TY - GEN
T1 - Quantum Advantage via Qubit Belief Propagation
AU - Rengaswamy, Narayanan
AU - Seshadreesan, Kaushik P.
AU - Guha, Saikat
AU - Pfister, Henry D.
N1 - Funding Information:
The work of NR and HP was supported in part by the National Science Foundation (NSF) under Grant No. 1908730 and 1910571. KPS and SG acknowledge support from NSF, Grant No. 1855879, and the Office of Naval Research MURI program on Optical Computing, Grant No. N00014-14-1-0505. Any opinions, findings, conclusions, and recommendations expressed in this material are those of the authors and do not necessarily reflect the views of these sponsors.
Publisher Copyright:
© 2020 IEEE.
PY - 2020/6
Y1 - 2020/6
N2 - Quantum technologies are maturing by the day and their near-term applications are now of great interest. Deep-space optical communication involves transmission over the pure-state classical-quantum channel. For optimal detection, a joint measurement on all output qubits is required in general. Since this is hard to realize, current (sub-optimal) schemes perform symbol-by-symbol detection followed by classical post-processing. In this paper we focus on a recently proposed belief propagation algorithm by Renes that passes qubit messages on the factor graph of a classical error-correcting code. More importantly, it only involves single-qubit Pauli measurements during the process. For an example 5-bit code, we analyze the involved density matrices and calculate the error probabilities on this channel. Then we numerically compute the optimal joint detection limit using the Yuen-Kennedy-Lax conditions and demonstrate that the calculated error probabilities for this algorithm appear to achieve this limit. This represents a first step towards achieveing quantum communication advantage. We verify our analysis using Monte-Carlo simulations in practice.
AB - Quantum technologies are maturing by the day and their near-term applications are now of great interest. Deep-space optical communication involves transmission over the pure-state classical-quantum channel. For optimal detection, a joint measurement on all output qubits is required in general. Since this is hard to realize, current (sub-optimal) schemes perform symbol-by-symbol detection followed by classical post-processing. In this paper we focus on a recently proposed belief propagation algorithm by Renes that passes qubit messages on the factor graph of a classical error-correcting code. More importantly, it only involves single-qubit Pauli measurements during the process. For an example 5-bit code, we analyze the involved density matrices and calculate the error probabilities on this channel. Then we numerically compute the optimal joint detection limit using the Yuen-Kennedy-Lax conditions and demonstrate that the calculated error probabilities for this algorithm appear to achieve this limit. This represents a first step towards achieveing quantum communication advantage. We verify our analysis using Monte-Carlo simulations in practice.
KW - Factor graphs
KW - Helstrom measurement
KW - belief propagation
KW - classical-quantum channels
KW - linear codes
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U2 - 10.1109/ISIT44484.2020.9174494
DO - 10.1109/ISIT44484.2020.9174494
M3 - Conference contribution
AN - SCOPUS:85090424663
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 1824
EP - 1829
BT - 2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2020 IEEE International Symposium on Information Theory, ISIT 2020
Y2 - 21 July 2020 through 26 July 2020
ER -