Controlling the dynamics of quantum states is a common demand in quantum technology. We theoretically study quantum transport and switching in long-range coupled quantum networks possessing a single excitation. The qubit networks of our study are affected by Markovian environments while one qubit is irreversibly connected to an additional site. Different goals are studied towards controlling quantum transport such as efficient single excitation transfer, switching quantum transport,and manipulating the quantum states of qubit networks. These goals have been previously investigated using different mechanisms, however in this thesis we approach them by proposing appropriate geometrical arrangements of sites. Regarding efficient single excitation transfer we follow two approaches: Checking if there exist a spatial dimension preference for qubit arrangements towards optimal quantum transport, and whether the efficient network designs are robust against geometrical variations. For dimension analysis a random walk optimization method is used to compare the transport efficiency of networks expanded in one and two spatial dimensions. We find that for some choices of network parameters the two-dimensional networks are slightly more efficient than the one dimensional equivalent networks. This assures that designing one-dimensional qubit channels are adequate for efficient transport and the two-dimensional networks should only be considered where the two-dimensional spatial expansion is more compatible with the surrounding architecture. To design a network, after deciding about the network dimensionality, one may attempt to optimize the channel geometry which might result in a non-robust optimal configuration against the geometrical errors. To achieve robust optimal configurations we follow two approaches: We investigate the efficient configurations of sites in both one and two dimensional arrangements and present some patterns of robust geometric arrangements of sites in geometrical parameter space. Another approach to achieve robust efficient transport is defining a quantity as the geometrical robustness (georobustness) of qubit networks. By optimising geo-robustness against the network-environment parameters one can efficiently transfer a single excitation with many arbitrary arrangements of the network sites. Switching of quantum states is another goal towards controlled quantum dynamics. We study the transport characteristics of highly symmetric three-dimensional networks and analytically prove that a fraction of the initially injected excitation can trap for long durations via the creation of dark states. Using this characteristic we suggest switching devices which are robust against environmental noises.
Controlling the dynamics of quantum states is a common demand in quantum technology. We theoretically study quantum transport and switching in long-range coupled quantum networks possessing a single excitation. The qubit networks of our study are affected by Markovian environments while one qubit is irreversibly connected to an additional site. Different goals are studied towards controlling quantum transport such as efficient single excitation transfer, switching quantum transport,and manipulating the quantum states of qubit networks. These goals have been previously investigated using different mechanisms, however in this thesis we approach them by proposing appropriate geometrical arrangements of sites. Regarding efficient single excitation transfer we follow two approaches: Checking if there exist a spatial dimension preference for qubit arrangements towards optimal quantum transport, and whether the efficient network designs are robust against geometrical variations. For dimension analysis a random walk optimization method is used to compare the transport efficiency of networks expanded in one and two spatial dimensions. We find that for some choices of network parameters the two-dimensional networks are slightly more efficient than the one dimensional equivalent networks. This assures that designing one-dimensional qubit channels are adequate for efficient transport and the two-dimensional networks should only be considered where the two-dimensional spatial expansion is more compatible with the surrounding architecture. To design a network, after deciding about the network dimensionality, one may attempt to optimize the channel geometry which might result in a non-robust optimal configuration against the geometrical errors. To achieve robust optimal configurations we follow two approaches: We investigate the efficient configurations of sites in both one and two dimensional arrangements and present some patterns of robust geometric arrangements of sites in geometrical parameter space. Another approach to achieve robust efficient transport is defining a quantity as the geometrical robustness (georobustness) of qubit networks. By optimising geo-robustness against the network-environment parameters one can efficiently transfer a single excitation with many arbitrary arrangements of the network sites. Switching of quantum states is another goal towards controlled quantum dynamics. We study the transport characteristics of highly symmetric three-dimensional networks and analytically prove that a fraction of the initially injected excitation can trap for long durations via the creation of dark states. Using this characteristic we suggest switching devices which are robust against environmental noises.
