Create new QBit from a bit. maps \(0 \mapsto |0>\) and \(1 \mapsto |1>\)

Performs a measurement operation, collapsing a QBit to a Bit. The qubit will still exist in the quantum state, but be collapsed.

Finds qubit probability to collapse to a zero and one. Uses random number generator to "measure it" to a zero or one. Updates quantum state to remove impossible states, and normalizes it so probabilites sum to one.

Run a quantum program producing a single bit reps times and print the results

Print results from a 100 runs of a program

Sets a classical bit as the controlbit for a quantum gate. Making it run only when the classical bit is equal to one.

Pointer to a qubit in QState. Represents the linking function in QLambda

The Quantum Monad Keeps a state of the complex vector representation while allowing pseudo-random number generation

Pauli-X gate

\[ \text{X} = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} \]

Pauli-Y gate

\[ \text{Y} = \begin{bmatrix} 0 & -i \\ i & 0 \end{bmatrix} \]

Pauli-Z gate

\[ \text{Z} = \begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix} \]

Hadamard gate

\[ \text{X} = \frac1{\sqrt2} \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} \]

Phase gate

\[ \text{S} = \begin{bmatrix} 1 & 0 \\ 0 & i \end{bmatrix} \]

Pi/8 gate (T gate)

\[ \text{T} = \begin{bmatrix} 1 & 0 \\ 0 & e^{i\pi/4} \end{bmatrix} \]

CNOT gate

\[ \text{CNOT} = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \end{bmatrix} \]

Identity gate

\[ \text{I} = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} \]

SWAP gate

\[ \text{SWAP} = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix} \]

Hermetian adjoint of T gate (phasePi8)

Fredkin gate

Toffoli gate

\[ \begin{bmatrix} 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \end{bmatrix} \]

UROT gate

Controlled UROT

Quantum fourier transform

Run quantum program, discarding it's final state

Run quantum program, prints the final quantum state and returns the result

Prepares bell state

Performs bell measurement