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 2-QSAT test on toy example |
Week 3:
September 4 | Write K-QSAT statisfiability checker |
Week 4:
September 11 | Generalize to a K-local Hamiltonian: Quantum Ising model |
Week 5:
September 18 | Generalize to a K-local Hamiltonian: Anti-ferromagnetic 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. 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.
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