arXiv subjects

Michael Liaofan Liu

Publications and source records attributed to Michael Liaofan Liu.

3 recordsLinked to original sources

arXiv2024

Subsystem CSS codes, a tighter stabilizer-to-CSS mapping, and Goursat's Lemma

The CSS code construction is a powerful framework used to express features of a quantum code in terms of a pair of underlying classical codes. Its subsystem extension allows for similar expressions, but the general case has not been fully explored. Extending previous work of Aly, Klappenecker, and Sarvepalli [quantph/0610153], we determine subsystem CSS code parameters, express codewords, and develop a Steane-type decoder using only data from the two underlying classical codes. Generalizing a result of Kovalev and Pryadko [Phys. Rev. A 88 012311 (2013)], we show that any subsystem stabilizer code can be "doubled" to yield a subsystem CSS code with twice the number of physical, logical, and gauge qudits and up to twice the code distance. This mapping preserves locality and is tighter than the Majorana-based mapping of Bravyi, Terhal, and Leemhuis [New J. Phys. 12 083039 (2010)]. Using Goursat's Lemma, we show that every subsystem stabilizer code can be constructed from two nested subsystem CSS codes satisfying certain constraints, and we characterize subsystem stabilizer codes based on the nested codes' properties.

quant-ph↗

arXiv2023

Bind-and-bend model for DNA looping

DNA looping is important in DNA condensation and regulation. One method for forming a DNA loop, thought to be used by the condensing agent protamine, is bind-and-bend. In bind-and-bend, molecules bind all along the DNA, each creating a bend in the DNA. Eventually, enough bending leads to the formation of a loop. Here, we adapt theory for DNA bending by cations to create a simple bind-and-bend model. To test the model, we simulate bending and looping by the condensing agent protamine and compare the output of the simulation to experimental data. The model captures several interesting features of the data including: the curvature of the DNA due to both protamine-induced bending and thermal fluctuations, the small circumference of the loops (200-300 bp), the bias in the location where the loop forms, and the emergence of multi-looped flower structures. The model leads to insight into where protamine binds, how it bends DNA, and how it creates one or more DNA loops. More broadly, the model could be useful in understanding the compaction of nucleic acids or polyelectrolytes.

physics.bio-ph↗

arXiv2023

Lipschitz continuity of quantum-classical conditional entropies with respect to angular distance and related properties

We derive a Lipschitz continuity bound for quantum-classical conditional entropies with respect to angular distance, with a Lipschitz constant that is independent of the dimension of the conditioning system. This bound is sharper in some situations than previous continuity bounds, which were either based on trace distance (where Lipschitz continuity is not possible), or based on angular distance but did not include a conditioning system. However, we find that the bound does not directly generalize to fully quantum conditional entropies. To investigate possible counterexamples in that setting, we study the characterization of states which saturate the Fuchs--van de Graaf inequality and thus have angular distance approximately equal to trace distance. We give an exact characterization of such states in the invertible case. For the noninvertible case, we show that the situation appears to be significantly more elaborate, and seems to be strongly connected to the question of characterizing the set of fidelity-preserving measurements.

quant-ph↗