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2D transverse field Ising-model quantum data set.
tfq.datasets.spin_system.tfi_rectangular(
qubits, boundary_condition='torus', data_dir=None
)
\[ H = - \sum_{\langle i,j angle} \sigma_i^z \sigma_{j}^z - g\sigma_i^x \]
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──────────────┼──────────┼───────────── ...
. . . .
. . . .
Args | |
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qubits
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Python lst of cirq.GridQubits. Supported number of spins
are [9, 12, 16].
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boundary_condition
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Python str indicating the boundary condition
of the chain. Supported boundary conditions are ["torus"].
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data_dir
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Optional Python str location where to store the data on
disk. Defaults to /tmp/.keras.
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Returns | |
|---|---|
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:
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