scholarly journals Dissipative encoding of quantum information

2021 ◽  
Vol 21 (9-10) ◽  
pp. 737-770
Author(s):  
Giacomo Baggio ◽  
Francesco Ticozzi ◽  
Peter D. Johnson ◽  
Lorenza Viola
Keyword(s):  
Quantum Information ◽  
Finite Time ◽  
Degrees Of Freedom ◽  
Basins Of Attraction ◽  
Quantum Codes ◽  
Quantum Code ◽  
Logical Space ◽  
Time Dynamics ◽  
Finite Time Convergence ◽  
Toric Code

We formalize the problem of dissipative quantum encoding, and explore the advantages of using Markovian evolution to prepare a quantum code in the desired logical space, with emphasis on discrete-time dynamics and the possibility of exact finite-time convergence. In particular, we investigate robustness of the encoding dynamics and their ability to tolerate initialization errors, thanks to the existence of non-trivial basins of attraction. As a key application, we show that for stabilizer quantum codes on qubits, a finite-time dissipative encoder may always be constructed, by using at most a number of quantum maps determined by the number of stabilizer generators. We find that even in situations where the target code lacks gauge degrees of freedom in its subsystem form, dissipative encoders afford nontrivial robustness against initialization errors, thus overcoming a limitation of purely unitary encoding procedures. Our general results are illustrated in a number of relevant examples, including Kitaev's toric code.

scholarly journals Hypermap-homology quantum codes

2014 ◽  
Vol 12 (01) ◽  
pp. 1430001 ◽  
Author(s):  
Martin Leslie
Keyword(s):  
Quantum Information ◽  
Error Correcting Code ◽  
Chain Complex ◽  
Error Correcting Codes ◽  
Quantum Computers ◽  
Quantum Codes ◽  
Straightforward Generalization ◽  
New Type ◽  
Quantum Error ◽  
Toric Code

We introduce a new type of sparse CSS quantum error correcting code based on the homology of hypermaps. Sparse quantum error correcting codes are of interest in the building of quantum computers due to their ease of implementation and the possibility of developing fast decoders for them. Codes based on the homology of embeddings of graphs, such as Kitaev's toric code, have been discussed widely in the literature and our class of codes generalize these. We use embedded hypergraphs, which are a generalization of graphs that can have edges connected to more than two vertices. We develop theorems and examples of our hypermap-homology codes, especially in the case that we choose a special type of basis in our homology chain complex. In particular the most straightforward generalization of the m × m toric code to hypermap-homology codes gives us a [(3/2)m2, 2, m] code as compared to the toric code which is a [2m2, 2, m] code. Thus we can protect the same amount of quantum information, with the same error-correcting capability, using less physical qubits.

The enhanced sampling in parallel finite-time dynamics method with replica exchange

2021 ◽  
Vol 263 ◽  
pp. 107911
Author(s):  
Chudong Xu ◽  
Shengdong Lu ◽  
Yongfeng Kong ◽  
Wanjie Xiong
Keyword(s):  
Finite Time ◽  
Replica Exchange ◽  
Enhanced Sampling ◽  
Time Dynamics ◽  
Dynamics Method

ON TWO PROBLEMS OF ASYMMETRIC QUANTUM CODES

2014 ◽  
Vol 28 (06) ◽  
pp. 1450017 ◽  
Author(s):  
RUIHU LI ◽  
GEN XU ◽  
LUOBIN GUO
Keyword(s):  
Cyclic Codes ◽  
Error Correcting Codes ◽  
Bch Code ◽  
Quantum Codes ◽  
Quantum Code ◽  
Asymmetric Quantum ◽  
Asymmetric Quantum Codes ◽  
Special Cases ◽  
Quantum Error ◽  
Better Than

In this paper, we discuss two problems on asymmetric quantum error-correcting codes (AQECCs). The first one is on the construction of a [[12, 1, 5/3]]2 asymmetric quantum code, we show an impure [[12, 1, 5/3 ]]2 exists. The second one is on the construction of AQECCs from binary cyclic codes, we construct many families of new asymmetric quantum codes with dz> δ max +1 from binary primitive cyclic codes of length n = 2m-1, where δ max = 2⌈m/2⌉-1 is the maximal designed distance of dual containing narrow sense BCH code of length n = 2m-1. A number of known codes are special cases of the codes given here. Some of these AQECCs have parameters better than the ones available in the literature.

scholarly journals A New Control Method for Second-Order Multiple Models Control System Based on Global Sliding Mode

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Dan-xu Zhang ◽  
Yang-wang Fang ◽  
Peng-fei Yang ◽  
You-li Wu ◽  
Tong-xin Liu
Keyword(s):  
Control System ◽  
Sliding Mode Control ◽  
Finite Time ◽  
Sliding Mode ◽  
Second Order ◽  
Multiple Models ◽  
Finite Time Convergence ◽  
Mode Control ◽  
Global Sliding Mode Control ◽  
Control Scheme

This paper proposed a finite time convergence global sliding mode control scheme for the second-order multiple models control system. Firstly, the global sliding surface without reaching law for a single model control system is designed and the tracking error finite time convergence and global stability are proved. Secondly, we generalize the above scheme to the second-order multimodel control system and obtain the global sliding mode control law. Then, the convergent and stable performances of the closed-loop control system with multimodel controllers are proved. Finally, a simulation example shows that the proposed control scheme is more effective and useful compared with the traditional sliding mode control scheme.

Time-varying sliding-mode control for finite-time convergence

2010 ◽  
Vol 92 (7-8) ◽  
pp. 257-268 ◽  
Author(s):  
Yu-Sheng Lu ◽  
Chien-Wei Chiu ◽  
Jian-Shiang Chen
Keyword(s):  
Sliding Mode Control ◽  
Finite Time ◽  
Sliding Mode ◽  
Time Varying ◽  
Finite Time Convergence ◽  
Mode Control

scholarly journals Exponential Mean-Square Stability of Numerical Solutions to Stochastic Differential Equations

2003 ◽  
Vol 6 ◽  
pp. 297-313 ◽  
Author(s):  
Desmond J. Higham ◽  
Xuerong Mao ◽  
Andrew M. Stuart
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Numerical Method ◽  
Finite Time ◽  
Mean Square ◽  
Convergence Conditions ◽  
Finite Time Convergence ◽  
Mean Square Stability ◽  
Exponential Mean Square Stability ◽  
Positive Results

AbstractPositive results are proved here about the ability of numerical simulations to reproduce the exponential mean-square stability of stochastic differential equations (SDEs). The first set of results applies under finite-time convergence conditions on the numerical method. Under these conditions, the exponential mean-square stability of the SDE and that of the method (for sufficiently small step sizes) are shown to be equivalent, and the corresponding second-moment Lyapunov exponent bounds can be taken to be arbitrarily close. The required finite-time convergence conditions hold for the class of stochastic theta methods on globally Lipschitz problems. It is then shown that exponential mean-square stability for non-globally Lipschitz SDEs is not inherited, in general, by numerical methods. However, for a class of SDEs that satisfy a one-sided Lipschitz condition, positive results are obtained for two implicit methods. These results highlight the fact that for long-time simulation on nonlinear SDEs, the choice of numerical method can be crucial.

Sign in / Sign up

Export Citation Format

Share Document