QuantumProject (quantum engineering, how to make quantum computers that work)

Study of two particle systems

• Von Neumann entropy and entaglemment
• Simple two-level model to illustrate avoided crossing and entanglement
• time evolution with electric fields/other mechanisms (raising/lowering of wells)
• state tomography and relation to density matrix (experimental interpretation)
• developing a specific analog-digital quantum simulator with two-qubits (operations on qubits)

Develop FCI code for ion traps and quantum dots

• MHJ's code
• Yoshida and Shimuzu https://arxiv.org/abs/2105.08256
• Set up mtx elements (one-body and twobody) in uncoupled basis for 2d quantum (3d and 1d systems).
• Øyvind's 3 and 4 particle code
• Veronika's master thesis, FCI for quantum dots
• Simen Kvaal's FCI code https://arxiv.org/abs/0810.2644
• Effective interaction for many particles and FCI
• Time development
• Adiabatic(?) switching on/off of Coulumb interaction

Basis sets

• DVR basis
• Is the basis 'the same' after and under a perturbation?

Operations on qubits

• Suggestions for circuits with given gates, how to make fields that perform different operations
• Model hamiltonians and observables
• Lowering and raising of wells and gates
• Setting up electric fields/laser with time evolution/dipole approx

Von Neumann Entropy and Entanglement

• 1d systems with two and more particle
• 2d systems with two electrons in two wells
• 3d system with two electrons in two wells
• Move to three electrons (qd) and four electrons

From FCI to many-body methods with time dependence

• Academic exercise: ground state evolution with time-dependence

Point defect theory and experiment