public void PhaseStartTest()
{
var eigenvector = new Qubit(0, 1);
var phaseTest = PhaseEstimator.GatePhaseEstimatorStart(Gates.S, 2);
var res = phaseTest.Transform(new MultiQubit(new[]
{
Qubit.ClassicZero, Qubit.ClassicZero, // t register set to zero
eigenvector
}));
// sanity check
res.TwoNorm().Should().BeApproximately(1, AssertionHelpers.Precision);
// hand calced
var resArr = res.ToArray();
resArr[0].ShouldBe(0);
resArr[1].ShouldBe(0.5);
resArr[2].ShouldBe(0);
resArr[3].ShouldBe(0.5 * Complex.ImaginaryOne);
resArr[4].ShouldBe(0);
resArr[5].ShouldBe(-0.5);
resArr[6].ShouldBe(0);
resArr[7].ShouldBe(-0.5 * Complex.ImaginaryOne);
}
public void PhaseHadamarTest()
{
long x = 2;
long n = 3;
int l = n.BitsCeiling();
int t = l;// OrderFindingTransform.GetPercision(n);
var regs = OrderFindingTransform.Registers(t, l).ToArray();
IUnitaryTransform orderfinder = PhaseEstimator.GetPhaseHadamar(t, l);
var regTwo = MultiQubit.BasisVector(1, l);
var regOne = new MultiQubit(Enumerable.Range(0, t).Select(i => Qubit.ClassicZero).ToArray());
var input = new MultiQubit(regOne, regTwo);
IQuantumState res = orderfinder.Transform(input);
string inputStr = input.Print(regs);
inputStr.Should().Be("+1.00|0>|1>");
string outStr = res.Print(regs);
// first reg is unchanged, second reg is maximally mixed
outStr.Should().Be("+0.50|0>|1>+0.50|1>|1>+0.50|2>|1>+0.50|3>|1>");
}
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
}
