public IQuantumState Transform(IQuantumState input)
{
if (input.Dimension != 2 * InnerTransform.Dimension)
{
throw new ArgumentException(nameof(input));
}
var firstHalf = new Complex[Dimension / 2];
var secHalf = new Complex[Dimension / 2];
for (long i = 0; i < Dimension; i++)
{
// first half of vector is just copied over as an identity
if (i < Dimension / 2)
{
firstHalf[i] = input.GetAmplitude(new ComputationalBasis(i, NumQubits));
}
else
{
secHalf[i - (Dimension / 2)] = input.GetAmplitude(new ComputationalBasis(i, NumQubits));
}
}
var transformedSecHalf = InnerTransform.Transform(new MultiQubit(secHalf));
return(new MultiQubit(firstHalf.Concat(transformedSecHalf).ToArray()));
}
/// <summary>
/// Calculate function self-scalar values
/// </summary>
/// <param name="f">Input values</param>
/// <param name="ff">Output values</param>
public static void Scalar(Complex[] f, Complex[] ff)
{
var length = ff.Length;
var complex = f.Concat(Enumerable.Repeat(Complex.Zero, length - f.Length)).ToArray();
Fourier(complex, FourierDirection.Forward);
complex = complex.Select(x => x*Complex.Conjugate(x)/length).ToArray();
Fourier(complex, FourierDirection.Backward);
Array.Copy(complex, 0, ff, 0, length);
}
/// <summary>
/// Calculate function self-convolution values
/// </summary>
/// <param name="f">Input values</param>
/// <param name="fxf">Output values</param>
public static void Convolution(Complex[] f, Complex[] fxf)
{
int length = fxf.Length;
Complex[] complex = f.Concat(Enumerable.Repeat(Complex.Zero, length - f.Length)).ToArray();
Fourier(complex, FourierDirection.Forward);
complex = complex.Select(x => x*x/length).ToArray();
Fourier(complex, FourierDirection.Backward);
Array.Copy(complex, 0, fxf, 0, length);
}
/// <summary>
/// Calculate convolution values
/// </summary>
/// <param name="f">Input values</param>
/// <param name="g">Input values</param>
/// <param name="fxg">Output values</param>
public static void Convolution(Complex[] f, Complex[] g, Complex[] fxg)
{
int length = fxg.Length;
Complex[] complex = f.Concat(Enumerable.Repeat(Complex.Zero, length - f.Length)).ToArray();
Fourier(complex, FourierDirection.Forward);
Complex[] complex1 = g.Concat(Enumerable.Repeat(Complex.Zero, length - g.Length)).ToArray();
Fourier(complex1, FourierDirection.Forward);
int index = 0;
foreach (Complex value in complex1)
complex[index++] *= value/length;
Fourier(complex, FourierDirection.Backward);
Array.Copy(complex, 0, fxg, 0, length);
}
/// <summary>
/// Calculate scalar values
/// </summary>
/// <param name="f">Input values</param>
/// <param name="g">Input values</param>
/// <param name="fg">Output values</param>
public static void Scalar(Complex[] f, Complex[] g, Complex[] fg)
{
var length = fg.Length;
var complex = f.Concat(Enumerable.Repeat(Complex.Zero, length - f.Length)).ToArray();
Fourier(complex, FourierDirection.Forward);
var complex1 = g.Concat(Enumerable.Repeat(Complex.Zero, length - g.Length)).ToArray();
Fourier(complex1, FourierDirection.Backward);
var index = 0;
foreach (var value in complex1)
complex[index++] *= value/length;
Fourier(complex, FourierDirection.Backward);
Array.Copy(complex, 0, fg, 0, length);
}
