Chris Pollett > Students > Yunxuan

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    [First Proposal]

    [Final Step of Shor's and Grover's Algorithms]

    [jQuantum QFT]

    [My Quantum Circuits]

    [Three Models]

    [Threshold of Error Correction]

    [jQuantum Manual]

    [Quantum State and LH]

    [QHC Scientists]

    [LH and Tensor Networks]

    [k-LH is QMA-complete]

    [Deutch Josza Algorithm]

    [Semester Report]

    [Second Proposal]

    [SolveQ Algorithm: 2-SAT]

    [Random-kSAT-Generator: Version 1]

    [Freezing Point Experiment]

    [Random-kQSAT-Generator: Version 2]

    [Random-kQSAT-Generator: Version 3]

    [Antiferromagnetic Heisenberg Model]

    [Ising Model]

    [Random-kQSAT-Generator: Version 4]

    [Random-kQSAT-Generator: Version 5]

    [Random-kQSAT-Generator: Version 6]

    [SolveQ Algorithm: 2-QSAT]


Physics Proposal

Quantum Hamiltonian Experiments

Yun Xuan Shi (

Advisor: Dr. Chris Pollett


My thesis is about quantum computation. The first part of my thesis is about the simulation of the Schrodinger equation; in this specific problem my matrix is called the Hamiltonian. In my thesis, I will discuss what causes a Hamiltonian matrix existing in nature to be implementable and simulatable on a quantum computer. I am interested in the ground state energy of the Hamiltonians. I am also interested in the degenerate eigen energies of the Hamiltonian and what causes them both mathematically and physically. 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 amount of error correcting codes as a function of number of qubits. Right now the smallest scale is 5 qubits, the largest scale is 50 qubits. I would like to research about implementing some number in between--say 20 qubits. I will be writing codes that simulate the quantum concepts on a classical computer for the experiment section of my project, most likely done in Java. To actually implement these algorithms for a large number of qubits will depend on being able to create Hamiltonians with a certain energy gaps needed to perform the final measurements of these algorithms, and in which the Hamiltonian affords the necessary unitary operations to carry out the algorithms steps. For general local Hamiltonians, meeting these constraints is known to be computationally realizable. 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. Quantum Hamiltonian Complexity is concerned with the questions of whether given a Hamiltonian, are there efficient algorithms for approximating its local properties, to what degree can the ground state of such a Hamiltonian be represented by an efficient data structure, and given an efficient approximate data structure to what degree can we use it to make predictions about future properties of the quantum system.


Week 1: Feb 20, 2018Presentation on threshold of quantum computation
Week 2: Feb 27, 2018Presentation on threshold of quantum computation
Week 3: Mar 6, 2018Learn how to use JQuantum
Week 4: Mar 13, 2018Prepare a Tutorial about JQuantum
Week 5: Mar 20, 2018Implement Shor's Algorithm to factor 21
Week 6: Mar 27, 2018Read about Deutsch Josza algorithm
Week 7: April 3, 2018Think about Deutsch Josza algorithm
Week 8: April 10, 2018Code Deutsch Josza algorithm
Week 9: April 17, 2018Code Deutsch Josza algorithm
Week 10: April 24, 2018Presentation on Hamiltonian Paper
Week 11: May 1, 2018Presentation on Hamiltonian Paper
Week 12: May 8, 2018Presentation on Hamiltonian Paper
Week 13: May 15, 2018Presentation on Hamiltonian Paper
Week 14: Calender_Date_1410 page report
Week 15: Calender_Date_1510 page report
Week 16: Calender_Date_1610 page report


The full project will be done when the second semester work is completed. The following will be done by the end of the semester:

1. Give a short presentation on the threshold for quantum computation result. Work out what would be p for Shor's. Then figure out what the size of a Shor's circuit would be if the error value was 10^-5.

2. Learn how to use jQuantum. Prepare a short tutorial for Dr. Pollett. Implement Shor's algorithm to factor 21.

3. Code in Java a program that takes simple input functions f(truth table given in file) and computes the Deutsch Josza algorithm for f (up to 5 qubits).

4. Create a presentation on Quantum Hamiltonian Complexity paper. In particular, work out the reduction for some particular concrete examples used to show 5-Local Hamiltonian is QMA-complete.

5. 10 page report on progress by end of semester


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.