public void PhaseEstComplexity()
{
// complexity = (sum(2^n) from 0 to n) + n + n*(n+1) / 2
// todo: add back swaps
PhaseEstimator.GatePhaseEstimator(Gates.X, 2).NumGates.Should().Be(3 + 2 + 1 + 2 + 3 * 1);
PhaseEstimator.GatePhaseEstimator(Gates.X, 3).NumGates.Should().Be(6 + 3 + 1 + 2 + 4 + 3 * 1);
PhaseEstimator.GatePhaseEstimator(Gates.X, 4).NumGates.Should().Be(10 + 4 + 1 + 2 + 4 + 8 + 3 * 2);
PhaseEstimator.GatePhaseEstimator(Gates.X, 5).NumGates.Should().Be(15 + 5 + 1 + 2 + 4 + 8 + 16 + 3 * 2);
}
public void PhaseTestTwo()
{
var eigenvector = new Qubit(ComplexExt.OneOverRootTwo, -ComplexExt.OneOverRootTwo);
var phaseTest = PhaseEstimator.GatePhaseEstimator(Gates.X, 4);
var res = phaseTest.Transform(new MultiQubit(new[]
{
// t register set to zero
Qubit.ClassicZero, Qubit.ClassicZero, Qubit.ClassicZero, Qubit.ClassicZero,
eigenvector,
}));
// sanity check
res.TwoNorm().Should().BeApproximately(1, AssertionHelpers.Precision);
// should be the same eigenvector
res.TrueChance(4).Should().BeApproximately(0.5, AssertionHelpers.Precision);
// eignenvalue is -1 -> i = e^(2pitheta) -> theta = 1/2
res.TrueChance(0).Should().BeApproximately(1, AssertionHelpers.Precision); // 1/2 bit
res.TrueChance(1).Should().BeApproximately(0, AssertionHelpers.Precision); // 1/4 bit
res.TrueChance(2).Should().BeApproximately(0, AssertionHelpers.Precision); // 1/8 bit
res.TrueChance(3).Should().BeApproximately(0, AssertionHelpers.Precision); // 1/16 bit
}