tfq.datasets.spin_system.tfi_rectangular

2D transverse field Ising-model quantum data set.

$$ H = - \sum_{\langle i,j angle} \sigma_i^z \sigma_{j}^z - g\sigma_i^x $$

Contains 51 circuit parameterizations corresponding to the ground states of the 2D TFI chain for g in [2.5,3.5]. This dataset contains 51 datapoints. Each datapoint is represented by a circuit (cirq.Circuit), a label (Python float) a Hamiltonian (cirq.PauliSum) and some additional metadata. Each Hamiltonian in a datapoint is a 2D TFI rectangular lattice with boundary condition boundary_condition on qubits whos order parameter dictates the value of label. The circuit in a datapoint prepares (an approximation to) the ground state of the Hamiltonian in the datapoint.

Example usage:

qbs = cirq.GridQubit.rect(9, 1)
circuits, labels, pauli_sums, addinfo  =
    tfq.datasets.tfi_rectangular(qbs, "torus")

You can print the available order parameters

[info.g for info in addinfo]
[2.5, 2.52, 2.54, ... ,3.46 , 3.48, 3.5]

and the circuit corresponding to the ground state for a certain order parameter

print(circuits[10])
                   ┌──────────────────────┐   ┌───────────────────── ...
(0, 0): ───H────ZZ─────────────────────────ZZ─────────────────────── ...
                │                          │
(1, 0): ───H────ZZ^0.948896────────────────┼──────────ZZ──────────── ...
                                           │          │
(2, 0): ───H────ZZ─────────────────────────┼──────────┼───────────── ...
                │                          │          │
(3, 0): ───H────┼──────────ZZ──────────────┼──────────┼───────────── ...
   .            .                          .          .
   .            .                          .          .

The labels indicate the phase of the system

>>> labels[10]
0

Additionally, you can obtain the cirq.PauliSum representation of the Hamiltonian

print(pauli_sums[10])
-2.700*X((0, 0))-2.700*X((1, 0))-2.700*X((2, 0))-2.700*X((3, 0))-
2.700*X((4, 0))-2.700*X((5, 0))-2.700*X((6, 0))-2.700*X((7, 0))- ...
-1.000*Z((3, 0))*Z((6, 0))-1.000*Z((4, 0))*Z((5, 0))

The fourth output, addinfo, contains additional information about each instance of the system (see tfq.datasets.spin_system.SpinSystem ).

For instance, you can print the ground state obtained from exact diagonalization

addinfo[10].gs
[-0.11843355-0.30690906j -0.04374221-0.11335368j -0.04374221-0.11335368j
 -0.02221491-0.0575678j  -0.04374221-0.11335368j -0.02221491-0.0575678j

 -0.04374221-0.11335368j -0.02221491-0.0575678j  -0.04374221-0.11335368j
 -0.04374221-0.11335368j -0.11843355-0.30690906j]

with corresponding ground state energy

addinfo[10].gs_energy
-26.974953331962762

You can also inspect the parameters

addinfo[10].params
{'theta_0': 0.948896, 'theta_1': 0.90053445, ...
'theta_8': 0.76966083, 'theta_9': 0.87608284}

and change them to experiment with different parameter values by using the unresolved variational circuit returned by tfichain

>>> new_params = {}
... for symbol_name, value in addinfo[10].params.items():
...    new_params[symbol_name] = 0.5 * value
>>> new_params
{'theta_0': 0.47444799542427063, 'theta_1': 0.4502672255039215, ...
'theta_8': 0.38483041524887085, 'theta_9': 0.43804141879081726}
>>> new_circuit = cirq.resolve_parameters(addinfo[10].var_circuit,
... new_params)
>>> print(new_circuit)
                   ┌──────────────────────┐   ┌───────────────────── ...
(0, 0): ───H────ZZ─────────────────────────ZZ─────────────────────── ...
                │                          │
(1, 0): ───H────ZZ^0.474───────────────────┼──────────ZZ──────────── ...
                                           │          │
(2, 0): ───H────ZZ─────────────────────────┼──────────┼───────────── ...
                │                          │          │
(3, 0): ───H────┼──────────ZZ──────────────┼──────────┼───────────── ...
   .            .                          .          .
   .            .                          .          .

qubits Python lst of cirq.GridQubits. Supported number of spins are [9, 12, 16].
boundary_condition Python str indicating the boundary condition of the chain. Supported boundary conditions are ["torus"].
data_dir Optional Python str location where to store the data on disk. Defaults to /tmp/.keras.

A Python lst cirq.Circuit of depth ceil(len(qubits) / 2) with resolved parameters. A Python lst of labels, 0, for the phase (g<3.04), 1 for the critical point (g==3.04) and 2 for the phase (g>3.04). A Python lst of cirq.PauliSums. A Python lst of namedtuple instances containing the following fields:

  • g: Numpy float order parameter.
  • gs: Complex np.ndarray ground state wave function from exact diagonalization.
  • gs_energy: Numpy float ground state energy from exact diagonalization.
  • res_energy: Python float residual between the circuit energy and the exact energy from exact diagonalization.
  • fidelity: Python float overlap between the circuit state and the exact ground state from exact diagonalization.
  • params: Dict with Python str keys and Numpyfloat values. Contains $M imes P $ parameters. Here $M$ is the number of parameters per circuit layer and $P$ the circuit depth.
  • var_circuit: Variational cirq.Circuit quantum circuit with unresolved Sympy parameters.