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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Quantum Error Correction: Foundation and Landscape
量子纠错 基础景观 量子纠错理论
2023/4/18
Quantum error correction theory lies at the heart of universal quantum computing. So far, people do not find or realize good-enough error correction codes yet. In this talk, I will survey the foundati...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Quantum Error Correction: Fault-tolerance and Universality
量子纠错 容错性 通用性
2023/4/17
There is a big gap between the so-called NISQ (noisy intermediate-scale quantum) and FTQ (fault-tolerant quantum) computing. Recently, we introduced QEQ (quasi-exact quantum) computing, which lies in ...
Highly Robust Error Correction by Convex Programming
Linear codes decoding of (random) linear codes sparse solutions to underdetermined systems `1 minimization linear programming second-order cone programming the Dantzig selector restricted orthonormality Gaussian random matrices and random projections
2015/6/17
This paper discusses a stylized communications problem where one wishes to transmit a real-valued signal x ∈ Rn (a block of n pieces of information) to a remote receiver. We ask whether it is possible...
Error Correction via Linear Programming
Linear codes decoding of (random) linear codes sparse solutions to underdetermined systems `1-minimization linear programming restricted orthonormality Gaussian random matrices.
2015/6/17
Suppose we wish to transmit a vector f ∈ Rn reliably. A frequently discussed approach consists in encoding f with an m by n coding matrix A. Assume now that a fraction of the entries of Af are corrupt...
Dense Error Correction for Low-Rank Matrices via Principal Component Pursuit
Dense Error Correction Low-Rank Matrices Principal Component Pursuit
2015/6/17
We consider the problem of recovering a lowrank matrix when some of its entries, whose locations are not known a priori, are corrupted by errors of arbitrarily large magnitude. It has recently been sh...
Network error correction with unequal link capacities
Network error correction unequal link capacities
2010/11/22
This paper studies the capacity of single-source single-sink noiseless networks under adversarial or arbitrary errors on no more than z edges. Unlike prior papers, which assume equal capacities on al...
Construction of Network Error Correction Codes in Packet Networks
Network Error Correction Codes Packet Networks
2010/11/11
Recently, network error correction coding (NEC) has been studied extensively. Several bounds in classical coding theory have been extended to network error correction coding, especially the Singleton...
5-qubit quantum error correction in a charge qubit quantum computer
quantum error correction 5-qubit code solid-state quantum register
2010/11/5
We implement the DiVincenzo-Shor 5 qubit quantum error correcting code into a solid-state quantum register. The quantum register is a multi charge-qubit system in a semiconductor environment, where th...
NP-hardness of decoding quantum error correction codes
NP-hardness quantum error correction codes
2010/10/18
Though the theory of quantum error correction is intimately related to the classical coding theory,in particular, one can construct quantum error correction codes (QECCs) from classical codes with the...
The E8 Lattice and Error Correction in Multi-Level Flash Memory
E8 Lattice Error Correction Multi-Level Flash Memory
2010/12/14
A construction using the E8 lattice and Reed-Solomon codes for error-correction in flash memory is given. Since E8 lattice decoding errors are bursty, a Reed-Solomon code over GF(28) is well suited. T...
Continuous Quantum Error Correction Through Local Operations
Continuous Quantum Error Correction Through Local Operations
2010/10/21
We propose local strategies to protect global quantum information. The protocols, which are
quantum error correcting codes for dissipative systems, are based on environment measurements,
direct feed...