quantum-computing-simulator

Goals

• Implement a quantum computing simulator in order to help us understand quantum mechanics / quantum phenomena better.
• Simulate Shor's algorithm for factoring numbers.
• Visualize quantum circuits to help explain what's going on.

Visualization

• Basis View

  • 2^n complex numbers for each input / output of each gate.

  • Use color to indicate the argument

  • Use height? Arrow? To indicate the modulus.

  • e.g.

    • x_0|00>
    • x_1|01>
    • x_2|10>
    • x_3|11>

  • e.g.

    • 1 |00>
    • 0 |01>
    • 0 |10>
    • 0 |11>

  • e.g.

    • i/sqrt(4) |00>
    • isqrt(3/8) |01>
    • -isqrt(1/4) |10>
    • isqrt(1/8) |11>

  • Show the probabilities at the outputs

Todo

• QuantumCircuit
  • Reimplement the interference example with QuantumCircuit
  • Implement Quantum Fourier Transform and its inverse

Concepts

Qubits

Example Qubit State:

phi = 1/sqrt(2) * (|0> + |1>)

If measured, Born Rule means that P(0) = 1/2, P(1) = 1/2.

In general: phi = alpha * |0> + beta * |1> where alpha^2 + beta^2 = 1

So, we can put alpha, beta, in a vector and call that the state of our Qubit.

(alpha, beta)^T on the unit sphere is an arbitrary state.

For multiple qubits, we have multiple vectors, but it's convenient to put them in one big vector and apply it.

e.g. CNOT

|00> -> |00> |01> -> |01> |10> -> |11> |11> -> |10>

We can represent this as a 4x4 matrix operating on a 4-component vector.

e.g.

|10> = [0, 1, 1, 0]^T