332 citations · 1.1k across the 33 of their papers we have counts for
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Topological Quantum Spin Glass Order and its realization in qLDPC codes
Benedikt Placke, Tibor Rakovszky, Nikolas P. Breuckmann +1
Ordered phases of matter have close connections to computation. Two prominent examples are spin glass order, with wide-ranging applications in machine learning and optimization, an…
Bottlenecks in quantum channels and finite temperature phases of matter
Tibor Rakovszky, Benedikt Placke, Nikolas P. Breuckmann +1
We prove an analog of the "bottleneck theorem," well-known for classical Markov chains, for Markovian quantum channels. In particular, we show that if two regions (subspaces) of Hi…
Low-Overhead Entangling Gates from Generalised Dehn Twists
Ryan Tiew, Nikolas P. Breuckmann
We generalise the implementation of logical quantum gates via Dehn twists from topological codes to the hypergraph and balanced products of cyclic codes. These generalised Dehn twi…
Cups and Gates I: Cohomology invariants and logical quantum operations
Nikolas P. Breuckmann, Margarita Davydova, Jens N. Eberhardt +1
We take initial steps towards a general framework for constructing logical gates in general quantum CSS codes. Viewing CSS codes as cochain complexes, we observe that cohomology in…