Quantum Algorithms for Quantum Many-body Problem with Applications to Chemistry and Physics
Technical University of Denmark
General course objectives:
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.
Learning objectives:
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
Contents:
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.
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