Quantum Computation and Information Storage in Quantum Double Models

The results of this thesis concern the real-world realization of quantum computers, specifically how to build their "hard drives" or quantum memories. These are many-body quantum systems, and their building blocks are qubits, the same way bits are the building blocks of classical computers. Quantum memories need to be robust against thermal noise, noise that would otherwise destroy the encoded information, similar to how strong magnetic field corrupts data classically stored in magnetic many-body systems (e.g., in hard drives). In this work I focus on a subset of many-body models, called quantum doubles, which, in addition to storing the information, could be used to perform the steps of the quantum computation, i.e., work as a "quantum processor". In the first part of my thesis, I investigate how long a subset of quantum doubles (qudit surface codes) can retain the quantum information stored in them, referred to as their memory time. I prove an upper bound for this memory time, restricting the maximum possible performance of qudit surface codes. Then, I analyze the structure of quantum doubles, and find two interesting properties. First, that the high-level description of doubles, utilizing only their quasi-particles to describe their states, disregards key components of their microscopic properties. In short, quasi-particles (anyons) of quantum doubles are not in a one-to-one correspondence with the energy eigenstates of their Hamiltonian. Second, by investigating phase transitions of a simple quantum double, D(S3), I map its phase diagram, and interpret the physical processes the theory undergoes through terms borrowed from the Landau theory of phase transitions.</p

Anyons are not energy eigenspaces of quantum double Hamiltonians

Kitaev's quantum double models, including the toric code, are canonical examples of quantum topological models on a two-dimensional spin lattice. Their Hamiltonian defines the ground space by imposing an energy penalty to any nontrivial flux or charge, but does not distinguish among those. We generalize this construction by introducing a family of Hamiltonians made of commuting four-body projectors that provide an intricate splitting of the Hilbert space by discriminating among nontrivial charges and fluxes. Our construction highlights that anyons are not in one-to-one correspondence with energy eigenspaces, a feature already present in Kitaev's construction. This discrepancy is due to the presence of local degrees of freedom in addition to topological ones on a lattice

Móricz Zsigmond levelezésének (1892–1913) digitális kritikai kiadása: Esettanulmány

2016-ban indult el a Petőfi Irodalmi Múzeumban az a hároméves NKFIH-projekt, amely Móricz Zsigmond levelezésének (1892–1913) digitális kritikai kiadását tűzte ki célul. A feladat kihívást jelentett a Móricz-műhely számára, hiszen a korábbi, papíralapú kiadási gyakorlatra csak részben támaszkodhattak. A múzeumi informatikai lehetőségek, a filológiai problémák és az alkalmazott szoftverek párbeszédéről szóló esettanulmány a projekt első évének problémafelvetéseiről, megoldásairól szól. Nem törekszik teljes áttekintésre, hiszen munkafolyamat közben ad hírt egy formálódó gyakorlatról

Self correction requires Energy Barrier for Abelian quantum doubles

We rigorously establish an Arrhenius law for the mixing time of quantum doubles based on any Abelian group Zd. We have made the concept of the energy barrier therein mathematically well-defined, it is related to the minimum energy cost the environment has to provide to the system in order to produce a generalized Pauli error, maximized for any generalized Pauli errors, not only logical operators. We evaluate this generalized energy barrier in Abelian quantum double models and find it to be a constant independent of system size. Thus, we rule out the possibility of entropic protection for this broad group of models

Necessity of an energy barrier for self-correction of Abelian quantum doubles

We rigorously establish an Arrhenius law for the mixing time of quantum doubles based on any Abelian group Z_d. We have made the concept of the energy barrier therein mathematically well defined; it is related to the minimum energy cost the environment has to provide to the system in order to produce a generalized Pauli error, maximized for any generalized Pauli errors, not only logical operators. We evaluate this generalized energy barrier in Abelian quantum double models and find it to be a constant independent of system size. Thus, we rule out the possibility of entropic protection for this broad group of models