Entropy, Fidelity, and Entanglement During Digitized Adiabatic Quantum Computing to Form a Greenberger–Horne–Zeilinger (GHZ) State

We analyzed the accuracy of digitized adiabatic quantum computing to form the entangled three-qubit Greenberger–Horne–Zeilinger (GHZ) state on two IBM quantum computers and four quantum simulators by comparison with direct calculations using a Python code (version 3.12). We initialized three-qubit systems in the ground state of the Hamiltonian for noninteracting spins in an applied magnetic field in the x direction. We then gradually varied the Hamiltonian to an Ising model form with nearest-neighbor zz spin coupling with an eight-step discretization. The von Neumann entropy provides an indicator of the accuracy of the discretized adiabatic evolution. The von Neumann entropy of the density matrix from the Python code (version 3.12) remains very close to zero, while the von Neumann entropy of the density matrices on the quantum computers increases almost linearly with the step number in the process. The GHZ witness operator indicates that the quantum simulators incorporate a GHZ component in part. The states on the two quantum computers acquire partial GHZ character, even though the trace of the product of the GHZ witness operator with the density matrix not only remains positive but also rises monotonically from Step 5 to Step 8. Each of the qubits becomes entangled during the adiabatic evolution in all of the calculations, as shown by the single-qubit reduced density matrices.