# Quantum Operations

There are a number of operations you can preform on quantum registers with QCGPU.

## Measurement

You can measure the register in two ways. You can either do a single measurement and return an integer with the measured value or you can measure multiple times and return a `HashMap<String, i32>`, with the key being the bitstring, and the value being the number of times it was measured.

The measurements don't collapse the state.

They are used as follows:

    # #![allow(unused_variables)]
    #fn main() {
    use qcgpu::State;

    let mut state = State::new(5, 0);
    state.measure(); // Returns an integer
    state.measure_many(1000); // Measures 1000 times, returns a HashMap<String, i32>
    #}

There is also a convenience method to measure the first \(n\) qubits in the register. Again, the state is not collapsed

    # #![allow(unused_variables)]
    #fn main() {
    use qcgpu::State;

    let mut state = State::new(5, 0);
    state.measure_first(3, 1000); // Measures the first 3 qubits 1000 times, returns a HashMap<String, i32>
    #}

## Probability

QCGPU provides another method for getting the probability of each outcome.

The probability is calculated for a state \(\lvert \psi \rangle = \sum_{j = 0}^{2^n - 1} \alpha_j \lvert j \rangle\),

\[P(j) = |\alpha_j|^2\]

The method `get_probabilities` returns a `Vec<f32>` with each of the values corresponding to \(|\alpha_j|^2\) for each index \(j\).

    # #![allow(unused_variables)]
    #fn main() {
    use qcgpu::State;

    let mut state = State::new(1, 0);
    state.h(0);
    state.get_probabilities(); // [0.5, 0.5]
    #}