This paper considers the extension of the non-Markovian stochastic approach for quantum open systems strongly coupled to a fermionic bath, to the models in which the system operators commute with the fermion bath. This technique can also be a useful tool for studying open quantum systems coupled to a spin-chain environment, which can be further transformed into an effective fermionic bath. We derive an exact stochastic Schrödinger equation (SSE), called fermionic quantum state diffusion (QSD) equation, from the first principle by using the fermionic coherent state representation. The reduced density operator for the open system can be recovered from the average of the solutions to the QSD equation over the Grassmann-type noise. By employing the exact fermionic QSD equation, we can derive the corresponding exact master equation. The power of our approach is illustrated by the applications of our stochastic approach to several models of interest including the one-qubit dissipative model, the coupled two-qubit dissipative model, the quantum Brownian motion model and the N-fermion model coupled to a fermionic bath. Different effects caused by the fermionic and bosonic baths on the dynamics of open systems are also discussed.

Non-Markovian dynamics is studied for two interacting quibts strongly coupled to a dissipative bosonic environment. For the first time, we have derived the non-Markovian quantum state diffusion (QSD) equation for the coupled two-qubit system without any approximations, and in particular, without the Markov approximation. As an application and illustration of our derived time-local QSD equation, we investigate the temporal behavior of quantum coherence dynamics. In particular, we find a strongly non-Markovian regime where entanglement generation is significantly modulated by the environmental memory. Additionally, we studied the residual entanglement in the steady state by analyzing the steady state solution of the QSD equation. Finally, we have discussed an approximate QSD equation.

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With silicon being the go-to material for spin qubits, and motivated by the demand of a scalable quantum computer architecture for fast and reliable quantum information transfer on-chip, we study coherent electron transport in a silicon double quantum dot. We first examine the valley-orbital dynamics in a silicon double dot, and discuss how to properly measure the tunnel couplings as well as the valley phase difference between two quantum dots. We then focus on possible phase and spin flip errors during spin transport across a silicon double dot. In particular, we clarify correction on the effective g-factor for the electron spin from the double dot confinement potential, and quantify the resulting phase error. We then study spin fidelity loss due to spin-valley mixing, which is a unique feature of silicon quantum dots. We show that a small phase correction between valleys can cause a significant coherence loss. We also investigate spin flip errors caused by either an external inhomogeneous magnetic field or the intrinsic spin-orbit coupling. We show that the presence of valleys makes it possible to have much broader (in terms of interdot detuning) level anticrossings compared to typical anti-crossings in, for example, a GaAs double dot, and such broad anti-crossings lead to amplification of spin flip errors. Lastly, we design a pulse sequence to suppress various possible spin flip errors by taking advantage of the multiple level anti-crossings in a silicon double dot and employing Landau-Zener transitions.

In this paper, a new quantum state restoration scheme is proposed based on the environmentassisted error correction (EAEC) scheme. By introducing a weak measurement reversal (WMR) operation, we shall show how to recover an initial state of a quantum open system without invoking random unitary decompositions which are known to be absent in many important physical systems. We illustrate our new scheme and compare it with a scheme purely based on the WMR operation in the case of dissipative channel. In the proposed new scheme, the successful probability of recovering an unknown initial state can be significantly improved when the information obtained from an environment measurement is taken into account. Moreover, we show that the applicable range of our proposed scheme is wider than the EAEC scheme. Finally, the optimization of the successful probability for possible Kraus decompositions is discussed.