SquareLattice class

class SquareLattice(rows, cols)

A class representing a square lattice that can be used to simulate quantum systems on a two-dimensional grid.

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_list

A dictionary representing the adjacency list of the lattice, where each key is a site index and the value is a list of neighboring site indices.

get_neighbors(site)

Retrieves the neighboring sites for a given site on the lattice.

Parameters:

site (int) – The index of the site for which neighbors are to be found.

Returns:

A list of indices of neighboring sites.

Return type:

list[int]

create_heisenberg_lattice_circuit function

create_heisenberg_lattice_circuit(lattice, t)

Creates a quantum circuit that simulates the Heisenberg model on a square lattice, using the provided lattice to determine qubit interactions.

Parameters:

• lattice (SquareLattice) – An instance of the SquareLattice class representing the lattice structure.

• t (Parameter) – A Qiskit Parameter representing the time evolution parameter in the simulation.

Returns:

A QuantumCircuit object representing the Heisenberg interaction on the lattice.

Return type:

QuantumCircuit

This function iterates over each site in the square lattice and applies RXX, RYY, and RZZ gates to simulate the Heisenberg interaction between each site and its neighbors as determined by the adjacency list of the lattice.

Example Usage

Here is how you can use the SquareLattice class and the create_heisenberg_lattice_circuit function to create a circuit:

from qiskit import Aer, transpile

# Create a square lattice with 2 rows and 2 columns
lattice = SquareLattice(rows=2, cols=2)

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

# Create the Heisenberg model circuit for the lattice
qc = create_heisenberg_lattice_circuit(lattice, t)

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

# Print the transpiled circuit
print(transpiled_circuit)

The output will be a Qiskit QuantumCircuit that simulates the Heisenberg model on a 2x2 square lattice.