We develop a general approach for monitoring and controlling evolution of open quantum systems. In contrast to the master equations describing time evolution of density operators, here, we formulate a dynamical equation for the evolution of the process matrix acting on a system. This equation is applicable to non-Markovian and/or strong-coupling regimes. We propose two distinct applications for this dynamical equation. We first demonstrate identification of quantum Hamiltonians generating dynamics of closed or open systems via performing process tomography. In particular, we argue how one can efficiently estimate certain classes of sparse Hamiltonians by performing partial tomography schemes. In addition, we introduce an optimal control theoretic setting for manipulating quantum dynamics of Hamiltonian systems, specifically for the task of decoherence suppression.
We develop a general approach for monitoring and controlling evolution of open quantum systems. In contrast to the master equations describing time evolution of density operators, here, we formulate a dynamical equation for the evolution of the process matrix acting on a system. This equation is applicable to non-Markovian and/or strong-coupling regimes. We propose two distinct applications for this dynamical equation. We first demonstrate identification of quantum Hamiltonians generating dynamics of closed or open systems via performing process tomography. In particular, we argue how one can efficiently estimate certain classes of sparse Hamiltonians by performing partial tomography schemes. In addition, we introduce an optimal control theoretic setting for manipulating quantum dynamics of Hamiltonian systems, specifically for the task of decoherence suppression.
Manipulation of a quantum system requires the knowledge of how it evolves. To impose that the dynamics of a system becomes a particular target operation (for any preparation of the system), it may be more useful to have an equation of motion for the dynamics itself, rather than the state. Here we develop a Markovian master equation for the process matrix of an open system interacting with a reservoir, which resembles the Lindblad Markovian master equation. We employ this equation to introduce a scheme for optimal local coherent process control at target times and extend the Krotov technique to obtain optimal control. We illustrate utility of this framework through several quantum coherent-control scenarios, such as optimal decoherence suppression, gate simulation, and passive and indirect control of the reservoir, in all of which we aim to simulate a given terminal process at a given final time.
An optimal quantum algorithm for "direct characterization of quantum dynamics" (DCQD) is introduced. The DCQD method can be utilized to completely determine the quantum dynamical superoperator acting on an open quantum system. In contrast to all other known quantum process tomography (QPT) schemes, this scheme relies on error-detection techniques and does not require any quantum state tomography. By analysis of the number of required experimental configurations and quantum operations in a given Hilbert space, it is demonstrated that this approach is more efficient than all other known QPT schemes. DCQD can be applied, by construction, to the task of partial characterization of quantum dynamics. Specifically, it is demonstrated that the DCQD algorithm can be efficiently used for Hamiltonian identification, and also for simultaneous determination of both the relaxation time T1 and dephasing time T2. Furthermore, it is argued that the DCQD scheme is experimentally implementable in a variety of prominent quantum information processing systems, and it is explicitly shown how it can be physically realized in photonic systems with present day technology. The ability of a quantum system to perform arbitrary or "universal" quantum operations is restricted to its naturally available/controllable interactions. It is shown that quantum systems with an effective exchange interaction can be made operationally universal by utilizing a subspace or a subsystem of the combined principal system and an auxiliary system. Moreover, it is demonstrated that universal fault-tolerant quantum computation can be performed on these systems without utilizing any form of single-qubit control. Characterization and control of open quantum systems are among the central and fundamental problems in quantum physics. A crucial primitive is the characterization of the dynamics of a quantum system that has an unknown interaction with its embedding environment. Another essential task is to control the decoherence of an open quantum system by using naturally available interactions. This thesis addresses the above fundamental problems in two separate parts. In the first part, a general theory for direct and complete characterization of quantum dynamics is introduced. In the second part, a scheme for performing arbitrary quantum operations on spin-based quantum systems is presented. This scheme can be implemented in the presence of environmental noise and faulty quantum operations without need to control the state of spins individually.
A central aim of physics is to describe the dynamics of physical sys-tems. Schrödinger’s equation does this for isolated quantum systems. Describing the time evolution of a quantum system that interacts with its environment, in its most general form, has proved to be difficult because the dynamics is dependent on the state of the environment and the corre-lations with it. For discrete processes, such as quantum gates or chemical reactions, quantum process tomography provides the complete descrip-tion of the dynamics, provided that the initial states of the system and the environment are independent of each other. However, many physical systems are correlated with the environment at the beginning of the ex-periment. Here, we give a prescription of quantum process tomography that yields the complete description of the dynamics of the system even when the initial correlations are present. Surprisingly, our method also gives quantitative expressions for the initial correlation. There is a rich history to the studies of decoherence of quantum systems due to the interactions with the surrounding degrees of freedom. When the dynamics of the system (S) is Markovian it can be described by a master equation [1, 2, 3]. Nowadays many researchers are interested in systems that are non-Markovian, as there is mounting evidence that some natural systems of importance may be non-Markovian [4] and such features may allow to manipulate and control quantum systems in desired ways. There is also a great deal of interest in systems that are initially correlated with their environments (E) because non-Markovianity and initial system-environment (SE) correlations are intimately related [5, 6, 7]. 1 ar
We provide a general framework for the identification of open quantum systems. By looking at the input-output behavior, we try to identify the system inside a black box in which some Markovian time evolution takes place. Due to the generally irreversible nature of the dynamics, it is difficult to assure full controllability over the system. Still, we show that the system is identifiable up to similarity under a certain rank condition. The framework also covers situations relevant to standard quantum process tomography, where we do not have enough control over the system but have a tomographically complete set of initial states and observables. Remarkably, the similarity cannot in general be reduced to unitarity even for unitary systems, and the spectra of Hamiltonians are not identifiable without additional knowledge.
Keeping a quantum system in a given instantaneous eigenstate is a control problem with numerous applications, e.g., in quantum information processing. The problem is even more challenging in the setting of open quantum systems, where environment-mediated transitions introduce additional decoherence channels. Adiabatic passage is a well-established solution but requires a sufficiently slow evolution time that is dictated by the adiabatic theorem. Here we develop a systematic projection theory formulation for the transitionless evolution of general open quantum systems described by time-local master equations. We derive a time-convolutionless dynamical equation for the target instantaneous eigenstate of a given time-dependent Hamiltonian. A transitionless dynamics then arises in terms of a competition between the average Hamiltonian gap and the decoherence rate, which implies optimal adiabaticity timescales. We show how eigenstate tracking can be accomplished via control pulses, without explicitly incorporating counter-diabatic driving, thus offering an alternative route to accelerate adiabaticity. We examine rectangular pulses, chaotic signals, and white noise, and find that, remarkably, the effectiveness of eigenstate tracking hardly depends on the details of the control functions. In all cases the control protocol keeps the system in the desired instantaneous eigenstate throughout the entire evolution, along an accelerated adiabatic path.
We present a general method to efficiently design optimal control sequences for non-Markovian open quantum systems, and illustrate it by optimizing the shape of a laser pulse to prepare a quantum dot in a specific state. The optimization of control procedures for quantum systems with strong coupling to structured environments-where time-local descriptions fail-is a computationally challenging task. We modify the numerically exact time evolving matrix product operator (TEMPO) method, such that it allows the repeated computation of the time evolution of the reduced system density matrix for various sets of control parameters at very low computational cost. This method is potentially useful for studying numerous optimal control problems, in particular in solid state quantum devices where the coupling to vibrational modes is typically strong.