PhD Courses in Denmark

To give the students specialized knowledge of several relevant aspects concerning quantum algorithms for simulating dynamics of physical systems and solving eigenvalue problems encountered in many-body quantum physics and quantum chemistry.

A student who has met the objectives of the course will be able to:

• Second quantization formalism and mappings between different sets of operators for realization of quantum Hamiltonians
• Abstract algebraic structures (e.g., groups, Lie and Clifford algebras) and their relevance to operators appearing in many-body problems
• Variational Quantum Eigensolver and its main challenges: state preparation and measurement; examples from quantum chemistry
• Other hybrid near-term algorithms, e.g., based on projective and Quantum Monte-Carlo ideas
• Error mitigation techniques for algorithms in near-term
• Quantum algorithms assuming fault-tolerance: Quantum Phase Estimation, Quantum Amplitude Estimation, and Quantum Amplitude Amplification
• Hamiltonian encoding: i) Trotter approximation; ii) Block-encodings: linear combination of unitaries, quantum signal processing techniques
• Error correction models and their efficiency limiting characteristics (e.g., magic state distillation)
• Various early-fault tolerant algorithms with the focus on extracting properties in a most efficient way
• Applications for near-term and fault-tolerant quantum algorithms

This course will cover quantum algorithms for simulating dynamics of physical systems and solving eigenvalue problems encountered in many-body quantum physics and quantum chemistry.