al. “A variational eigenvalue solver on a photonic quantum processor”. In: Nature communications 5.1 (2014), pp. 1–7. doi: 10.1038/ncomms5213.
• John Preskill. “Quantum computing in the NISQ era and beyond”. In: Quantum 2 (2018), p. 79.
• Stuart Hadfield et al. “From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz”. In: Algorithms 12.2 (2019). issn: 1999-4893. doi: 10 .3390/a12020034.
• Marco Cerezo et al. “Variational quantum algorithms”. In: Nature Reviews Physics 3.9 (2021), pp. 625–644.
• M. Schuld and F. Petruccione. Supervised Learning with Quantum Computers. Quantum Science and Technology. Springer International Publishing, 2018. isbn: 9783319964249.