Applications of quantum control: scaling of quantum computers and BEC-based quantum sensors

Abstract

Quantum systems are intrinsically interesting due to their counterintuitive physical behaviour. Quantum physics also has direct technological applications, such as quantum computing and quantum sensor technologies. Precise control benefits both studies of the fundamental, counterintuitive properties of quantum systems, as well as improving the performance of quantum technologies. In this thesis, I develop applications of novel control techniques for two types of quantum system.

In Part I, I investigate a faster method to implement entangling quantum gate operations in a trapped ion quantum computer. I place requirements on sources of error in these fast gates for them to be used in implementing a simulation of the Fermi-Hubbard model with 20 lattice sites, a quantum simulation at a scale rivalling the largest possible simulation with a classical computer. I also suggest that fast gates could be applied to proposed scalable ion trap computer architectures, where individual ion qubits are more isolated from each other, making engineering of interactions between them more difficult but also making the design of the computer more 'modular' and flexible, enabling better connectivity and scaling. I show that fast gates are effective even when the qubits are in separate traps with a spacing of 100 micrometres.

In Part II, I investigate the use of closed-loop feedback control to remove excitations from atomic Bose gases. I investigate removal of thermal excitations from a low-temperature thermal state of a Bose gas, finding that it is possible to produce a state with over 90% condensate fraction from an initial state with as low as 68% condensate. This result is promising for possible future application to augmenting lossy evaporative cooling techniques in the creation of Bose-Einstein condensates (BECs) for quantum sensors or experiments. Finally, I investigate the use of a simpler model to estimate feedback outputs from the measurement signal, as would be necessary to produce real-time feedback in an experiment. I find that the simple model is at least able to remove a simple excitation from a BEC, which gives further promise for experimental applications of feedback control to Bose gases.

Through examining applications of novel control techniques to trapped-ion quantum computers and atomic Bose gases, this thesis advances the field of quantum control, providing future directions for experimental applications of the techniques to produce better quantum computers, quantum sensors and BEC experiments.