Quantum Simulation of the Heisenberg model

This project was done in collaboration with Debarghya Chakraborty and Nikolaos Angelinos as part of our participation in IBM's Open Science Prize 2021. The goal of the competition was to improve the fidelity of simulating the 3-qubit Heisenberg model on IBM's quantum processor, Jakarta. By employing trotterization, error mitigation techniques, and efficient block-diagonalization of the Hamiltonian, we achieved a fidelity of approximately 99% in the final state compared to the ideal evolution.

Our implemented quantum circuit evolves the initial $3$-qubit state $|110\rangle$, for time from $t=0$ to $t=\pi$, according to the Hamiltonian

$$H= X_1 X_{2} + Y_1 Y_2 +Z_{1}Z_{2} + X_{2} X_{3} + Y_2 Y_3 + Z_{2}Z_{3},$$

where indices (1,2,3) correspond to qubits 5, 3 and 1 on ibmq_jakarta. Our submission managed to implement the quantum circuit using only 2 CNOT gates, achieving the $99$% fidelity.