Within a deterministic theory, based on Schroedinger's time dependent equation, accounting for the coupling of a high dimensional continuum of environmental excitations (called gravonons) to massive particle in a very localized and very weak fashion, we investigate a model of four qubits with one qubit coupled to a phonon and (optionally) to the gravonons. The calculations indicate that when no gravonons are present, the current in the qubit is flipped at some time and adiabatic evolution is discontinued. The time dependent wave functional becomes a non-correctable superposition of many excited states. The results demonstrate the possibility of effectively suppressing the current flip and allowing for continued adiabatic evolution when the entanglement to gravonons is included.
This adiabatic evolution is a coherent evolution in high dimensional spacetime and cannot be understood as a solution of Schroedinger's time dependent equation in 4 dimensional spacetime. Compared to Schroedinger's time development in 4D, the evolution is considerably slowed down, though still adiabatic.
The properties of our model reflect correctly the experimentally found behaviour of the D-Wave machine and explain 8 orders of magnitude discrepancy between decoherence time and quantum computation time. The observation and our explanation are in anology to the eight orders of magnitude discrepancy found, when comparing experimental results on adsorbate quantum diffusion rate with predictions of Schroedinger's time dependent equation, which can also be resolved in a model with the coupling to gravonons included.
The result of a sudden perturbation of a 4 qubit model system by a single phonon mode is destroyed adiabaticity. The figure shows that a fast entanglement to the phonon field around t=1000 s perturbs the eigenstates dramatically and the system cannot recover the adiabatic development.
Destroyed adiabaticity and spin flips in one of four qubits as a result of the fast entanglement to the phonon field. The development with time of the occupation summed up over basis states with spin 0 and spin 1 in the third qubit shows the destroyed adiabaticity and the chaotic occupation of spin 0 and spin 1 states in the third qubit as a result of the entanglement of the phonon field to this qubit. The spin on the third qubit, which is affected by the phonon field, flips completely arbitrarily after the destroyed adiabaticity.
Entanglement to gravonons restores the adiabatic development of the 4 qubit system by hindering the effect of the phonons. In the Josephson junction the electron currents are normal currents and the electron wave functions, having non-zero amplitudes in the region of the atom nuclei, entangle with gravonons. The result is an adiabatic development of the 4 qubit system on the energy ground state potential curve till the end of the quantum annealing procedure.
D. Drakova and G. Doyen, How can the D-Wave machine exhibit long-time quantum behaviour,
J. Phys.: Conf. Ser. vol. 626, p. 012057 (2015).