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Quantum Computing Demo

You are required to do either this Quantum Computation demo OR the Lambda Calculus demo

Quantum computing is a form of computation that uses quantum phenomena such as superposition and entanglement. Its pervasiveness will only increase as it comes out of infancy and there continues to be major advancements. It is expected to become prominent part in computing and algorithms of the future. Surpassing the computational power of classical supercomputers by "harnessing" the power of quantum computation is one of the 21st century's biggest challenges.

Quantum computers uses `qubits,' bits that are in superposition of between states instead of being one or the other (like a classical binary bit). Qubits still collapse into binary bits, but its actual final state has a probabilistic outcome given by a probability density as opposed to a deterministic one.

In this laboratory we'll be using Qiskit, a open-source framework for quantum computing that allows you to simulate and use real quantum bits on IBM's quantum computers. There's a few different ways of using Qiskit:

- You can use Qiskit through IBM's online environment, accessible here.
- You can install Qiskit as a Python library through here.

This prac will allow you to explore qubits and the different classical and quantum operations you can use to manipulate qubits in a quantum circuit. Qiskit's documentation can be found here.

1. What does a Hadamard gate do?

2. Draw a simple quantum circuit with three qubits that returns 1111)> with certainty.

3. Draw a quantum circuit with three qubits that returns 1111) or 1101) with 50% probability each

4. Draw a quantum circuit with three qubits that returns 1000), 1001), 1010), 1011), 1100), 1101) or 1111) with equal probability.

5. What does the Bloch sphere represent? Describe the Bloch sphere created by the circuit in the previous question.

6. Make a quantum circuit whose final Bell state is *(101) -110)).

7. Simulate a coin toss using qubit(s) in a quantum circuit. Why does this lead to better 'randomness' than a normal/classical coin toss? How could you extend this to be a random number generator?

8. Implement a solution to the Deutsch oracle problem as discussed in lectures in Qiskit (using the Deutsch-Jozsa Algorithm).