Quantum many-body physics datasets

Simulating quantum many-body physics is an area of research with the potential for practical quantum advantage. This field investigates spin models displaying quantum correlations. Here you can explore our available quantum spin datasets for some common spin systems.

Spin systems

These datasets provide access to the following spin systems, with up to 16 particles:

• Transverse-field Ising model

  Parameterized by energy prefactor \(J\), and external field \(h\).

  Hamiltonian: \(J\sum_{\langle i,j\rangle} \sigma_i^z\sigma_j^z + h\sum_i \sigma_i^x\)

  Order parameter: \(\langle M_z \rangle =\langle |\sum_i \sigma_i^z|\rangle\)
• XXZ Heisenberg model

  Parameterized by coupling term \(J_{xy}\) and \(J_z\).

  Hamiltonian: \(J_{xy}\sum_{\langle i,j\rangle}(\sigma_i^x\sigma_j^x+\sigma_i^y\sigma_j^y) + J_z\sum_{\langle i,j\rangle} \sigma_i^z \sigma_j^z\)

  Order parameter: \(\langle M_z \rangle =\langle |\sum_i \sigma_i^z|\rangle\)
• Fermi-Hubbard model

  Parameterized by hopping term \(t\), on-site interaction term \(U\) and spin direction \(\sigma \in \{ \uparrow, \downarrow \}\).

  Hamiltonian: \(-t(\sum_{\langle i, j\rangle, \sigma} \hat{c}^\dagger_i\hat{c}_j + h.c.) + U \sum_i \hat{n}_{i\uparrow} \hat{n}_{i\downarrow}\)
• Bose-Hubbard model

  Parameterized by hopping term \(t\), and on-site interaction term \(U\) with Fock space truncation of \(4\).

  Hamiltonian: \(-t ( \sum_{\langle i, j\rangle} \hat{b}^\dagger_i\hat{b}_j + h.c.) + U \sum_i \hat{n}_{i}\hat{n}_{i}\)

For each spin system, datasets are available for 1-D lattices (linear chain) and 2-D lattices (rectangular grid) with and without periodic boundary conditions. Each dataset contains results for 100 different values of a tunable parameter such as the external magnetic field, coupling constants, etc. Additionally, each dataset contains classical shadows obtained with 1000-shot randomized measurements in the Pauli basis.

Accessing spin datasets

The spin datasets can be downloaded and loaded to memory using the load() function as follows:

>>> data = qml.data.load(
...     "qspin", sysname="Ising", periodicity="closed", lattice="chain", layout=(1, 4)
... )[0]
>>> print(data)
<Dataset = description: qspin/Ising/closed/chain/1x4, attributes: ['spin_system', 'hamiltonians', ...]>

Here, the positional argument "qspin" denotes that we are loading a spin dataset, while the keyword arguments sysname, periodicity, lattice, and layout specify the requested dataset. The values for these keyword arguments are included in the table below. For more information on using PennyLane functions please see the PennyLane Documentation.

Spin system (sysname)	Lattices	Periodicity	Layout	Description
Transverse-field Ising model (Ising)	Chain Rectangular	Open, Closed	(1, 4), (1, 8), (1, 16) (2, 2), (2, 4), (2, 8)	Varied Parameter - \(h\) Order Parameter - \(M_z\)
XXZ-Heisenberg model (Heisenberg)	Chain Rectangular	Open, Closed	(1, 4), (1, 8), (1, 16) (2, 2), (2, 4), (2, 8)	Varied Parameter - \(J_z\) Order Parameter - \(M_z\)
Fermi Hubbard model (FermiHubbard)	Chain Rectangular	Open, Closed	(1, 4), (1, 8) (2, 2), (2, 4)	Varied Parameter - \(U\) Order Parameter - N/A
Bose Hubbard model (BoseHubbard)	Chain Rectangular	Open, Closed	(1, 4), (1, 8) (2, 2), (2, 4)	Varied Parameter - \(U\) Order Parameter - N/A

Data features

For each spin system, we can obtain the following characteristics for each of the 100 different system configurations:

Spin systems data

Information regarding the spin system, including a text description and parameters for each configuration.

Name	Type	Description
spin_system	dict	Basic description of the spin system including its name, Hamiltonian string, etc.
parameters	numpy.ndarray	Tunable parameters that determine the spin system configuration

Hamiltonians and ground-state data

Hamiltonians for the spin systems (under the Jordan-Wigner transformation for the Fermi Hubbard model and Binary Bosonic mapping for the Bose Hubbard Model).

Name	Type	Description
hamiltonian	list[Hamiltonian]	Hamiltonian of the system in the Pauli basis
ground_energies	numpy.ndarray	Ground state energies of each configuration of the spin system
ground_states	numpy.ndarray	Ground state of each configuration of the spin system

Phase transition data

Values of the order parameters, which can be used to investigate the phases of the spin systems.

Name	Type	Description
num_phases	int	Number of phases for the considered configurations
order_params	numpy.ndarray	Value of order parameters for identifying phases

Classical shadow data

Classical shadows measurement results and the randomized basis for each configuration using 1000 shots.

Name	Type	Description
shadow_basis	numpy.ndarray	Randomized Pauli basis for the classical shadow measurements
shadow_meas	numpy.ndarray	Results from the classical shadow measurements

datasets_qspin

 

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