Added simple VQE sample

samples/algorithms/SimpleVQE.qs

@@ -0,0 +1,200 @@
+/// # Sample
+/// Simplified Sample of a Variational Quantum Eigensolver
+///
+/// # Description
+/// This is an example of a Variational Quantum Eigensolver (VQE).
+/// This example includes:
+///   1. Simple classical optimization to find minimum of a multi-variable function
+///      in order to find an approximation to the minimum eigenvalue of a hamiltonian
+///   2. Finding Hamiltonian expectation value as a weighted sum of terms.
+///   3. Finding one term expectation value by performing multiple shots.
+///   4. Ansatz state preparation similar to the circuit in the referenced paper.
+/// To keep this sample simple hamiltonian terms are generated randomly.
+///
+/// # 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.Arrays.IsEmpty;
+import Std.Arrays.IndexRange;
+import Std.Convert.IntAsDouble;
+import Std.Diagnostics.Fact;
+import Std.Math.AbsD;
+import Std.Math.PI;
+
+/// # Summary
+/// Find the approximation to the minimum eigenvalue of a Hamiltonian by applying VQE
+operation Main() : Double {
+
+    // Find the approximation to the minimum eigenvalue of a Hamiltonian
+    // by varying ansatz parameters to minimize its expectation value.
+    SimpleDescent(
+        // Use a number of shots when estimating hamiltonian terms
+        // Actual VQE implementations may require very large number of shots.
+        FindHamiltonianExpectationValue(_, 100),
+        // Start from these angles for ansatz state preparation
+        [1.0, 1.0],
+        // Initial step to search for minimum
+        0.5,
+        // Stop optimization if step is 0
+        0.0,
+        // Stop optimization after several attempts.
+        // Actual VQE would need to make enough iterations
+        // to find energy with sufficient chemical accuracy.
+        50
+    )
+}
+
+/// # Summary
+/// Find expectation value of a Hamiltonian given parameters for the
+/// ansatz state and number of shots to evaluate each term.
+/// Different VQE applications will have different measurements and
+/// coefficients depending on the Hamiltonian being evaluated.
+operation FindHamiltonianExpectationValue(thetas : Double[], shots : Int) : Double {
+    let terms = [
+        ([PauliZ, PauliI, PauliI, PauliI], 0.16),
+        ([PauliI, PauliI, PauliZ, PauliI], -0.25),
+        ([PauliZ, PauliZ, PauliI, PauliI], 0.17),
+        ([PauliI, PauliI, PauliZ, PauliZ], 0.45),
+        ([PauliX, PauliX, PauliX, PauliX], 0.2),
+        ([PauliY, PauliY, PauliY, PauliY], 0.1),
+        ([PauliY, PauliX, PauliX, PauliY], -0.02),
+        ([PauliX, PauliY, PauliY, PauliX], -0.22),
+    ];
+    mutable value = 0.0;
+    for (basis, coefficient) in terms {
+        value += coefficient * FindTermExpectationValue(thetas, basis, shots);
+    }
+    value
+}
+
+/// # Summary
+/// Find expectation value of a Hamiltonian term given parameters for the
+/// ansatz state, measurement basis and number of shots to evaluate each term.
+operation FindTermExpectationValue(
+    thetas : Double[],
+    pauliBasis : Pauli[],
+    shots : Int
+) : Double {
+
+    mutable zeroCount = 0;
+    for _ in 1..shots {
+        use qs = Qubit[4];
+        PrepareAnsatzState(qs, thetas);
+        if Measure(pauliBasis, qs) == Zero {
+            zeroCount += 1;
+        }
+        ResetAll(qs);
+    }
+    IntAsDouble(zeroCount) / IntAsDouble(shots)
+}
+
+/// # Summary
+/// Prepare the ansatz state for given parameters on a qubit register
+/// This is an example of ansatz state preparation similar to the
+/// unitary couple clustered method used in the referenced paper.
+/// Actual VQE application will have different ansatz preparation operations.
+operation PrepareAnsatzState(qs : Qubit[], thetas : Double[]) : Unit {
+    BosonicExitationTerm(thetas[0], qs[0], qs[2]);
+    CNOT(qs[0], qs[1]);
+    NonBosonicExitataionTerm(thetas[1], qs[0], qs[1], qs[2], qs[3]);
+}
+
+/// # Summary
+/// Bosonic exitation circuit from the referenced paper.
+operation BosonicExitationTerm(
+    theta : Double,
+    moX : Qubit,
+    moY : Qubit
+) : Unit {
+    X(moX);
+    Adjoint S(moX);
+    Rxx(theta, moX, moY);
+    S(moX);
+    Adjoint S(moY);
+    Rxx(-theta, moX, moY);
+    S(moY);
+}
+
+/// # Summary
+/// Non-bosonic exitation circuit from the referenced paper.
+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);
+        Rz(theta, moXsoX);
+        CNOT(moXsoY, moXsoX);
+        Rz(theta, moXsoX);
+        CNOT(moYsoY, moXsoX);
+        Rz(-theta, moXsoX);
+        CNOT(moXsoY, moXsoX);
+        Rz(-theta, moXsoX);
+    } apply {
+        Adjoint S(moYsoX);
+        CNOT(moYsoX, moXsoX);
+    }
+    S(moYsoX);
+}
+
+/// # Summary
+/// Simple classical optimizer. A descent to a local minimum of function `f`.
+/// Tries to takes steps in all directions and proceeds if the new point is better.
+/// If no moves result in function value improvement the step size is halved.
+/// Actual VQE implementations use more elaborate optimizers.
+operation SimpleDescent(
+    f : Double[] => Double,
+    initialPoint : Double[],
+    initialStep : Double,
+    minimalStep : Double,
+    attemptLimit : Int
+) : Double {
+    Fact(not IsEmpty(initialPoint), "Argument array must contain elements.");
+    Fact(initialStep > 0.0, "Initial step must be positive.");
+    Fact(minimalStep >= 0.0, "Minimal step must be non-negative.");
+
+    mutable bestPoint = initialPoint;
+    mutable bestValue = f(bestPoint);
+    mutable currentStep = initialStep;
+    mutable currentAttempt = 0;
+
+    Message($"Beginning descent from value {bestValue}.");
+
+    while (currentAttempt < attemptLimit) and (currentStep > minimalStep) {
+        mutable hadImprovement = false;
+        for i in IndexRange(initialPoint) {
+            let nextPoint = bestPoint w/ i <- bestPoint[i] + currentStep;
+            let nextValue = f(nextPoint); // Evaluate quantum part
+            currentAttempt = currentAttempt + 1;
+            if nextValue < bestValue {
+                hadImprovement = true;
+                bestValue = nextValue;
+                bestPoint = nextPoint;
+                Message($"Value improved to {bestValue}.");
+            }
+            let nextPoint = bestPoint w/ i <- bestPoint[i] - currentStep;
+            let nextValue = f(nextPoint); // Evaluate quantum part
+            currentAttempt = currentAttempt + 1;
+            if nextValue < bestValue {
+                hadImprovement = true;
+                bestValue = nextValue;
+                bestPoint = nextPoint;
+                Message($"Value improved to {bestValue}.");
+            }
+        }
+
+        if not hadImprovement {
+            currentStep = currentStep / 2.0;
+        }
+    }
+    Message($"Descent done. Attempts: {currentAttempt}, Step: {currentStep}, Arguments: {bestPoint}, Value: {bestValue}.");
+    bestValue
+}

