/// <summary>
/// Controlled not (CNOT) gate.
/// [ 1 0 0 0 ]
/// [ 0 1 0 0 ]
/// [ 0 0 0 1 ]
/// [ 0 0 1 0 ]
///
/// The CNOT gate works by combining the two input qubits (control and target) into a vector (of length 4, using tensor product).
/// Then it uses the assumption that the output control qubit is constant to calculate the target output qubit.
/// </summary>
/// <returns>Target qubit affected by the CNOT gate. The target qubit os constant (and is therefore not returned).</returns>
public static Qubit CNOT(Qubit control, Qubit target) // TODO: introduce qubit pair? or Qubit vector?
{
// First get tensor product of the two qubits
complex[] tensorProduct = TensorProduct(control, target);
// Put result here
complex[] result = new complex[4];
// Multiply with CNOT gate matrix
result[0] = tensorProduct[0];
result[1] = tensorProduct[1];
result[2] = tensorProduct[3];
result[3] = tensorProduct[2];
// Assumptions
// 1) control output qubit α equals control qubit α
// 2) control output qubit β equals control qubit β
// =>
// result[0] = α_control * α2 => α2 = result[0] / α_control
// result[1] = α_control * β2 => β2 = result[1] / α_control
// => (or, if α_control is zero)
// result[2] = β_control * α2 => α2 = result[2] / β_control
// result[3] = β_control * β2 => β2 = result[3] / β_control
if (control.Alpha != complex.Zero)
{
return(new Qubit(result[0] / control.Alpha, result[1] / control.Alpha));
}
else
{
return(new Qubit(result[2] / control.Beta, result[3] / control.Beta));
}
}
public override bool Equals(object obj)
{
complex c = (complex)obj;
return(c.Real == Real && c.Imaginary == Imaginary);
}
public complex(complex c)
{
this.Real = c.Real;
this.Imaginary = c.Imaginary;
}
/// <summary>
/// Constructs a qubit.
/// </summary>
/// <param name="alpha"></param>
/// <param name="beta"></param>
public Qubit(complex alpha, complex beta)
{
Debug.Assert(Math.Pow(alpha.Abs(), 2) + Math.Pow(beta.Abs(), 2) - 1 < 0.000001);
this.Alpha = alpha;
this.Beta = beta;
}