We study the robustness of quantum transport in four-site one-dimensional (1D) particle quantum networks irreversibly connected to a target site in the presence of environmental dephasing noise. Under conditions of Markovian decoherence we define a quantity---which we denote as geometrical robustness---to quantify the robustness of transport with regard to the geometrical arrangement of the spin network. We examine the behavior of this geometrical robustness for both nearest and non-nearest site interactions and show that for some values of dephasing noise and other network parameters the robustness undergoes revivals, i.e., the robustness periodically increases with dephasing. In addition, we find that for high amounts of dephasing noise, the pattern of optimal network configurations changes noticeably from central symmetric configurations to laterally gathered ones, and we show that this change of pattern seems to occur for any number of network sites in the 1D chain.
For several decades it has been appreciated that quantum computers hold incredible promise to perform calculations intractable to classical computation. However, this promise has be slow to realize. Dozens of quantum systems are currently being investigated for use in quantum information processing - none of which have yet demonstrated algorithms involving more than a handful of qubits and it remains unclear which, if any, of these systems will ultimately compose a scalable, robust quantum information processing architecture. In this thesis we employ analytical, optimal and algebraic control techniques to evaluate various quantum systems for their potential use in quantum information processing. In doing so, we have additionally identified several novel characterization procedures capable of probing both the coherent and incoherent dynamics of quantum systems. The first part of this thesis discusses work motivated by attempts to utilize donor qubits in silicon as quantum bits. We first propose a measurement of the state of a single donor electron spin using two-dimensional electron gas of a field-effect transistor and electrically detected magnetic resonance. We analyze the potential sensitivity of this measurement and show that it is a quantum nondemolition measurement of an electron-encoded state. We then present the first of two novel qubit characterization procedures. We consider the problem of rapidly characterizing a large number of similarly prepared qubits using techniques from optimal experiment design. All qubits are assumed to evolve according to the same physical processes, though the Hamiltonian parameters may vary from device to device - an inevitability in solid state qubits. We use the Cram\\'er-Rao bound on the variance of a point estimator to construct the optimal series of experiments to estimate these free parameters, and present a complete analysis of the optimal experimental configuration. Though applied to dipole- and exchange-coupled qubits, this technique is widely applicable to other systems. The second part of the thesis discusses the role that control can play in measuring and mitigating noise in qubit systems. Our first result describes a method for quickly simulating the effects of arbitrary markovian noise on qubit systems through the use of a numerically optimized, multi-state Markovian fluctuator. This ability to rapidly simulate the noisy qubit evolution allows us to compute control sequences capable of maximally decoupling the qubit from the noise source. We then introduce the second characterization procedure of the these, showing that a single measurable and controllable qubit may act as a spectrometer of dephasing noise. We show that the formalism of dynamical decoupling can be used to estimate the short-time correlation function of the noise source, while long time correlations may be estimated by a very simple series of free evolution experiments. This technique is applicable to the wide range of physical implementations which suffer from dephasing noise.The final part of this thesis demonstrates that trapped neutral atoms may be utilized for the robust simulation of complex systems exhibiting a topological phase. We present a method to simulate the toric code Hamiltonian stroboscopically, and demonstrate that our technique preserves the ground state degeneracy . Furthermore, we introduce a dissipative mechanism allowing for thermalization of the system to a finite temperature or direct cooling to the ground state manifold.
Abstract Optimal energy transport is one of the primary goals for designing efficient quantum networks. In this work, the maximum energy transport is investigated for three-dimensional quantum networks with Platonic geometries affected by dephasing and dissipative Markovian noise. The network and the environmental characteristics corresponding the optimal design are obtained and investigated for five Platonic networks with 4, 6, 8, 12, and 20 number of sites that one of the sites is connected to a sink site through a Markovian dissipative process. Such optimal designs could have various applications like switching and multiplexing in quantum circuits.
We develop an approach for controllable single-photon transport between two remote one-dimensional coupled-cavity arrays, used as quantum registers, mediated by an additional one-dimensional coupled-cavity array, acting as a quantum channel. A single two-level atom located inside one cavity of the intermediate channel is used to control the long-range coherent quantum coupling between two remote registers, thereby functioning as a quantum switch. With a time-independent perturbative treatment, we find that the leakage of quantum information can in principle be made arbitrarily small. Furthermore, our method can be extended to realize a quantum router in multiregister quantum networks, where single-photons can be either stored in one of the registers or transported to another on demand. These results are confirmed by numerical simulations.
