6 papers
Quantum phase transitions of interacting bosons on hyperbolic lattices
Xingchuan Zhu, Jiaojiao Guo, Nikolas P. Breuckmann +2
The effect of many-body interaction in curved space is studied based on the extended Bose--Hubbard model on hyperbolic lattices. Using the mean-field approximation and quantum Mont…
Quantum Low-Density Parity-Check Codes
Nikolas P. Breuckmann, Jens Niklas Eberhardt
Quantum error correction is an indispensable ingredient for scalable quantum computing. In this Perspective we discuss a particular class of quantum codes called low-density parity…
Balanced Product Quantum Codes
Nikolas P. Breuckmann, Jens N. Eberhardt
This work provides the first explicit and non-random family of LDPC quantum codes which encode logical qubits with distance $D \in Ω(N^\frac{3}…
Subsystem codes with high thresholds by gauge fixing and reduced qubit overhead
Oscar Higgott, Nikolas P. Breuckmann
We introduce a technique that uses gauge fixing to significantly improve the quantum error correcting performance of subsystem codes. By changing the order in which check operators…
Critical properties of the Ising model in hyperbolic space
Nikolas P. Breuckmann, Benedikt Placke, Ananda Roy
The Ising model exhibits qualitatively different properties in hyperbolic space in comparison to its flat space counterpart. Due to the negative curvature, a finite fraction of the…
PhD thesis: Homological Quantum Codes Beyond the Toric Code
Nikolas P. Breuckmann
PhD thesis investigating homological quantum codes derived from curved and higher dimensional geometries. In the first part we will consider closed surfaces with constant negative…