quairkit.database.hamiltonian

The library of common Hamiltonians.

quairkit.database.hamiltonian.ising_hamiltonian(edges, vertices)

Compute the Ising Hamiltonian.

\[\begin{align} H_{Ising}= \sum_{(u,v) \in E(u>v)}\gamma_{uv}Z_u Z_v + \sum_{k \in V}\beta_k X_k \end{align}\]
Parameters:
edges : Tensor

A tensor E shape=[V, V], where E[u][v] is gamma_{uv}.

vertices : Tensor

A tensor V shape=[V], where V[k] is beta_{k}.

Returns:

Hamiltonian representation of the Ising Hamiltonian.

Return type:

Hamiltonian

Examples

import torch
from quairkit.database.hamiltonian import ising_hamiltonian

edges = torch.tensor([[0, 1, 0.5],
                      [1, 0, 0.2],
                      [0.5, 0.2, 0]])
vertices = torch.tensor([0.3, 0.4, 0.1])
hamiltonian = ising_hamiltonian(edges, vertices)
print(f'The Ising_Hamiltonian is \n {hamiltonian}')

The Ising_Hamiltonian is
1.0 Z0, Z1
0.5 Z0, Z2
0.20000000298023224 Z1, Z2
0.30000001192092896 X0
0.4000000059604645 X1
0.10000000149011612 X2
quairkit.database.hamiltonian.xy_hamiltonian(edges)

Compute the XY Hamiltonian.

\[\begin{align} H_{XY}= \sum_{(u,v) \in E(u>v)}(\alpha_{uv}X_u X_v + \beta_{uv}Y_u Y_v) \end{align}\]
Parameters:
edges : Tensor

A tensor E shape=[2, V, V], where E[0][u][v] is alpha_{uv} and E[1][u][v] is beta_{uv}.

Returns:

Hamiltonian representation of the XY Hamiltonian.

Return type:

Hamiltonian

Examples

import torch
from quairkit.database.hamiltonian import xy_hamiltonian

edges = torch.tensor([
    [
        [0, 0.7, 0],
        [0.7, 0, 0.2],
        [0, 0.2, 0]
    ],
    [
        [0, 0.5, 0],
        [0.5, 0, 0.3],
        [0, 0.3, 0]
    ]
])
H_XY = xy_hamiltonian(edges)
print(f'The XY Hamiltonian is:\n{H_XY}')

The XY Hamiltonian is:
0.699999988079071 X0, X1
0.5 Y0, Y1
0.20000000298023224 X1, X2
0.30000001192092896 Y1, Y2
quairkit.database.hamiltonian.heisenberg_hamiltonian(edges)

Compute the Heisenberg Hamiltonian.

\[\begin{align} H_{Heisenberg}= \sum_{(u,v) \in E(u>v)}(\alpha_{uv}X_u X_v + \beta_{uv}Y_u Y_v + \gamma_{uv}Z_u Z_v) \end{align}\]
Parameters:
edges : Tensor

A tensor E shape=[3, V, V], where E[0][u][v] is alpha_{uv}, E[1][u][v] is beta_{uv}, and E[2][u][v] is gamma_{uv}.

Returns:

Hamiltonian representation of the Heisenberg Hamiltonian.

Return type:

Hamiltonian

Examples

import torch
from quairkit.database.hamiltonian import heisenberg_hamiltonian

edges = torch.tensor([
    [
        [0, 0.5, 0],
        [0.5, 0, 0.2],
        [0, 0.2, 0]
    ],
    [
        [0, 0.3, 0],
        [0.3, 0, 0.4],
        [0, 0.4, 0]
    ],
    [
        [0, 0.7, 0],
        [0.7, 0, 0.1],
        [0, 0.1, 0]
    ]
])
H_Heisenberg = heisenberg_hamiltonian(edges)
print(f'The Heisenberg Hamiltonian is:\n{H_Heisenberg}')

The Heisenberg Hamiltonian is:
0.5 X0, X1
0.30000001192092896 Y0, Y1
0.699999988079071 Z0, Z1
0.20000000298023224 X1, X2
0.4000000059604645 Y1, Y2
0.10000000149011612 Z1, Z2