SquareLatticeMatrix class

class SquareLatticeMatrix(rows, cols)

Represents a square lattice using an adjacency matrix, suitable for modeling two-dimensional quantum systems.

Parameters:

rows (int) – The number of rows in the lattice.
cols (int) – The number of columns in the lattice.

rows: The number of rows in the lattice.

cols: The number of columns in the lattice.

adjacency_matrix: A matrix representing the connections between lattice sites. Each entry (i, j) is 1 if the sites i and j are adjacent, and 0 otherwise.

are_neighbors(site1, site2)

Checks if two sites in the lattice are neighbors.

Parameters:

site1 (int) – The index of the first site.
site2 (int) – The index of the second site.

Returns:

True if site1 and site2 are adjacent, False otherwise.

Return type:

bool

create_heisenberg_square_lattice_matrix_circuit function

create_heisenberg_square_lattice_matrix_circuit(lattice_matrix, t)

Generates a quantum circuit for the Heisenberg model based on the provided square lattice matrix. The function adds entangling gates between neighboring qubits as defined by the lattice’s adjacency matrix.

Parameters:

lattice_matrix (SquareLatticeMatrix) – An instance of SquareLatticeMatrix defining the lattice structure.
t (Parameter) – A Qiskit Parameter representing the time evolution parameter for the Heisenberg model.

Returns:

A QuantumCircuit object with the Heisenberg interactions applied between neighbors.

Return type:

QuantumCircuit

The quantum circuit is constructed with RXX, RYY, and RZZ gates between qubits that are neighbors according to the lattice matrix.

Example Usage

To use the SquareLatticeMatrix class and create_heisenberg_square_lattice_matrix_circuit function to create a Heisenberg model circuit on a 2x2 square lattice, follow this example:

from qiskit import Aer, transpile

# Initialize a square lattice matrix for a 2x2 lattice
lattice_matrix = SquareLatticeMatrix(rows=2, cols=2)

# Define the time evolution parameter 't'
t = Parameter('t')

# Create the Heisenberg circuit using the lattice matrix
qc = create_heisenberg_square_lattice_matrix_circuit(lattice_matrix, t)

# Transpile the circuit for a quantum simulator backend
simulator = Aer.get_backend('aer_simulator')
transpiled_circuit = transpile(qc, simulator)

# Print the transpiled quantum circuit
print(transpiled_circuit)

This script will output a quantum circuit that applies the Heisenberg interaction to a system modeled by a 2x2 square lattice.