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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.
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Fast decay of classification error in variational quantum circuits
Abstract Variational quantum circuits (VQCs) have shown great potential in near-term applications. However, the discriminative power of a VQC, in connection to its circuit architecture and depth, is not understood. To unleash the genuine discriminative power of a VQC, we propose a VQC system with the optimal classical post-processing—maximum-likelihood estimation on measuring all VQC output qubits. Via extensive numerical simulations, we find that the error of VQC quantum data classification typically decays exponentially with the circuit depth, when the VQC architecture is extensive—the number of gates does not shrink with the circuit depth. This fast error suppression ends at the saturation towards the ultimate Helstrom limit of quantum state discrimination. On the other hand, non-extensive VQCs such as quantum convolutional neural networks are sub-optimal and fail to achieve the Helstrom limit, demonstrating a trade-off between ansatz complexity and classification performance in general. To achieve the best performance for a given VQC, the optimal classical post-processing is crucial even for a binary classification problem. To simplify VQCs for near-term implementations, we find that utilizing the symmetry of the input properly can improve the performance, while oversimplification can lead to degradation.
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- PAR ID:
- 10378465
- Date Published:
- Journal Name:
- Quantum Science and Technology
- Volume:
- 7
- Issue:
- 3
- ISSN:
- 2058-9565
- Page Range / eLocation ID:
- 035017
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1088/2058-9565/ac70f5
