create_heisenberg_circuit function

create_heisenberg_circuit(N, trotter_steps=1)

Generates a quantum circuit that simulates the Heisenberg model. The simulation uses the Trotter-Suzuki decomposition to approximate the time evolution of the system under the Heisenberg Hamiltonian with periodic boundary conditions.

Parameters:

• N (int) – The number of qubits representing spins in the chain.

• trotter_steps (int, optional) – The number of Trotter steps to use in the decomposition, which determines the approximation accuracy.

Returns:

A Qiskit QuantumCircuit object that represents the simulation circuit.

Return type:

QuantumCircuit

The function creates a QuantumCircuit object and applies a series of RXX, RYY, and RZZ gates to simulate the interactions between adjacent spins in a 1D Heisenberg chain. The periodic boundary conditions are implemented by connecting the last qubit with the first one.

Example Usage

The following example demonstrates how to create a Heisenberg model circuit for a chain of 4 qubits with a single Trotter step:

from qiskit import Aer, transpile

# Create a quantum circuit for the Heisenberg model with 4 qubits and 1 Trotter step
N = 4
trotter_steps = 1
qc = create_heisenberg_circuit(N, trotter_steps)

# 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)