Homework 1

Important: Write Name and Unity ID on every submission file. Name the submission file correctly as asked for.

  1. (0 points) Get a D-Wave account, download and install D-Wave Ocean as follows:
  2. (15 points, 5+15) Similar to the example with the 3-qubit solution of the 3-qubit OR, create a NOR relation (the opposite of an OR relation):

    Turn in a screen shot of both tabs of spreadsheet as file nor.pdf

  3. (30 points, 15 each) Create an Ocean program for the NOR relation in simulation and on actual hardware.

    Turn in files nor-sim.py and nor-hw.py

  4. (20 points) Generalize D-Wave's factoring example to return 4-bit factors. D-Wave factoring tutorial provides a rough idea of the problem.
  5. The Jupiter Notebook (Factoring Example) gives more details.

    Turn in files demo.py and interfaces.py

  6. (20 points) Prove that there is no solution of XOR with only 3 qubits. (You can experiment with the quantum apprentice worksheet to gain some intuition why there is no solution, but the proof has to be formal.)

    Submit proof.pdf

  7. (15 points) Construct a correct 4 qubit XOR Hamiltonian utilizing 1 ancilla qubit and assuming qubits to be either in state 0 or 1 by Notice that adding an ancilla is similar to creating a 4-qubit embedding for a 3-qubit problem --- in that you add a qubit. It differs in that you don't create an alignment (equal) between two qubits, i.e., the ancilla may have different values than any other qubit for the correct solution (ground states). In fact, it has to have different values or there was no point in adding the ancilla in first place (to extend your Hamiltonian space).

    Submit xor.pdf, the snapshot of the Quantum Apprentice spreadsheet.