View source on GitHub
|
1D XXZ model quantum data set.
tfq.datasets.xxz_chain(
qubits, boundary_condition='closed', data_dir=None
)
Used in the notebooks
| Used in the tutorials |
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\[ H = \sum_{i} \sigma_i^x \sigma_{i+1}^x + \sigma_i^y \sigma_{i+1}^y + \Delta\sigma_i^z \sigma_{i+1}^z \]
Contains 76 circuit parameterizations corresponding to
the ground states of the 1D XXZ chain for g in [0.3,1.8].
This dataset contains 76 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 XXZ 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.xxz_chain(qbs, "closed")
You can print the available order parameters
[info.g for info in addinfo][0.30, 0.32, 0.34, ... ,1.76, 1.78, 1.8]
and the circuit corresponding to the ground state for a certain order parameter
print(circuits[10])┌──────────────────┐ ┌──────────────────┐(0, 0): ───X───H───@─────────────ZZ─────────────────────YY────────── ...│ │ │(1, 0): ───X───────X────ZZ───────┼─────────────YY───────┼─────────── ...│ │ │ │(2, 0): ───X───H───@────ZZ^-0.922┼─────────────YY^-0.915┼─────────── ...│ │ │(3, 0): ───X───────X─────────────ZZ^-0.922──────────────YY^-0.915─── ...└──────────────────┘ └──────────────────┘
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])0.400*Z((0, 0))*Z((1, 0))+0.400*Z((1, 0))*Z((2, 0))+ ...+1.000*Y((0, 0))*Y((3, 0))+1.000*X((0, 0))*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
addinfo[10].gs[-8.69032854e-18-6.58023246e-20j 4.54546402e-17+3.08736567e-17j-9.51026525e-18+2.42638062e-17j 4.52284042e-02+3.18111120e-01j4.52284042e-02+3.18111120e-01j -6.57974275e-18-3.84526414e-17j-1.60673943e-17+5.79767820e-17j 2.86193021e-17-5.06694574e-17j]
with corresponding ground state energy
addinfo[10].gs_energy-6.744562646538039
You can also inspect the parameters
addinfo[10].params{'theta_0': 1.0780547, 'theta_1': 0.99271035, 'theta_2': 1.0854135, ...
and change them to experiment with different parameter values by using the unresolved variational circuit returned by xxzchain
>>> new_params = {}
... for symbol_name, value in addinfo[10].params.items():
... new_params[symbol_name] = 0.5 * value
>>> new_params
{'theta_0': 0.5390273332595825, 'theta_1': 0.49635517597198486, ...
>>> new_circuit = cirq.resolve_parameters(addinfo[10].var_circuit,
... new_params)
>>> print(new_circuit)
┌──────────────────┐ ┌──────────────────┐
(0, 0): ───X───H───@─────────────ZZ─────────────────────YY────────── ...
│ │ │
(1, 0): ───X───────X────ZZ───────┼─────────────YY───────┼─────────── ...
│ │ │ │
(2, 0): ───X───H───@────ZZ^(7/13)┼─────────────YY^0.543 ┼─────────── ...
│ │ │
(3, 0): ───X───────X─────────────ZZ^(7/13)──────────────YY^0.543 ─── ...
└──────────────────┘ └──────────────────┘
Args:
qubits: Python `lst` of `cirq.GridQubit`s. 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`.
Returns:
A Python `lst` cirq.Circuit of depth len(qubits) / 2 with resolved
parameters.
A Python `lst` of labels, 0, for the critical metallic phase
(`Delta<=1`) and 1 for the insulating phase (`Delta>1`).
A Python `lst` of `cirq.PauliSum`s.
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 Numpy`float` 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.