Notes and Research
Policy Projects
- Developing an Agent-Based Model for the housing market in Singapore Here. Still a work in progress!
Personal Notes
Learning Quant Finance
Learning quantitative finance. Notes and code so far are found here. Right now, notes mainly taken from Market Risk Analysis, Quantitative Methods in Finance by Carol Alexander.
All the links can be found Here.
Basics
1.1 Introduction to probability and stats Here.
1.2 Introduction to statistical interference Here.
1.3 Very short introduction to stochastic processes Here.
1.4 Introduction to linear regression Here.
Short Survey of Methods
2.1 Principal Component Analysis Here.
2.2 Finding Roots through Iteration Here.
2.3 Interpolation and Extrapolation Here.
2.4 Optimization Here.
2.5 Finite Difference Approximations Here.
2.6 Binomial Lattices Here
Portfolio Theory
3.1 Utility Theory Here
3.2 Portfolio Allocation Here
3.3 Introduction to Asset Pricing Here
3.4 Risk Adjusted Performance Measures Here
Random studies
Physics Research Interests
My research interests are somewhat broad, but the common theme is investigating how we might use the energing platforms that the field of quantum technologies is providing us (in particular quantum simulators and near term quantum computers) for practical purposes. In particular, we have an interest in utilizing such platforms to study dynamics in many-body physics.
I actively work with experimentalists, and have ongoing collaborations with the experimental photonics group at the Quantum Science and Engineering Centre in NTU, and the experimental atomtronics group under Rainer Dumke.
Noisy Intermediate Scale Quantum (NISQ) Simulation Algorithms: With the development of near term quantum computers, we are entering the NISQ era of quantum computing, which is characterized by us having access to quantum computers with a hundred to a few thousand qubits. The number of qubits of such computers is large enough such that classical computers should not be able to accurately simulate the results of calculations run by such quantum computers, however not large enough to implement error-correcting codes, implying that he calculations of such computers are subject to high levels of noise. Such computers also commonly face architectural constraints, with limited connectivity between qubits. While we should continue to strive to develop larger and less noisy quantum computers, we foresee that we will be in this era for a long period of time. As such, we should aim to develop and characterize algorithms that are able to deal with the limitations posed by such computers. One of the biggest hoped-for advantages of having a useful quantum computer is its theoretical capability to perform simulations of quantum many-body dynamics problems. However, the algorithms so far developed for NISQ computers are in their infacy and we do not fully understand how much the effect of noise will affect their calculations, nor do we know if it is even possible to achieve quantum advantage over classical computers in the NISQ era.
Atomtronics: Recent developments in cold atom systems has allowed us the ability to control atomic matter-waves of ultra-cold atoms. This allows us to realize circuits of atoms, which are analogs of electrical circuits, but with the current carriers being bosons or generic fermions as opposed to electrons. Furthermore, we have the ability to manipulate such atoms coherently in a large variety of trap potentials, giving us the tools to study physics in many different geometries. Such systems allow us a method to perform analog simulations of quantum many-body problems, and allow us a tool to develop new technologies.
Integrated Photonic Chips: Such platforms have many potential applications, such as in quantum computing. We are exploring alternative uses, like speeding up and efficiently implementing classical machine learning models on such devices.
The application of Density Functional Theory to cold atom systems.