In Quantum Information Processing by NMR one of the major challenges is relaxation or decoherence. Often it is found that the equilibrium mixed state of a spin system is not suitable as an initial state for computation and a definite initial state is required to be prepared prior to the computation. As these preferred initial states are non-equilibrium states, they are not stationary and are destroyed with time as the spin system relaxes toward its equilibrium, introducing error in computation. Since it is not possible to cut off the relaxation processes completely, attempts are going on to develop alternate strategies like Quantum Error Correction Codes or Noiseless Subsystems. Here we study the relaxation behavior of various Pseudo Pure States and analyze the role of Cross terms between different relaxation processes, known as Cross-correlation. It is found that while cross-correlations accelerate the relaxation of certain pseudo pure states, they retard that of others.
"Spectral Implementation" for creating a labeled pseudo-pure state and the Bernstein-Vazirani's algorithm in a four-qubit nuclear magnetic resonance quantum processor
We construct a complete set of Wannier functions which are localized at both given positions and momenta. This allows us to introduce the quantum phase space, onto which a quantum pure state can be mapped unitarily. Using its probability distribution in quantum phase space, we define an entropy for a quantum pure state. We prove an inequality regarding the long time behavior of our entropy's fluctuation. For a typical initial state, this inequality indicates that our entropy can relax dynamically to a maximized value and stay there most of time with small fluctuations. This result echoes the q…
Multirate characterization of relaxation mechanisms for two nonequivalent nuclear spins 1/2 in a liquid using maximally entangled pseudo-pure quantum states
Felix Bloch Institute for Solid State Physics, University of Leipzig（莱比锡大学菲利克斯·布洛赫固体物理研究所）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）；Institute for Theoretical Physics, University of Leipzig（莱比锡大学理论物理研究所）
Adiabatic preparation of the ground states of many-body Hamiltonians in the closed system limit is at the heart of adiabatic quantum computation, but in reality systems are always open. This motivates a natural comparison between, on the one hand, adiabatic preparation of steady states of Lindbladian generators and, on the other hand, relaxation towards the same steady states subject to the final Lindbladian of the adiabatic process. In this work we thus adopt the perspective that the goal is the most efficient possible preparation of such steady states, rather than ground states. Using known …
We explore the relaxation dynamics of quantum many-body systems that undergo purely dissipative dynamics through non-classical jump operators that can establish quantum coherence. Our goal is to shed light on the differences in the relaxation dynamics that arise in comparison to systems evolving via classical rate equations. In particular, we focus on a scenario where both quantum and classical dissipative evolution lead to a stationary state with the same values of diagonal or "classical" observables. As a basis for illustrating our ideas we use spin systems whose dynamics becomes correlated …
Quantum systems are affected by interactions with their environments, causing decoherence through two processes: pure dephasing and energy relaxation. For quantum information processing it is important to increase the coherence time of Josephson qubits and other artificial two-level atoms. We show theoretically that if the coupling between these qubits and a cavity field is longitudinal and in the ultrastrong-coupling regime, the system is strongly protected against relaxation. Vice versa, if the coupling is transverse and in the ultrastrong-coupling regime, the system is protected against pur…
