2020 IEEE International Symposium
on Information Theory
21-26 June 2020 • Los Angeles, California, USA
| Paper ID | Q.3.2 | ||
| Paper Title | Linear programming bounds for quantum amplitude damping codes | ||
| Authors | Yingkai Ouyang, University of Sheffield, United Kingdom; Ching-Yi Lai, National Chiao Tung University, Taiwan | ||
| Session | Q.3: Quantum Error Correcting Codes and Decoding | ||
| Presentation | Lecture | ||
| Track | Quantum Systems, Codes, and Information | ||
| Manuscript | Click here to download the manuscript | ||
| Virtual Presentation | Click here to watch in the Virtual Symposium | ||
| Abstract | Given that approximate quantum error-correcting (AQEC) codes have a potentially better performance than perfect quantum error correction codes, it is pertinent to quantify their performance. While quantum weight enumerators establish some of the best upper bounds on the minimum distance of quantum error-correcting codes, these bounds do not directly apply to AQEC codes. Herein, we introduce quantum weight enumerators for amplitude damping (AD) errors and work within the framework of approximate quantum error correction. In particular, we introduce an auxiliary exact weight enumerator that is intrinsic to a code space and moreover, we establish a linear relationship between the quantum weight enumerators for AD errors and this auxiliary exact weight enumerator. This allows us to establish a linear program that is infeasible only when AQEC AD codes with corresponding parameters do not exist. To illustrate our linear program, we numerically rule out the existence of three-qubit AD codes that are capable of correcting an arbitrary AD error. | ||
Plan Ahead
2021 IEEE International Symposium on Information Theory
11-16 July 2021 | Melbourne, Victoria, Australia
