Added simple VQE sample - quantum step of VQE

samples/algorithms/SimpleVQE.qs

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+/// # Sample
+/// A part of ansatz circuit used in water molecule simulation
+/// This sample is suitable for adaptive profile.
+///
+/// # Description
+/// This is an example of the quantum part of a Variational Quantum Eigensolver (VQE) method.
+/// This example shows one variant of ansatz circuit used in a water molecule simulation
+/// in the referenced paper. To keep this sample suitable for adaptive profile,
+/// random angles are used and optimization part is omitted.
+///
+/// # Reference
+/// Ground-state energy estimation of the water molecule on a trapped ion quantum
+/// computer by Yunseong Nam et al., 2019. https://arxiv.org/abs/1902.10171
+
+import Std.Diagnostics.Fact;
+
+/// # Summary
+/// Bosonic exitation circuit
+operation BosonicExitationTerm(
+    theta: Double,
+    moX: Qubit,
+    moY: Qubit): Unit {
+
+    Adjoint S(moX);
+    Rxx(theta, moX, moY);
+    S(moX);
+    Adjoint S(moY);
+    Rxx(-theta, moX, moY);
+    S(moY);
+}
+
+/// # Summary
+/// Non-bosonic exitation circuit
+operation NonBosonicExitataionTerm(
+    theta: Double,
+    moXsoX : Qubit,
+    moXsoY : Qubit,
+    moYsoX : Qubit,
+    moYsoY : Qubit) : Unit {
+
+    Adjoint S(moXsoX);
+    within {
+        CNOT(moXsoX, moYsoY);
+        CNOT(moXsoX, moYsoX);
+        CNOT(moXsoX, moXsoY);
+        H(moXsoX);
+    } apply {
+        Rz(theta, moXsoX);
+        CNOT(moXsoY, moXsoX);
+        Rz(theta, moXsoX);
+        CNOT(moYsoY, moXsoX);
+        Rz(-theta, moXsoX);
+        CNOT(moXsoY, moXsoX);
+        Rz(-theta, moXsoX);
+        Adjoint S(moYsoX);
+        CNOT(moYsoX, moXsoX);
+        Rx(theta, moXsoX);
+        CNOT(moXsoY, moXsoX);
+        Rx(theta, moXsoX);
+        CNOT(moYsoY, moXsoX);
+        Rz(-theta, moXsoX);
+        CNOT(moXsoY, moXsoX);
+        Rz(-theta, moXsoX);
+    }
+    S(moYsoX);
+}
+
+/// # Summary
+/// Prepare state containing both bosonic and non-bosinic interactions
+/// And measure the result in PauliZ basis.
+operation PrepareAndMeasureAnsatzInZ(
+    thetasMo: Double[],
+    thetasSo: Double[]) : Result[] {
+
+    Fact(Length(thetasMo) == 4, "Length of thetasMo should be 4.");
+    Fact(Length(thetasSo) == 4, "Length of thetasSo should be 4.");
+
+    use mo = Qubit[4];
+
+    BosonicExitationTerm(thetasMo[0], mo[0], mo[1]);
+    BosonicExitationTerm(thetasMo[1], mo[2], mo[3]);
+    BosonicExitationTerm(thetasMo[2], mo[0], mo[3]);
+    BosonicExitationTerm(thetasMo[3], mo[1], mo[2]);
+
+    use so = Qubit[4];
+    CNOT(mo[0], so[0]);
+    CNOT(mo[1], so[1]);
+    CNOT(mo[2], so[2]);
+    CNOT(mo[3], so[3]);
+
+    NonBosonicExitataionTerm(thetasSo[0], mo[0], so[0], mo[1], so[1]);
+    NonBosonicExitataionTerm(thetasSo[1], mo[2], so[2], mo[3], so[3]);
+    NonBosonicExitataionTerm(thetasSo[2], mo[1], so[1], mo[2], so[2]);
+    NonBosonicExitataionTerm(thetasSo[3], mo[0], so[0], mo[3], so[3]);
+
+    MResetEachZ(mo+so)
+}
+
+/// # Summary
+/// Count number of zeroes when performing measurements
+/// on a state determined by some predefined angles.
+operation FindZeroFrequencies(shots: Int): Int[] {
+    let thetasMo = [0.5, 0.5, 0.5, 0.5];
+    let thetasSo = [0.3, 0.3, 0.3, 0.3];
+    mutable c0 = 0;
+    mutable c1 = 0;
+    mutable c2 = 0;
+    mutable c3 = 0;
+    mutable c4 = 0;
+    mutable c5 = 0;
+    mutable c6 = 0;
+    mutable c7 = 0;
+    for _ in 1..shots {
+        let results = PrepareAndMeasureAnsatzInZ(thetasMo, thetasSo);
+        set c0 = c0 + if results[0] == Zero {1} else {0};
+        set c1 = c1 + if results[1] == Zero {1} else {0};
+        set c2 = c2 + if results[2] == Zero {1} else {0};
+        set c3 = c3 + if results[3] == Zero {1} else {0};
+        set c4 = c4 + if results[4] == Zero {1} else {0};
+        set c5 = c4 + if results[5] == Zero {1} else {0};
+        set c6 = c4 + if results[6] == Zero {1} else {0};
+        set c7 = c4 + if results[7] == Zero {1} else {0};
+    }
+    [c0, c1, c2, c3, c4, c5, c6, c7]
+}
+
+/// # Summary
+/// Prepare one ansatz state and perform measurements multiple times
+/// In actual VQE state parameters will be varied based on measurement
+/// results.
+operation Main() : Int[] {
+    FindZeroFrequencies(1000)
+}