arXiv subjects

Lucy Liuxuan Zhang

Publications and source records attributed to Lucy Liuxuan Zhang.

3 recordsLinked to original sources

arXiv2017

Fibre bundle framework for unitary quantum fault tolerance

We introduce a differential geometric framework for describing families of quantum error-correcting codes and for understanding quantum fault tolerance. This work unifies the notion of topological fault tolerance with fault tolerance in other kinds of quantum error-correcting codes. In particular, we use fibre bundles with a natural flat projective connection to study the transformation of codewords under unitary fault-tolerant evolutions. We show that the fault-tolerant logical operations are given by the monodromy group for either of two bundles, both of which have flat projective connections. As concrete realizations of the general framework, we construct the bundles explicitly for two examples of fault-tolerant families of operations, the qudit transversal gates and the string operators in the toric code.

quant-ph↗

arXiv2013

Sequential attacks against differential-phase-shift quantum key distribution with weak coherent states

We investigate limitations imposed by sequential attacks on the performance of differential-phase-shift quantum key distribution protocols that use pulsed coherent light. In particular, we analyze two sequential attacks based on unambiguous state discrimination and minimum error discrimination, respectively, of the signal states emitted by the source. Sequential attacks represent a special type of intercept-resend attacks and, therefore, they do not allow the distribution of a secret key.

quant-ph↗

arXiv2005

Fast n-point correlation functions and three-point lensing application

We present a new algorithm to rapidly compute the two-point (2PCF), three-point (3PCF) and n-point (n-PCF) correlation functions in roughly O(N log N) time for N particles, instead of O(N^n) as required by brute force approaches. The algorithm enables an estimate of the full 3PCF for as many as 10^6 galaxies. This technique exploits node-to-node correlations of a recursive bisectional binary tree. A balanced tree construction minimizes the depth of the tree and the worst case error at each node. The algorithm presented in this paper can be applied to problems with arbitrary geometry. We describe the detailed implementation to compute the two point function and all eight components of the 3PCF for a two-component field, with attention to shear fields generated by gravitational lensing. We also generalize the algorithm to compute the n-point correlation function for a scalar field in k dimensions where n and k are arbitrary positive integers.

astro-ph↗