TY - JOUR

T1 - Belief propagation with quantum messages for quantum-enhanced classical communications

AU - Rengaswamy, Narayanan

AU - Seshadreesan, Kaushik P.

AU - Guha, Saikat

AU - Pfister, Henry D.

N1 - Funding Information:
The authors acknowledge helpful discussions with Prof. Bane Vasic, Prof. Mark Neifeld, Prof. Iman Marvian, Kevin Stubbs, Sarah Brandsen, and Nithin Raveendran. The authors would like to thank Dr. Zachary Dutton for sharing his code to numerically evaluate the YKL limit of decoding a general binary linear code21. The authors would also like to thank the reviewers for helpful feedback, in particular for the suggestion to compute the mutual information per photon for BPQM. K.P.S. and S.G. acknowledge the support of a National Science Foundation (NSF) project “CIF: Medium: Iterative Quantum LDPC Decoders”, award number: 1855879, and the Office of Naval Research (ONR) MURI program on Optical Computing, grant number N00014-14-1-0505. The work of N.R. and H.P. was supported in part by the National Science Foundation (NSF) under grant no. 1718494, 1908730, and 1910571. 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:
© 2021, The Author(s).

PY - 2021/12

Y1 - 2021/12

N2 - For space-based laser communications, when the mean photon number per received optical pulse is much smaller than one, there is a large gap between communications capacity achievable with a receiver that performs individual pulse-by-pulse detection, and the quantum-optimal “joint-detection receiver” that acts collectively on long codeword-blocks of modulated pulses; an effect often termed “superadditive capacity”. In this paper, we consider the simplest scenario where a large superadditive capacity is known: a pure-loss channel with a coherent-state binary phase-shift keyed (BPSK) modulation. The two BPSK states can be mapped conceptually to two non-orthogonal states of a qubit, described by an inner product that is a function of the mean photon number per pulse. Using this map, we derive an explicit construction of the quantum circuit of a joint-detection receiver based on a recent idea of “belief-propagation with quantum messages” (BPQM). We quantify its performance improvement over the Dolinar receiver that performs optimal pulse-by-pulse detection, which represents the best “classical” approach. We analyze the scheme rigorously and show that it achieves the quantum limit of minimum average error probability in discriminating 8 (BPSK) codewords of a length-5 binary linear code with a tree factor graph. Our result suggests that a BPQM receiver might attain the Holevo capacity of this BPSK-modulated pure-loss channel. Moreover, our receiver circuit provides an alternative proposal for a quantum supremacy experiment, targeted at a specific application that can potentially be implemented on a small, special-purpose, photonic quantum computer capable of performing cat-basis universal qubit logic.

AB - For space-based laser communications, when the mean photon number per received optical pulse is much smaller than one, there is a large gap between communications capacity achievable with a receiver that performs individual pulse-by-pulse detection, and the quantum-optimal “joint-detection receiver” that acts collectively on long codeword-blocks of modulated pulses; an effect often termed “superadditive capacity”. In this paper, we consider the simplest scenario where a large superadditive capacity is known: a pure-loss channel with a coherent-state binary phase-shift keyed (BPSK) modulation. The two BPSK states can be mapped conceptually to two non-orthogonal states of a qubit, described by an inner product that is a function of the mean photon number per pulse. Using this map, we derive an explicit construction of the quantum circuit of a joint-detection receiver based on a recent idea of “belief-propagation with quantum messages” (BPQM). We quantify its performance improvement over the Dolinar receiver that performs optimal pulse-by-pulse detection, which represents the best “classical” approach. We analyze the scheme rigorously and show that it achieves the quantum limit of minimum average error probability in discriminating 8 (BPSK) codewords of a length-5 binary linear code with a tree factor graph. Our result suggests that a BPQM receiver might attain the Holevo capacity of this BPSK-modulated pure-loss channel. Moreover, our receiver circuit provides an alternative proposal for a quantum supremacy experiment, targeted at a specific application that can potentially be implemented on a small, special-purpose, photonic quantum computer capable of performing cat-basis universal qubit logic.

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U2 - 10.1038/s41534-021-00422-1

DO - 10.1038/s41534-021-00422-1

M3 - Article

AN - SCOPUS:85108098204

VL - 7

JO - npj Quantum Information

JF - npj Quantum Information

SN - 2056-6387

IS - 1

M1 - 97

ER -