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arXiv:1202.0357 · Australian Communications Theory Workshop

Channel identification and its impact on quantum LDPC code performance

Yixuan Xie, Jun Li, Robert Malaney, Jinhong Yuan

Published Jan 1, 2012• 12 citations
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Abstract

In this work we probe the impact of channel estimation on the performance of quantum LDPC codes. Our channel estimation is based on an optimal estimate of the relevant decoherence parameter via its quantum Fisher information. Using state-of-the art quantum LDPC codes designed for the quantum depolarization channel, and utilizing various quantum probes with different entanglement properties, we show how the performance of such codes can deteriorate by an order of magnitude when optimal channel identification is fed into a belief propagation decoding algorithm. Our work highlights the importance in quantum communications of a viable channel identification campaign prior to decoding, and highlights the tradeoff between entanglement consumption and quantum LDPC code performance.

DOI
10.1109/ausctw.2012.6164921

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In this work we probe the impact of channel estimation on the performance of quantum LDPC codes. Our channel estimation is based on an optimal estimate of the relevant decoherence parameter via its quantum Fisher information. Using state-of-the art quantum LDPC codes designed for the quantum depolarization channel, and utilizing various quantum probes with different entanglement properties, we show how the performance of such codes can deteriorate by an order of magnitude when optimal channel identification is fed into a belief propagation decoding algorithm. Our work highlights the importance in quantum communications of a viable channel identification campaign prior to decoding, and highlights the tradeoff between entanglement consumption and quantum LDPC code performance.
Quantum cryptography via key distribution mechanisms that utilize quantum entanglement between sender-receiver pairs will form the basis of future large-scale quantum networks. A key engineering challenge in such networks will be the ability to correct for decoherence effects in the distributed entanglement resources. It is widely believed that sophisticated quantum error correction codes, such as quantum low-density parity-check (LDPC) codes, will be pivotal in such a role. However, recently the importance of the channel mismatch effect in degrading the performance of deployed quantum LDPC codes has been pointed out. In this work we help remedy this situation by proposing new quantum LDPC decoding strategies that can significantly reduce performance degradation by as much as 50%50\%50%. Our new strategies for the quantum LDPC decoder are based on previous insights from classical LDPC decoders in mismatched channels, where an asymmetry in performance is known as a function of the estimated channel noise. We show how similar asymmetries carry over to the quantum depolarizing channel, and how an estimate of the depolarization flip parameter weighted to larger values leads to significant performance improvement.
Quantum low-density parity-check (LDPC) codes are a promising family of quantum error-correcting codes for fault tolerant quantum computing with low overhead. Decoding quantum LDPC codes on quantum erasure channels has received more attention recently due to advances in erasure conversion for various types of qubits including neutral atoms, trapped ions, and superconducting qubits. Belief propagation with guided decimation (BPGD) decoding of quantum LDPC codes has demonstrated good performance in bit-flip and depolarizing noise. In this work, we apply BPGD decoding to quantum erasure channels. Using a natural modification, we show that BPGD offers competitive performance on quantum erasure channels for multiple families of quantum LDPC codes. Furthermore, we show that the performance of BPGD decoding on erasure channels can sometimes be improved significantly by either adding damping or adjusting the initial channel log-likelihood ratio for bits that are not erased. More generally, our results demonstrate BPGD is an effective general-purpose solution for erasure decoding across the quantum LDPC landscape.
In this work, the importance of the channel mismatch effect in degrading the performance of deployed quantum LDPC codes has been pointed out. We help remedy this situation by proposing new quantum LDPC decoding strategies that can significantly reduce performance degradation by as much as 50%. Our new strategies for the quantum LDPC decoder are based on previous insights from classical LDPC decoders in mismatched channels, where an asymmetry in performance is known as a function of the estimated channel noise. We show how similar asymmetries carry over to the quantum depolarizing channel, and how an estimate of the depolarization flip parameter weighted to larger values leads to significant performance improvement.
This paper presents a novel approach to quantum information coding and decoding leveraging the unique properties of quantum entanglement. The core idea is to develop a self-adaptive system capable of dynamically adjusting encoding and decoding parameters based on the observed noise levels and channel losses within the quantum channel. This adaptive strategy aims to significantly improve the efficiency and reliability of quantum information transmission. The proposed framework utilizes a quantum decoherence model to accurately represent channel losses and employs an optimization algorithm rooted in quantum control theory to optimize the generation and measurement strategies of entangled states in real-time. The algorithm's objective is to minimize information loss. The key innovation lies in the system's ability to respond in real-time to fluctuating channel conditions, moving beyond the limitations of static encoding/decoding schemes commonly employed in existing quantum communication protocols. Mathematical models and formulations are presented to illustrate the design and optimization process, focusing on key performance metrics such as channel capacity and fidelity. The system's potential impact on future quantum communication networks is discussed.
This article develops a general method for constructing entanglement-assisted quantum low-density parity-check (LDPC) codes, which is based on combinatorial design theory. Explicit constructions are given for entanglement-assisted quantum error-correcting codes with many desirable properties. These properties include the requirement of only one initial entanglement bit, high error-correction performance, high rates, and low decoding complexity. The proposed method produces several infinite families of codes with a wide variety of parameters and entanglement requirements. Our framework encompasses the previously known entanglement-assisted quantum LDPC codes having the best error-correction performance and many other codes with better block error rates in simulations over the depolarizing channel. We also determine important parameters of several well-known classes of quantum and classical LDPC codes for previously unsettled cases.
Quantum low-density parity-check (QLDPC) codes are among the most promising candidates for future quantum error correction schemes. However, a limited number of short to moderate-length QLDPC codes have been designed and their decoding performance is sub-optimal with a quaternary belief propagation (BP) decoder due to unavoidable short cycles in their Tanner graphs. In this paper, we propose a novel joint code and decoder design for QLDPC codes. The constructed codes have a minimum distance of about the square root of the block length. In addition, it is, to the best of our knowledge, the first QLDPC code family where BP decoding is not impaired by short cycles of length 4. This is achieved by using an ensemble BP decoder mitigating the influence of assembled short cycles. We outline two code construction methods based on classical quasi-cyclic codes and finite geometry codes. Numerical results demonstrate outstanding decoding performance over depolarizing channels.