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IEICE Technical Report; IEICE Tech. Rep.

Study on the performance of the entanglement distillation protocol using the quantum error correcting code

M. Yoshida, Manabu Hagiwara, Takayuki Miyadera, Hideki Imai

Published Sep 14, 2010• 0 citations
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Bell-state measurement (BSM) on entangled states shared between quantum repeaters is the fundamental operation used to route entanglement in quantum networks. Performing BSMs on Werner states shared between repeaters leads to exponential decay in the fidelity of the end-to-end Werner state with the number of repeaters, necessitating entanglement distillation. In this work, we use quantum error correcting codes for deterministic entanglement distillation to route Werner states on a chain of repeaters. To maximize the end-to-end distillable entanglement, we utilize global link-state knowledge to determine the optimal policy for scheduling distillation and BSMs at the repeaters. We observe that low-rate codes produce high-fidelity end-to-end states owing to their excellent error-correcting capability, whereas high-rate codes yield a larger number of end-to-end states but of lower fidelity. The number of quantum memories used at repeaters increases with the code rate as well as the classical computation time of the decoder.

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Entanglement is essential for quantum information processing, but is limited by noise. We address this by developing high-yield entanglement distillation protocols with several advancements. (1) We extend the 2-to-1 recurrence entanglement distillation protocol to higher-rate n -to- ( n − 1 ) protocols that can correct any single-qubit errors. These protocols are evaluated through numerical simulations focusing on fidelity and yield. We also outline a method to adapt any classical error-correcting code for entanglement distillation, where the code can correct both bit-flip and phase-flip errors by incorporating Hadamard gates. (2) We propose a constant-depth decoder for stabilizer codes that transforms logical states into physical ones using single-qubit measurements. This decoder is applied to entanglement distillation protocols, reducing circuit depth and enabling protocols derived from high-performance quantum error-correcting codes. We demonstrate this by evaluating the circuit complexity for entanglement distillation protocols based on surface codes and quantum convolutional codes. (3) Our stabilizer entanglement distillation techniques advance quantum computing. We propose a fault-tolerant protocol for constant-depth encoding and decoding of arbitrary states in surface codes, with potential extensions to more general quantum low-density parity-check codes. This protocol is feasible with state-of-the-art reconfigurable atom arrays and surpasses the limits of conventional logarithmic depth encoders. Overall, our study integrates stabilizer formalism, measurement-based quantum computing, and entanglement distillation, advancing both quantum communication and computing.
Quantum entanglement distillation refers to the process of extracting higher quality entangled pairs from a larger set of lower-quality pairs. Here, we present a basic structure of entanglement distillation protocol based on quantum error correction code. We perform the distillation procedure of this protocol in bit flip channel and show the performance in terms of output fidelity. Combining the characteristics of QEC and EDP, QEC-based EDP holds great promise for future applications in quantum network.
Bell-state measurement (BSM) on entangled states shared between quantum repeaters is the fundamental operation used to route entanglement in quantum networks. Performing BSMs on Werner states shared between repeaters leads to exponential decay in the fidelity of the end-to-end Werner state with the number of repeaters, necessitating entanglement distillation. In this work, we use quantum error correcting codes for deterministic entanglement distillation to route Werner states on a chain of repeaters. To maximize the end-to-end distillable entanglement, we utilize global link-state knowledge to determine the optimal policy for scheduling distillation and BSMs at the repeaters. We observe that low-rate codes produce high-fidelity end-to-end states owing to their excellent error-correcting capability, whereas high-rate codes yield a larger number of end-to-end states but of lower fidelity. The number of quantum memories used at repeaters increases with the code rate as well as the classical computation time of the decoder.