相关论文: Renormalization Group Approach To Error-Correcting…
Series of maximum distance quantum error-correcting codes are developed and analysed. For a given rate and given error-correction capability, quantum error-correcting codes with these specifications are constructed. The codes are explicit…
In a previous work it was shown that the best measure for the efficiency of a single burst-correcting code is obtained using the Gallager bound as opposed to the Reiger bound. In this paper, an efficient algorithm that searches for the best…
Error-correcting codes over the real field are studied which can locate outlying computational errors when performing approximate computing of real vector--matrix multiplication on resistive crossbars. Prior work has concentrated on…
We develop a renormalization group method to investigate synchronization clusters in a one-dimensional chain of nearest-neighbor coupled phase oscillators. The method is best suited for chains with strong disorder in the intrinsic…
In this paper, we consider a simplified error-correcting problem: for a fixed encoding process, to find a cascade connected quantum channel such that the worst fidelity between the input and the output becomes maximum. With the use of the…
Group testing is the process of pooling arbitrary subsets from a set of $n$ items so as to identify, with a minimal number of tests, a "small" subset of $d$ defective items. In "classical" non-adaptive group testing, it is known that when…
Multi-class classification is mandatory for real world problems and one of promising techniques for multi-class classification is Error Correcting Output Code. We propose a method for constructing the Error Correcting Output Code to obtain…
Efficient and accurate decoding of quantum error-correcting codes is essential for fault-tolerant quantum computation, however, it is challenging due to the degeneracy of errors, the complex code topology, and the large space for logical…
The analysis of the decoding failure rate of the bit-flipping algorithm has received increasing attention. For a binary linear code we consider the minimum number of rows in a parity-check matrix such that the bit-flipping algorithm is able…
Quantum error correction will likely be essential for building a large-scale quantum computer, but it comes with significant requirements at the level of classical control software. In particular, a quantum error-correcting code must be…
We study a discrete model of repelling particles, and we show using linear programming bounds that many familiar families of error-correcting codes minimize a broad class of potential energies when compared with all other codes of the same…
Concatenating quantum error correction codes scales error correction capability by driving logical error rates down double-exponentially across levels. However, the noise structure shifts under concatenation, making it hard to choose an…
We use convex relaxation techniques to provide a sequence of solutions to the matrix completion problem. Using the nuclear norm as a regularizer, we provide simple and very efficient algorithms for minimizing the reconstruction error…
Modern neural networks are over-parametrized. In particular, each rectified linear hidden unit can be modified by a multiplicative factor by adjusting input and output weights, without changing the rest of the network. Inspired by the…
Using the method of renormalization group, we improve the two-loop effective potential of the massive $\phi^4$ theory to obtain the next-next-to-leading logarithm correction in the $\bar{MS}$ scheme. Our result well reproduces the…
The performance of iterative decoding techniques for linear block codes correcting erasures depends very much on the sizes of the stopping sets associated with the underlying Tanner graph, or, equivalently, the parity-check matrix…
The advantages of using more than one renormalization group (RG) in problems with more than one important length scale are discussed. It is shown that: i) using different RG's can lead to complementary information, i.e. what is very…
Achieving fault-tolerance will require a strong relationship between the hardware and the protocols used. Different approaches will therefore naturally have tailored proof-of-principle experiments to benchmark progress. Nevertheless,…
Detectability of failures of linear programming (LP) decoding and its potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the LP problem. In this paper, we make a…
Renormalization group (RG) methods, which model the way in which the effective behavior of a system depends on the scale at which it is observed, are key to modern condensed-matter theory and particle physics. We compare the ideas behind…