During the last five to six years years we have started a large scientific activity on Quantum Computing and Machine Learning at the Center for Computing in Science Education (CCSE), with four PhD students hired since October 2019 and several master of Science students (six second year students as of now). This activity spans from the development of quantum-mechanical many-particle theories for studying systems of interest for making quantum computers, via the development of machine learning and quantum algorithms for solving classical and quantum mechanical problems to exploring quantum machine learning algorithms.
Representations of two events from the Argon-46 experiment. Each row is one event in two projections, where the color intensity of each point indicates higher charge values recorded by the detector. The bottom row illustrates a carbon event with a large fraction of noise, while the top row shows a proton event almost free of noise.
Given a hamiltonian \( H \) and a trial wave function \( \Psi_T \), the variational principle states that the expectation value of \( \langle H \rangle \), defined through
$$ \langle E \rangle = \frac{\int d\boldsymbol{R}\Psi^{\ast}_T(\boldsymbol{R})H(\boldsymbol{R})\Psi_T(\boldsymbol{R})} {\int d\boldsymbol{R}\Psi^{\ast}_T(\boldsymbol{R})\Psi_T(\boldsymbol{R})}, $$is an upper bound to the ground state energy \( E_0 \) of the hamiltonian \( H \), that is
$$ E_0 \le \langle E \rangle. $$In general, the integrals involved in the calculation of various expectation values are multi-dimensional ones. Traditional integration methods such as the Gauss-Legendre will not be adequate for say the computation of the energy of a many-body system. Basic philosophy: Let a neural network find the optimal wave function
Machine Learning and Quantum Computing hold great promise in tackling the ever increasing dimensionalities. A hot new field is Quantum Machine Learning, see for example the recent textbook by Maria Schuld and Francesco Petruccione.
We have developed theoretical tools for generating motional entanglement between two (and more) electrons trapped above the surface of superfluid helium. In this proposed scheme these electronic charge qubits are laterally confined via electrostatic gates to create an anharmonic trapping potential. When the system is cooled to sufficiently low temperature these in-plane charge qubit states are quantized and circuit quantum electrodynamic methods can be used to control and readout single qubit operations. We work now on Perspectives for quantum simulations with quantum dots systems.
Electrons on superfluid helium represent a promising platform for investigating strongly-coupled qubits.
Therefore a systematic investigation of the controlled generation of entanglement between two trapped electrons under the influence of coherent microwave driving pulses, taking into account the effects of the Coulomb interaction between electrons, is of significant importance for quantum information processing using trapped electrons.