public static CompositeTransform GetGroverDiffusionOperator(bool[] blackBoxFunc)
{
int n = blackBoxFunc.LongLength.BitsCeiling();
// 1. oracle
var grover = new CompositeTransform(GetOracle(blackBoxFunc));
// 2. hadamar all bits
foreach (int i in Enumerable.Range(0, n))
{
grover = grover.Apply(Gates.H, i);
}
// 3. TODO: phase flip every basis except |0> (how do i do this with basic gates?? going to do a custom MultiGate for now)
// from mike and ike: 'can be implemented using the techniques of section 4.3 using O(n) gates
long dim = blackBoxFunc.LongLength;
var elements = new Complex[dim, dim];
foreach (long i in LongExt.Range(0, dim))
{
elements[i, i] = i == 0 ? 1 : -1;
}
grover = grover.Apply(new MultiGate(elements, n));
//4. hadamar all bits again
foreach (int i in Enumerable.Range(0, n))
{
grover = grover.Apply(Gates.H, i);
}
return(grover);
}
/// <summary>
/// The blackBoxFunc represents a search problem, where the goal is to find the inputs that
/// result in true. This function turns the classical search problem into a quantum transformation
/// by either flipping the input when the function is true, or leaving it unchanged when it is false.
/// |x> -> (-1)^f(x) |x>
/// </summary>
public static IUnitaryTransform GetOracle(bool[] blackBoxFunc)
{
long dim = blackBoxFunc.LongLength;
var elements = new Complex[dim, dim];
foreach (long i in LongExt.Range(0, dim))
{
elements[i, i] = blackBoxFunc[i] ? -1 : 1;
}
return(new MultiGate(elements, 1));
}
/// <summary>
/// Takes a (hopefully linear function) from int to int and turns it into
/// a complex unitary transform that reproducest he function when input with
/// classical bits that represent the integer input.
/// </summary>
public static IUnitaryTransform FromFunction(
Func <long, long> func,
int numBits,
Func <long, long, long> powVersion = null)
{
long dimension = (long)Math.Pow(2, numBits);
var elements = new Complex[dimension, dimension];
foreach (long i in LongExt.Range(0, dimension))
{
elements[func(i), i] = 1;
}
return(new MultiGate(
elements,
(int)Math.Pow(numBits, 3), // simulated with O(L^3) gates
exp => FromFunction(
input => powVersion(input, exp),
numBits, // same input bits
powVersion))); // same method for powering
}
public IUnitaryTransform Pow(long exponent)
{
IUnitaryTransform wtf = this;
return(new CompositeTransform(LongExt.Range(0, exponent).Select(exp => wtf).ToArray()));
}
public IUnitaryTransform Pow(long exponent) => new CompositeTransform(LongExt.Range(0, exponent).Select(exp => this).ToArray());