Simulating of X-states and the two-qubit XYZ Heisenberg system on IBM quantum computer

TL;DR

This paper develops a quantum circuit to simulate general two-qubit X-states and the two-spin Heisenberg XYZ system on IBM quantum computers, demonstrating robustness against noise and extending previous Bell Diagonal State simulations.

Contribution

It introduces a generalized quantum circuit for X-state simulation, applies it to the XYZ Heisenberg model, and shows the robustness of X-shape under noisy quantum gates.

Findings

Successfully simulated general X-states on IBM quantum hardware.

Demonstrated the approximate robustness of X-shape against noise.

Showed that two qubits suffice to simulate XYZ Heisenberg dynamics.

Abstract

Two qubit density matrices, which are of X-shape, are a natural generalization of Bell Diagonal States (BDSs) recently simulated on the IBM quantum device. We generalize the previous results and propose a quantum circuit for simulation of a general two qubit X-state, implement it on the same quantum device, and study its entanglement for several values of the extended parameter space. We also show that their X-shape is approximately robust against noisy quantum gates. To further physically motivate this study, we invoke the two-spin Heisenberg XYZ system and show that for a wide class of initial states, it leads to dynamical density matrices which are X-states. Due to the symmetries of this Hamiltonian, we show that by only two qubits, one can simulate the dynamics of this system on the IBM quantum computer.