Chris Pollett > Students > Yunxuan

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Physics Proposal

Quantum Hamiltonian Experiments

Yun Xuan Shi (yunxuan2633@hotmail.com)

Advisor: Dr. Chris Pollett

Description:

Description_Here

My thesis is about quantum computation. It is about computation based on the Schrodinger equation. I will discuss what causes a Hamiltonian to be implementable on a quantum computer and simulatable on a quantum computer. The second topic I will discuss is how does the amount of error correcting codes circuits grow due to the growing number of qubits. So in effect I would like to find the function that defines the size of error correcting codes as a function of number of qubits. I will be writing java codes that simulate the quantum concepts on a classical computer for the experiment section of my project. To actually implement a quantum algorithms for a large number of qubits will depend on being able to create Hamiltonians with certain energy gaps needed to perform the final measurements of these algorithms, and in which the total Hamiltonian is good enough to allow the necessary unitary operations to carry out the algorithms steps. Next I will discuss how the Quantum Hamiltonian Complexity is concerned with the questions of whether given a Hamiltonian, are there efficient algorithms for approximating its local properties, and to what degree can the ground state of such a Hamiltonian be represented by an efficient data structure. I will also introduce how to make predictions about the time evolution of the quantum system. Overall this thesis is to affirm that quantum computer is indeed realistic, and that it is possible to be efficient in energy and circuit complexity.

Schedule:

Week 1: August 21Go to Prof. Kahtami and Madura's offices to explain my research.
Week 2: August 28Implement 2-QSAT test on toy example
Week 3: September 4Write K-QSAT statisfiability checker
Week 4: September 11Generalize to a K-local Hamiltonian: Quantum Ising model
Week 5: September 18Generalize to a K-local Hamiltonian: Anti-ferromagnetic Heisenberg model
Week 6: September 25Review Quantum Mechanics
Week 7: Calender_Date_7Review Linear Algebra
Week 8: october 2Review Discrete Mathematics
Week 9: October 9Defense Presentation
Week 10: october 16Distribute my finished Thesis to Prof.Pollett, Prof. Kahtami, and Prof. Madura
Week 11: October 23Defense Presentation
Week 12: October 30Defense Presentation
Week 13: November 6Defense Presentation
Week 14: November 13Review Thesis
Week 15: November 20Review Thesis
Week 16: November 27Review Thesis

Deliverables:

1. 2-QSAT test on toy example

2. k-QSAT satisfiability checker

3. specific k-Local Hamiltonian example: quantum Ising model

4. specific k-Local Hamiltonian example: anti-feromagnetic Heisenberg model

5. Experiment with above models to see quantum threshold

References:

1. [M.Nielsen,I.Chuang2010] Quantum Computation and Quantum Information. M.A.Nielsen & Issac L.Chuang. Cambridge University Press. 2010.

2. [Gharibian2014] Quantum Hamiltonian Complexity. S.Gharibian, Y. Huang, Z. Landau and S.W.Shin. Foundation and Trends in Theoretical Computer Science. 2014.