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This thesis addresses whether it is possible to build a robust memory device for quantum information. A three-dimensional gapped lattice spin model is found which demonstrates for the first time that a reliable quantum memory at finite…
Memory effects can lead to history-dependent behavior of a system, and they are ubiquitous in our daily life and have broad applications. Here we explore possibilities of generating memory effects in simple isolated quantum systems. By…
We discuss the existence of stable topological quantum memory at finite temperature. At stake here is the fundamental question of whether it is, in principle, possible to store quantum information for macroscopic times without the…
We consider two-dimensional lattice models that support Ising anyonic excitations and are coupled to a thermal bath. We propose a phenomenological model for the resulting short-time dynamics that includes pair-creation, hopping, braiding,…
Topological error correction codes are promising candidates to protect quantum computations from the deteriorating effects of noise. While some codes provide high noise thresholds suitable for robust quantum memories, others allow…
Arrays of atoms trapped in optical lattices are appealing as storage media for photons, since motional dephasing of the atoms is eliminated. The regular lattice is also associated with band structure in the dispersion experienced by…
We compute the topological entropy of the toric code models in arbitrary dimension at finite temperature. We find that the critical temperatures for the existence of full quantum (classical) topological entropy correspond to the…
To use quantum systems for technological applications we first need to preserve their coherence for macroscopic timescales, even at finite temperature. Quantum error correction has made it possible to actively correct errors that affect a…
The ability to store information is of fundamental importance to any computer, be it classical or quantum. To identify systems for quantum memories which rely, analogously to classical memories, on passive error protection…
We propose a scheme to manipulate a topological spin qubit which is realized with cold atoms in a one-dimensional optical lattice. In particular, by introducing a quantum opto-electro-mechanical interface, we are able to first transfer a…
A two-dimensional topologically ordered quantum memory is well protected against error if the energy gap is large compared to the temperature, but this protection does not improve as the system size increases. We review and critique some…
Quantum memory effects are essential in understanding and controlling open quantum systems, yet distinguishing them from classical memory remains challenging. We introduce a convex geometric framework to analyze quantum memory propagating…
Proposals for quantum information processing often require the development of new quantum tech- nologies. However, here we build quantum memory by ultracold atoms in one-dimensional optical lattices with existing state-of-the-art…
We investigate fundamental bounds on the curvature of quantum correlation functions in imaginary time. Focusing first on topological phases, we show that quantum geometry can qualitatively modify the imaginary-time decay of correlations,…
The following open problems, which concern a fundamental limit on coding properties of quantum codes with realistic physical constraints, are analyzed and partially answered here: (a) the upper bound on code distances of quantum…
Storing quantum information for long times without disruptions is a major requirement for most quantum information technologies. A very appealing approach is to use self-correcting Hamiltonians, i.e. tailoring local interactions among the…
The performance of superconducting quantum circuits for quantum computing has advanced tremendously in recent decades; however, a comprehensive understanding of relaxation mechanisms does not yet exist. In this work, we utilize a multimode…
Topological quantum codes are intrinsically fault-tolerant to local noise, and underlie the theory of topological phases of matter. We explore geometry to enhance the performance of topological quantum codes by rotating the four dimensional…
Many proposals for quantum information processing are subject to detectable loss errors. In this paper, we give a detailed account of recent results in which we showed that topological quantum memories can simultaneously tolerate both loss…
Topological quantum computing has recently proven itself to be a powerful computational model when constructing viable architectures for large scale computation. The topological model is constructed from the foundation of a error correction…