## Graduate Student Council Research Grants

#### Title

Analytical and numerical computations of AKLT model

#### Document Type

Article

#### Degree

Ph.D. in Physics

#### Publication Date

3-15-2019

#### Abstract

Quantum computation recently emerges as one of the most interesting and active research fields which overlaps between quantum physics, mathematics and computational science. In near future, scientists hope to build a commercial quantum computer that is believed exponentially faster speed than ordinary computers (laptop, desktop, and supercomputer)[1, 2]. Conventional computers store data in term of binary bits such as 0 or 1, whereas the quantum computers use a quantum bit (qubit) as the superposition of 0 and 1 (qubit“α0`β1 with any complex numbersαandβsatisfied|α|2`|β|2“1). One of the methods to design the quantum computer is “measurement-based paradigm” that is based on the physical properties of spin model, namely Affleck-Kennedy-Lieb-Tasaki (AKLT) state. There are three key parameters to construct the prototypical quantum computer are entanglement, superposition and optimization. AKLT state is an example of interacting spin model that is satisfied all above requirements for quantum computation. (For solving any quantum mechanics problem, we want to find the energy and wave function of the system). The ground state energy (lowest and most stable energy) of AKLT model is exactly known, but the excited state ones are not (except for the one dimension where spins are arranged in a chain). Here, I have derived exactly analytical representation of non-deformed and deformed states, and use projector Monte Carlo to simulate number of spins up to a million particles. We hope to make clear the physical properties of the model for further quantum computing applications.

#### Relational Format

report

#### Recommended Citation

Do, Huu, "Analytical and numerical computations of AKLT model" (2019). *Graduate Student Council Research Grants*. 18.

https://egrove.olemiss.edu/gsc_researchgrants/18