Hutter, Adrian. Stable quantum information in topological systems. 2015, Doctoral Thesis, University of Basel, Faculty of Science.

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Abstract
The superposition principle of quantum mechanics implies that the amount of classical (i.e., nonquantum) information needed to describe a quantum system is in general exponentially large in the size of the system. This makes simulating quantum physics on a classical computer quickly infeasible, even for moderatelysized systems and using the best presentday supercomputers in the world. This is unfortunate, since systems for which quantum effects are relevant are of interest in many areas of science and engineering, ranging from drug design to materials research. In 1982, Richard Feynman gave birth to the idea of a quantum computer, when he realized that simulating quantum physics could be achieved much more efficiently with a computer that was itself a quantum system. Since then, the number of problems for which a quantum computer is known to enjoy an advantage over a classical computer has steadily increased, ranging now far beyond the task of simulating quantum physics. A quantum computation of any interest will need to create complicated superposition states, for otherwise it would not achieve anything that could not be simulated on a classical computer. These superposition states, however, are highly fragile, and this fragility is the main obstacle that the scientific community faces on the road towards a useful quantum computer. Quantum computing will only be possible if it can be performed in a faulttolerant way. It is due to seminal work by Alexei Kitaev from 1997 that the modern theory of quantum faulttolerance is closely related to the term topology. Topology, as a subfield of mathematics, is concerned with the properties of space that are preserved under continuous deformations. Topological order, a purely quantum phenomenon, refers to states which cannot be distinguished or evolved into each other locally, yet are globally distinct. The information that distinguishes between these states is stored in nonlocal degrees of freedom. If it were possible to store quantum information in these nonlocal degrees of freedom, this would be hugely attractive from a practical perspective, as it would mean that the information stored this way is immune to many forms of local errors. Twodimensional topologically ordered states support excitations known as anyons. These are exotic quasiparticles that defy the dichotomy between fermions and bosons that applies to quantum particles in three spatial dimensions. In a topological quantum computer, the nonlocally stored quantum information is processed by braiding these anyons around each other. Such a computation would be insensitive to small perturbations of the path along which anyons are braided, but would only depend on its topological properties. An open problem is whether topological order can persist at finite temperature. Equivalently, one can ask whether it is possible to build a system in which quantum information can be stored in a stable manner for arbitrarily long times, without performing active error correction and despite constant influence of a thermal environment. Such a system would constitute a selfcorrecting quantum memory and would extend the concept of a hard disk drive to the quantum realm. Whether nature allows for such a system to be built is of tremendous interest from both a fundamental and a practical perspective. Twodimensional topologically ordered systems – those hosting anyons – do not qualify as selfcorrecting quantum memories; any finite temperature corrupts them in a time that is independent of the size of the system. In the present thesis, we propose and study systems in which the thermal stability of a simple toy model of an anyonic system, Kitaev’s toric code, is enhanced in various ways. We consider coupling it to optical cavity modes, to bosonic particles, or to a ferromagnet. These auxiliary systems then induce longranged interactions between the anyons, which allow to increase the finitetemperature lifetime of the stored quantum information arbitrarily by increasing the size of the system. While a topological quantum computer is naturally immune to many forms of imperfections and perturbations, accidental creation of anyonic quasiparticles due to coupling to an external environment is a form of error that requires active correction. This problem has seen surprisingly little attention until recently and is still poorly understood. In this thesis, we develop algorithms that are able to perform this task and provide the first proofs of its inprinciple feasibility. Furthermore, we develop a system with the rare property that it both supports anyons that can be used for topological quantum computing, and allows for error correction with wellestablished techniques. Historically, the first proposals for building a faulttolerant quantum
computer involved an array of qubits (quantum bits) and a set of elementary operations that can be performed on individual and pairs of qubits. Faulttolerant qubitbased quantum computing has been inspired tremendously from the insights gained in the study of topological quantum information processing. The surface code, which combines a qubitbased architecture with topological methods, is now at the forefront of the quest towards a faulttolerant, scalable quantum computer. In the surface code, a large number of measurements are performed on a continuous basis to get some information about what errors have occurred. This information then needs to be converted by a classical algorithm into a prescription for performing error correction. In this thesis, we develop such an algorithm that, at the time of its publication, was the best efficient algorithm known for the surface code. Error correction for qubitbased quantum computers is typically studied with simplistic error models in which the errors on each qubit are independent from each other. We study what kinds of spatial and temporal correlations between the errors arise when a surface code is coupled to a typical model of an environment, and how they affect its correctability.
computer involved an array of qubits (quantum bits) and a set of elementary operations that can be performed on individual and pairs of qubits. Faulttolerant qubitbased quantum computing has been inspired tremendously from the insights gained in the study of topological quantum information processing. The surface code, which combines a qubitbased architecture with topological methods, is now at the forefront of the quest towards a faulttolerant, scalable quantum computer. In the surface code, a large number of measurements are performed on a continuous basis to get some information about what errors have occurred. This information then needs to be converted by a classical algorithm into a prescription for performing error correction. In this thesis, we develop such an algorithm that, at the time of its publication, was the best efficient algorithm known for the surface code. Error correction for qubitbased quantum computers is typically studied with simplistic error models in which the errors on each qubit are independent from each other. We study what kinds of spatial and temporal correlations between the errors arise when a surface code is coupled to a typical model of an environment, and how they affect its correctability.
Advisors:  Loss, Daniel and Pachos, Jiannis K. 

Faculties and Departments:  05 Faculty of Science > Departement Physik > Physik > Theoretische Physik Mesoscopics (Loss) 
UniBasel Contributors:  Hutter, Adrian and Loss, Daniel 
Item Type:  Thesis 
Thesis Subtype:  Doctoral Thesis 
Thesis no:  11562 
Thesis status:  Complete 
Number of Pages:  1 OnlineRessource (xi, 338 Seiten) 
Language:  English 
Identification Number: 

edoc DOI:  
Last Modified:  22 Jan 2018 15:52 
Deposited On:  29 Feb 2016 15:29 
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