Quantum.Gates

Reexports

Definitions

gate : Num a => (1 _ : Matrix r1 c1 a) -> (1 _ : Matrix c1 n a) -> Matrix r1 n a

  Apply a quantum gate to a quantum system via matrix multiplication.
  Example: `gate (H >< ID) myVec`
  Note: Both inputs to `gate` are linear.

Visibility: export

(|>) : Num a => (1 _ : Matrix c1 n a) -> (1 _ : Matrix r1 c1 a) -> Matrix r1 n a

  An infix operator for `gate`.
  m |> g = gate g m
  
  This is useful for chaining gates together.

Visibility: export
Fixity Declaration: infixl operator, level 4

ID : Matrix 2 2 Double

  The Identity gate. This gate does nothing.

Visibility: public export

IDN : (n : Nat) -> Matrix n n Double

  The Identity gate of size `n`. where `n` is the rows and cols of the matrix.

Visibility: public export

X : Matrix 2 2 Double

  The Pauli-X gate. This gate flips the state of a qubit.
  This is equivalent to the classical NOT gate.

Visibility: public export

H : Matrix 2 2 Double

  The Hadamard Gate.
  This gate acts upon a single qubit and puts it into a superposition.

Visibility: public export

CNOT : Matrix 4 4 Double

  Controlled Not Gate.
  This gate flips the second qubit if the first qubit is in the state |1>.
  
  NOTE: This gate is only defined for 2 qubits that are adjacent to each other.
  Use `CNOTN` for non adjacent qubits.

Visibility: public export

pow2 : Num a => Nat -> a

  A helper function to calculate the powers of 2.

Visibility: public export

COND : (n : Nat) -> Matrix (pow2 (minus n 1)) (pow2 (minus n 1)) Double -> Matrix (2 * pow2 (minus n 1)) (2 * pow2 (minus n 1)) Double

  Conditional gate. Applies a gate to a system if the control bit is |1>
  n is the number of qbits in the system (including the control bit)
  See https://quantumcomputing.stackexchange.com/questions/4252/how-to-derive-the-cnot-matrix-for-a-3-qubit-system-where-the-control-target-qu

Visibility: public export

measurePure : Double -> (1 _ : QSystem n) -> QSystem n

  Deterministically measure a quantum system

Visibility: export

measure : (1 _ : QSystem n) -> Q (QSystem n)

  Non-deterministically measure a quantum system

Visibility: export