Added Ising model sample (#2060)

This adds Ising model sample with explanations.

---------

Co-authored-by: Dmitry Vasilevsky <[email protected]>

samples/algorithms/SimpleIsing.qs

@@ -0,0 +1,113 @@
+/// # Sample
+/// Simulation of a simple Ising model evolution on a 2D grid
+///
+/// # Description
+/// This example demonstrates simulation of an Ising model Hamiltonian
+/// on an N1xN2 2D grid. This example can be easily simulated classically
+/// with 3x3 grid and about 500 shots.
+/// This sample is suitable for Base Profile.
+/// For the purpose of simplicity this sample intentionally doesn't
+/// post-process results or perform eigenvalue estimation.
+operation Main() : Result[] {
+    // Dimensions of a 2D grid is N1 x N2
+    let N1 : Int = 3;
+    let N2 : Int = 3;
+
+    // Total evolution time
+    let evolutionTime : Double = 4.0;
+    // Number of steps
+    let numberOfSteps : Int = 5;
+
+    // Coefficient for 2-qubit interactions between neighboring qubits
+    let J : Double = 1.0;
+    // Coefficient for external field interaction for individual qubits
+    let g : Double = 1.4;
+
+    // Also try simulating with different strength of external field:
+    // let g = 0.2;
+    // let g = 1.0;
+    // let g = 1.4;
+    // let g = 2.0;
+
+    // Model evolution
+    IsingModel2DEvolution(N1, N2, J, g, evolutionTime, numberOfSteps)
+}
+
+/// # Summary
+/// Simulate simple Ising model evolution
+///
+/// # Description
+/// Simulates state |𝜓⟩ evolution to find |𝜓(t)⟩=U(t)|𝜓(0)⟩.
+/// |𝜓(0)⟩ is taken to be |0...0⟩.
+/// U(t)=e⁻ⁱᴴᵗ, where H is an Ising model Hamiltonian H = -J·Σ'ᵢⱼZᵢZⱼ + g·ΣᵢXᵢ
+/// Here Σ' is taken over all pairs of neighboring qubits <i,j>.
+/// Simulation is done by performing K steps assuming U(t)≈U(t/K)ᴷ.
+operation IsingModel2DEvolution(
+    N1 : Int,
+    N2 : Int,
+    J : Double,
+    g : Double,
+    evolutionTime : Double,
+    numberOfSteps : Int
+) : Result[] {
+
+    // Allocate qubit grid and structure it as a 2D array.
+    use qubits = Qubit[N1 * N2];
+    let qubitsAs2D = Std.Arrays.Chunks(N2, qubits);
+
+    // Compute the step time
+    import Std.Convert.IntAsDouble;
+    let stepTime : Double = evolutionTime / IntAsDouble(numberOfSteps);
+
+    let theta_x = - g * stepTime;
+    let theta_zz = J * stepTime;
+
+    // Perform K steps
+    for i in 1..numberOfSteps {
+
+        // Single-qubit interaction with external field
+        for q in qubits {
+            Rx(2.0 * theta_x, q);
+        }
+
+        // All Rzz gates applied in the following two loops commute so they can be
+        // applied in any order. To reduce the depth of the algorithm, Rzz gates
+        // between horizontal "even" pairs of qubits are applied first - pairs
+        // that start at even indices. Then Rzz gates between "odd" pairs are
+        // applied. That way all Rzz between horizontal "even" pairs can potentially
+        // be done in parallel. Same is true about horizontal "odd"  pairs,
+        // vertical "even" pairs and vertical "odd" pairs.
+
+        // Horizontal two-qubit interactions
+        for row in 0..N1-1 {
+            // Horizontal interactions between "even" pairs
+            for col in 0..2..N2-2 {
+                Rzz(2.0 * theta_zz, qubitsAs2D[row][col], qubitsAs2D[row][col + 1]);
+            }
+
+            // Horizontal interactions between "odd" pairs
+            for col in 1..2..N2-2 {
+                Rzz(2.0 * theta_zz, qubitsAs2D[row][col], qubitsAs2D[row][col + 1]);
+            }
+        }
+
+        // Vertical two-qubit interactions
+        for col in 0..N2-1 {
+
+            // Vertical interactions between "even" pairs
+            for row in 0..2..N1-2 {
+                Rzz(2.0 * theta_zz, qubitsAs2D[row][col], qubitsAs2D[row + 1][col]);
+            }
+
+            // Vertical interactions between "odd" pairs
+            for row in 1..2..N1-2 {
+                Rzz(2.0 * theta_zz, qubitsAs2D[row][col], qubitsAs2D[row + 1][col]);
+            }
+
+        }
+
+    }
+
+    MResetEachZ(qubits)
+}
+

samples_test/src/tests/algorithms.rs

@@ -254,6 +254,10 @@ pub const SHOR_EXPECT_DEBUG: Expect = expect![[r#"
     Found factor=13
     Found factorization 143 = 13 * 11
     (13, 11)"#]];
+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 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"];