Quantum algorithms for one-dimensional infrastructures

Quantum algorithms for one-dimensional infrastructures

Infrastructures are group-like structures that make their appearance in arithmetic geometry in the study of computational problems related to number fields and functional fields over finite fields. The most prominent computational tasks of infrastructures are the computation of the circumference of the infrastructure and the generalized discrete logarithms. Both these problems are not known to ...

Post-quantum algorithms for digital signing in Public Key Infrastructures

One emerging threat to Public Key Infrastructures is the possible development of largescale quantum computers, which would be able to break the public-key cryptosystems used today. Several possibly post-quantum secure cryptographic algorithms have been proposed but so far they have not been used in many practical settings. The purpose of this thesis was to find post-quantum digital signature al...

One-dimensional Quantum Wires

In this paper we investigate the properties of a one-dimensional quantum wire of interacting electrons in the Wigner crystal limit. Recent theoretical work has explored some of the classical and quantum phase transitions associated with this system. For example, there exists a critical density above which the system can lower its energy by forming a quasi-one-dimensional zig-zag chain. We also ...

Spherical Deformation for one-dimensional Quantum Systems

System-size dependence of the ground-state energy E is investigated for N-site onedimensional (1D) quantum systems with open boundary condition, where the interaction strength decreases towards the both ends of the system. For the spinless Fermions on the 1D lattice we have considered, it is shown that the finite-size correction to the energy per site, which is defined as E/N − limN→∞ E /N , is...

One-dimensional spline interpolation algorithms