microsoft/qdk
Publicmirrored from https://github.com/microsoft/qdkAvailable
samples/algorithms/Ising/Simple2dIsingOrder1.qs
112lines · modeblame
8f28aa96DmitryVasilevsky1 years ago | 1 | /// # Sample |
3f3bde67DmitryVasilevsky1 years ago | 2 | /// Simulation of a simple Ising model evolution |
| 3 | /// on a 2D grid with first-order Trotterization. | |
8f28aa96DmitryVasilevsky1 years ago | 4 | /// |
| 5 | /// # Description | |
3f3bde67DmitryVasilevsky1 years ago | 6 | /// This sample demonstrates simulation of an Ising model Hamiltonian |
| 7 | /// on N1xN2 2D grid using a first-order Trotter-Suzuki approximation. | |
| 8 | /// This sample can be easily simulated classically with 3x3 grid and | |
| 9 | /// about 1000 shots. This sample is suitable for Base Profile. | |
8f28aa96DmitryVasilevsky1 years ago | 10 | /// For the purpose of simplicity this sample intentionally doesn't |
| 11 | /// post-process results or perform eigenvalue estimation. | |
| 12 | operation Main() : Result[] { | |
| 13 | // Dimensions of a 2D grid is N1 x N2 | |
| 14 | let N1 : Int = 3; | |
| 15 | let N2 : Int = 3; | |
| 16 | | |
| 17 | // Total evolution time | |
| 18 | let evolutionTime : Double = 4.0; | |
| 19 | // Number of steps | |
| 20 | let numberOfSteps : Int = 5; | |
| 21 | | |
| 22 | // Coefficient for 2-qubit interactions between neighboring qubits | |
| 23 | let J : Double = 1.0; | |
| 24 | // Coefficient for external field interaction for individual qubits | |
| 25 | let g : Double = 1.4; | |
| 26 | | |
| 27 | // Also try simulating with different strength of external field: | |
| 28 | // let g = 0.2; | |
| 29 | // let g = 1.0; | |
| 30 | // let g = 1.4; | |
| 31 | // let g = 2.0; | |
| 32 | | |
| 33 | // Model evolution | |
| 34 | IsingModel2DEvolution(N1, N2, J, g, evolutionTime, numberOfSteps) | |
| 35 | } | |
| 36 | | |
| 37 | /// # Summary | |
| 38 | /// Simulate simple Ising model evolution | |
| 39 | /// | |
| 40 | /// # Description | |
| 41 | /// Simulates state |𝜓⟩ evolution to find |𝜓(t)⟩=U(t)|𝜓(0)⟩. | |
| 42 | /// |𝜓(0)⟩ is taken to be |0...0⟩. | |
| 43 | /// U(t)=e⁻ⁱᴴᵗ, where H is an Ising model Hamiltonian H = -J·Σ'ᵢⱼZᵢZⱼ + g·ΣᵢXᵢ | |
| 44 | /// Here Σ' is taken over all pairs of neighboring qubits <i,j>. | |
3f3bde67DmitryVasilevsky1 years ago | 45 | /// Simulation is done by performing K steps assuming U(t)≈(U(t/K))ᴷ. |
8f28aa96DmitryVasilevsky1 years ago | 46 | operation IsingModel2DEvolution( |
| 47 | N1 : Int, | |
| 48 | N2 : Int, | |
| 49 | J : Double, | |
| 50 | g : Double, | |
| 51 | evolutionTime : Double, | |
| 52 | numberOfSteps : Int | |
| 53 | ) : Result[] { | |
| 54 | | |
| 55 | // Allocate qubit grid and structure it as a 2D array. | |
| 56 | use qubits = Qubit[N1 * N2]; | |
| 57 | let qubitsAs2D = Std.Arrays.Chunks(N2, qubits); | |
| 58 | | |
71ade5dcDmitryVasilevsky1 years ago | 59 | // Compute the time step |
| 60 | let dt : Double = evolutionTime / Std.Convert.IntAsDouble(numberOfSteps); | |
8f28aa96DmitryVasilevsky1 years ago | 61 | |
71ade5dcDmitryVasilevsky1 years ago | 62 | let theta_x = - g * dt; |
| 63 | let theta_zz = J * dt; | |
8f28aa96DmitryVasilevsky1 years ago | 64 | |
| 65 | // Perform K steps | |
| 66 | for i in 1..numberOfSteps { | |
| 67 | | |
| 68 | // Single-qubit interaction with external field | |
| 69 | for q in qubits { | |
| 70 | Rx(2.0 * theta_x, q); | |
| 71 | } | |
| 72 | | |
| 73 | // All Rzz gates applied in the following two loops commute so they can be | |
| 74 | // applied in any order. To reduce the depth of the algorithm, Rzz gates | |
| 75 | // between horizontal "even" pairs of qubits are applied first - pairs | |
| 76 | // that start at even indices. Then Rzz gates between "odd" pairs are | |
| 77 | // applied. That way all Rzz between horizontal "even" pairs can potentially | |
| 78 | // be done in parallel. Same is true about horizontal "odd" pairs, | |
| 79 | // vertical "even" pairs and vertical "odd" pairs. | |
| 80 | | |
| 81 | // Horizontal two-qubit interactions | |
| 82 | for row in 0..N1-1 { | |
| 83 | // Horizontal interactions between "even" pairs | |
| 84 | for col in 0..2..N2-2 { | |
| 85 | Rzz(2.0 * theta_zz, qubitsAs2D[row][col], qubitsAs2D[row][col + 1]); | |
| 86 | } | |
| 87 | | |
| 88 | // Horizontal interactions between "odd" pairs | |
| 89 | for col in 1..2..N2-2 { | |
| 90 | Rzz(2.0 * theta_zz, qubitsAs2D[row][col], qubitsAs2D[row][col + 1]); | |
| 91 | } | |
| 92 | } | |
| 93 | | |
| 94 | // Vertical two-qubit interactions | |
| 95 | for col in 0..N2-1 { | |
| 96 | | |
| 97 | // Vertical interactions between "even" pairs | |
| 98 | for row in 0..2..N1-2 { | |
| 99 | Rzz(2.0 * theta_zz, qubitsAs2D[row][col], qubitsAs2D[row + 1][col]); | |
| 100 | } | |
| 101 | | |
| 102 | // Vertical interactions between "odd" pairs | |
| 103 | for row in 1..2..N1-2 { | |
| 104 | Rzz(2.0 * theta_zz, qubitsAs2D[row][col], qubitsAs2D[row + 1][col]); | |
| 105 | } | |
| 106 | | |
| 107 | } | |
| 108 | | |
| 109 | } | |
| 110 | | |
| 111 | MResetEachZ(qubits) | |
| 112 | } |