Quantum information and quantum computing (QIQC) systems, relying on the phenomena of superposition and entanglement, offer the potential for vast improvements in certain computations. A practical QC realization requires maintaining the stored information for time-scales long enough to implement algorithms. One primary cause of information loss is decoherence, i.e., the loss of coherence between two energy levels in a quantum system. This work attributes decoherence to dissipation occurring as the system evolves and uses steepest-entropy-ascent quantum thermodynamics (SEAQT) to predict the evolution of system state. SEAQT asserts that, at any instant of time, the system state evolves such that the rate of system entropy change is maximized while conserving system energy. With this principle, the SEAQT equation of motion is applicable to systems in any state, near or far from stable equilibrium, making SEAQT particularly well suited for predicting the dissipation occurring as quantum algorithms are implemented. In the present research, the dynamics of qubits (quantum-bits) using the SEAQT framework are first examined during common quantum gates (combinations of which form algorithms). This is then extended to modeling a system of multiple qubits implementing Shor's algorithm on a nuclear-magnetic-resonance (NMR) QC. Additionally, the SEAQT framework is used to predict experimentally observed dissipation occurring in a two-qubit NMR QC undergoing a so called ``quenching'' process. In addition, several methods for perturbing the density or so-called ``state'' operator used by the SEAQT equation of motion subject to an arbitrary set of expectation value constraints are presented. These are then used as the basis for randomly generating states used in analyzing the dynamics of entangled, non-interacting systems within SEAQT. Finally, a reservoir interaction model is developed for general quantum systems where each system locally experiences a heat interaction with an external reservoir. This model is then used as the basis for developing a decoherence control scheme, which effectively transfers entropy out of the QIQC system as it is generated, thus, reducing the decoherence. Reservoir interactions are modeled for single qubits and the control scheme is employed in modeling an NMR QC and shown to eliminate nearly all of the noise caused by decoherence/dissipation. / Doctor of Philosophy / Quantum computers (QCs) have the potential to perform certain tasks much more efficiently than today0 s supercomputers. One primary challenge in realizing a practical QC is maintaining the stored information, the loss of which is known as decoherence. This work attributes decoherence to dissipation (a classical analogue being heat generated due to friction) occurring while an algorithm is run on the QC. Standard quantum modeling approaches assume that for any dissipation to occur, the QC must interact with its environment. However, in this work, steepest-entropy-ascent quantum thermodynamics (SEAQT) is used to model the evolution of the QC as it runs an algorithm. SEAQT, developed by Hatsopolous, Gyftopolous, Beretta, and others over the past 40 years, supplements the laws of quantum mechanics with those of thermodynamics and in contrast to the standard quantum approaches does not require the presence of an environment to account for the dissipation which occurs. This work first applies the SEAQT framework to modeling single qubits (quantum bits) to characterize the effect of dissipation on the information stored on the qubit. This is later extended to a nuclear-magnetic-resonance (NMR) QC of 7 qubits. Additionally, SEAQT is used to predict experimentally observed dissipation in a two-qubit NMR QC. Afterwards, several methods for constrained perturbations of a QC0 s state are presented. These methods are then used with SEAQT to analyze the effect of dissipation on the entanglement of two qubits. Finally, a model is derived within the SEAQT framework accounting for a qubit interacting with its environment, which is at a constant temperature. This model is then used to develop a method for limiting the decoherence and shown to significantly lowering the resulting error due to decoherence.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/94630 |
| Date | 17 October 2019 |
| Creators | Holladay, Robert Tyler |
| Contributors | Mechanical Engineering, von Spakovsky, Michael R., Paul, Mark R., Hin, Celine, Cano-Andrade, Sergio, Qiao, Rui, Beretta, Gian Paolo |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Detected Language | English |
| Type | Dissertation |
| Format | ETD, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
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