Deterministic quantum controlled-PHASE gates based on non-Markovian environments

Abstract

We study the realization of the quantum controlled-PHASE gate in an atom-cavity system beyond the Markovian approximation. The general description of the dynamics for the atom-cavity system without any approximation is presented. When the spectral density of the reservoir has the Lorentz form, by making use of the memory backflow from the reservoir, we can always construct the deterministic quantum controlled-PHASE gate between a photon and an atom, no matter the atomcavity coupling strength is weak or strong. While, the phase shift in the output pulse hinders the implementation of quantum controlled-PHASE gates in the sub-Ohmic, Ohmic or super-Ohmic reservoirs.

Any four orthogonal ququad–ququad maximally entangled states are locally markable

“…However, the unavoidable noise makes perfect LQSM hardly possible in the current experiments. For example, regarding the qubits as the atoms or photons in the cavity QED [30,31], it is also interesting to study the LQSM process under the influences of Markovian and non-Markovian effects from the environments, which is however beyond the scope of the paper [32,33].…”

Fractional quantum Hall effect in optical lattices

“…The state preparation of FQH states with dissipative pumping of particles from higher to lower bands has been studied in [55]. The effect of non-Markovian environments has been studied for atomcavity systems [56][57][58][59]. However, this effect needs to be explored for the topologically ordered phases.…”

Fast quantum search driven by environmental engineering

“…An effective way is to use the existing quantum algorithms with consideration of decoherence and make every effort to reduce the influence of this decoherence. Recent work regarding the realization of quantum logic in a noisy environment motivates us to engineer dissipation for quantum search algorithms [30]. It is necessary that we know the noise spectrum of the environment, and engineer the corresponding environment by using open quantum system theory.…”

“…The essential difference between Markovian and non-Markovian environments lies in whether the probability or energy can flow back from the environment to the quantum system. Studies have demonstrated that the dynamics of the quantum system are quite different between Markovian and non-Markovian scenarios [24][25][26][27][28][29][30]. Therefore, in the non-Markovian case, the environment cannot be viewed as a leakage only, but it is capable of intentionally controlling the interacting quantum system [19,20,22,30].…”

“…Studies have demonstrated that the dynamics of the quantum system are quite different between Markovian and non-Markovian scenarios [24][25][26][27][28][29][30]. Therefore, in the non-Markovian case, the environment cannot be viewed as a leakage only, but it is capable of intentionally controlling the interacting quantum system [19,20,22,30]. Recently, dissipative quantum-state engineering and quantum computation have attracted much attention.…”