samples_test/src/tests/algorithms.rs

@@ -258,6 +258,22 @@ pub const SIMPLEISING_EXPECT: Expect =
     expect!["[Zero, Zero, Zero, One, One, Zero, One, One, Zero]"];
 pub const SIMPLEISING_EXPECT_DEBUG: Expect =
     expect!["[Zero, Zero, Zero, One, One, Zero, One, One, Zero]"];
+pub const SIMPLEVQE_EXPECT: Expect = expect![[r#"
+   Beginning descent from value 0.43300000000000005.
+   Value improved to 0.35300000000000004.
+   Value improved to 0.3454.
+   Value improved to 0.3422.
+   Value improved to 0.3216.
+   Descent done. Attempts: 52, Step: 0.0009765625, Arguments: [1.5, 1.0625], Value: 0.3216.
+   0.3216"#]];
+pub const SIMPLEVQE_EXPECT_DEBUG: Expect = expect![[r#"
+   Beginning descent from value 0.43300000000000005.
+   Value improved to 0.35300000000000004.
+   Value improved to 0.3454.
+   Value improved to 0.3422.
+   Value improved to 0.3216.
+   Descent done. Attempts: 52, Step: 0.0009765625, Arguments: [1.5, 1.0625], Value: 0.3216.
+   0.3216"#]];
 pub const SUPERDENSECODING_EXPECT: Expect = expect!["((false, true), (false, true))"];
 pub const SUPERDENSECODING_EXPECT_DEBUG: Expect = expect!["((false, true), (false, true))"];
 pub const SUPERPOSITION_EXPECT: Expect = expect!["Zero"];