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1D Transverse field Ising-model quantum data set.

$$ H = - \sum_{i} \sigma_i^z \sigma_{i+1}^z - g\sigma_i^x $$

Contains 81 circuit parameterizations corresponding to the ground states of the 1D TFI chain for g in [0.2,1.8]. This dataset contains 81 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 1D TFI chain 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(4, 1)
circuits, labels, pauli_sums, addinfo  =
    tfq.datasets.tfi_chain(qbs, "closed")

You can print the available order parameters

[info.g for info in addinfo]
[0.20, 0.22, 0.24, ... ,1.76, 1.78, 1.8]

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

                                                      ┌─────── ...
(0, 0): ───H───ZZ──────────────────────────────────ZZ───────── ...
               │                                   │
(1, 0): ───H───ZZ^0.761───ZZ─────────X^0.641───────┼────────── ...
                          │                        │
(2, 0): ───H──────────────ZZ^0.761───ZZ────────────┼────────── ...
                                     │             │
(3, 0): ───H─────────────────────────ZZ^0.761──────ZZ^0.761─── ...
                                                  └─────────── ...

The labels indicate the phase of the system

>>> labels[10]

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

-1.000*Z((0, 0))*Z((1, 0))-1.000*Z((1, 0))*Z((2, 0))-1.000*Z((2, 0))*
Z((3, 0))-1.000*Z((0, 0))*Z((3, 0))-0.400*X((0, 0))-0.400*X((1, 0))-
0.400*X((2, 0))-0.400*X((3, 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



with corresponding ground state energy


You can also inspect the parameters

{"theta_0": 0.7614564630036476, "theta_1": 0.6774991338794768,
"theta_2": 0.6407093304791429, "theta_3": 0.7335369771742435}

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": 0.3807282315018238, "theta_1": 0.3387495669397384,
"theta_2": 0.32035466523957146, "theta_3": 0.36676848858712174}
>>> new_circuit = cirq.resolve_parameters(addinfo[10].var_circuit,
... new_params)
>>> print(new_circuit)
                                                       ┌─────── ...
(0, 0): ───H───ZZ──────────────────────────────────ZZ───────── ...
               │                                   │
(1, 0): ───H───ZZ^0.761───ZZ─────────X^0.32────────┼────────── ...
                          │                        │
(2, 0): ───H──────────────ZZ^0.761───ZZ────────────┼────────── ...
                                     │             │
(3, 0): ───H─────────────────────────ZZ^0.761──────ZZ^0.761─── ...
                                                  └─────────── ...

qubits Python lst of cirq.GridQubits. Supported number of spins are [4, 8, 12, 16].
boundary_condition Python str indicating the boundary condition of the chain. Supported boundary conditions are ["closed"].
data_dir Optional Python str location where to store the data on disk. Defaults to /tmp/.keras.

A Python lst cirq.Circuit of depth len(qubits) / 2 with resolved parameters. A Python lst of labels, 0, for the ferromagnetic phase (g<1), 1 for the critical point (g==1) and 2 for the paramagnetic phase (g>1). 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.