The challenge of making nano-scale quantum systems experimentally accessible is being overcome for an increasing diversity of systems by improved fabrication techniques and experimental control. Despite rapid progress, one of the main hindrances in all experiments is the difficulty of isolating the quantum system from the surrounding environment and its fluctuations. This experimental “noise” perturbs the quantum system, a process that is generally referred to as decoherence: the system slowly loses its distinguishing quantum features. In this thesis the effects of spatial correlations in the noise environment with a finite correlation length are investigated. The consequences for the experimental design of controlled quantum systems as well as the dynamics of solid state systems are presented. We utilize the Bloch-Redfield formalism, a Markovian master equation approach, which gives a close connection to the underpinning system-environment model. We show how to use this formalism to model any spatial correlation function of the noise environment. Using microscopic environmental models, several correlation functions are derived and their properties connected to the environmental parameters. Several phenomenological correlation functions are also studied and a mapping to the Lindblad master equation is presented, which provides a test of positivity for phenomenological models. For quantum transport through spin chains and networks, noise is generally detrimental. Spatial correlations however reduce the effect of dephasing noise and can reinstate the transport dynamics. The critical correlation length proves to be closely connected to the maximal packet width of one excitation in the transfer process. For dissipation noise, relaxation-free states emerge with spatial correlations. The decay of an excitation is therefore fundamentally modified into a fast decay towards an intermediate relaxation-reduced state and a subsequent decay to the ground state on a much longer time scale. In quantum metrology noise correlations have been observed in experiments with trapped ions, in which they limit the use of such experiments for metrology. Quantum advantage, i.e. a better precision scaling than the standard quantum limit has been proven impossible in the presence of uncorrelated Markovian noise only. We show that for certain optimized states the best possible quantum advantage, Heisenberg scaling, can be achieved in the presence of noise with a finite spatial decay of correlations. We furthermore identify how dephasing effects change and a topology dependence arises in strength with increasing correlation length for entangled states in a general way. Biological photosynthetic complexes have recently been found to potentially include quantum coherent dynamics, particularly in the process of transmitting an exciton from the point of creation to the reaction centre. We show how the formalism of spatially correlated decoherence adapts to this significantly different energy regime. Typical effects of decoherence in this field are presented and we show how the light-harvesting efficiency is influenced by spatial correlations in the noise. This thesis highlights the fundamental relevance of noise correlations to several fields of quantum physics and the importance of the efficient and comprehensive modelling techniques presented.
This thesis is concerned with modelling the dynamics of open quantum systems in several different contexts. Of principal interest is the manner in which the environment can modify, or even dominate, a system’s quantum behaviour in order to facilitate the transport of energetic excitations. In the first research chapter, a time-local, non-Markovian quantum master equation is derived in a variationally defined reference frame, for networks of two-level systems coupled to bosonic environments. The predictions of this master equation are then compared with those derived using both weak-coupling and polaron approximations. The variational master equation is found to agree with these standard approaches in their regimes of validity, whilst interpolating between them in intermediate parameter regimes. The second research chapter focusses on the dynamics of a superconducting double quantum dot embedded in a resonant circuit. The device is considered in a regime where the ground state consists of a coherent spatial superposition of a single Cooper pair, which can be excited by a variety of interactions with the environment. The relevant transition rates are calculated and the processes responsible are identified. A numerical simulation of the system is then used to explain experimental data, and show that for certain parameters a significant fraction of excitations occur via absorption of photons from the environment. The final chapter considers a model for an olfactory receptor, in which odorant molecules are recognised by their vibrational modes. Electron transfer occurs in the receptor, dependent on the presence of a vibrational mode of the right frequency. A quantum master equation for the system is derived, and the resulting dynamics is compared to earlier semi-classical treatments. The behaviour of the receptor is found to be sensitive not only to the frequency of the vibrational mode, but also to the character of the surrounding environment. Increased dissipation on the odorant mode, as well as the presence of higher frequencies in the environment is found to improve the frequency resolution of the receptor.