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 21  Go to Prof. Kahtami and Madura's offices to explain my research. 
Week 2:
August 28  Implement 2QSAT test on toy example 
Week 3:
September 4  Write KQSAT statisfiability checker 
Week 4:
September 11  Generalize to a Klocal Hamiltonian: Quantum Ising model 
Week 5:
September 18  Generalize to a Klocal Hamiltonian: Antiferromagnetic Heisenberg model 
Week 6:
September 25  Review Quantum Mechanics 
Week 7:
Calender_Date_7  Review Linear Algebra 
Week 8:
october 2  Review Discrete Mathematics 
Week 9:
October 9  Defense Presentation 
Week 10:
october 16  Distribute my finished Thesis to Prof.Pollett, Prof. Kahtami, and Prof. Madura 
Week 11:
October 23  Defense Presentation 
Week 12:
October 30  Defense Presentation 
Week 13:
November 6  Defense Presentation 
Week 14:
November 13  Review Thesis 
Week 15:
November 20  Review Thesis 
Week 16:
November 27  Review Thesis 
Deliverables:
1. 2QSAT test on toy example
2. kQSAT satisfiability checker
3. specific kLocal Hamiltonian example: quantum Ising model
4. specific kLocal Hamiltonian example: antiferomagnetic 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.
