26th Australian Institute of Physics Congress and the Australian and New Zealand Conference on Optics and Photonics

Memory-efficient quantum transducers for input-output decoding

Not scheduled

20m

Belinda Hutchinson Building (The University of Sydney )

Contributed Oral AIP | Quantum Science and Technology (QST)

Speaker

Jianjun Chen (Nanyang Technological University)

Description

Predicting a stochastic process requires memory, and the minimal memory that a model needs — its statistical complexity — can be reduced by using quantum rather than classical states. We focus on a concrete operational task: the decoding of convolutional codes over noisy channels. The theoretically optimal decoder tracks a continuous belief state, making its exact classical model infinite-dimensional, with its statistical complexity diverging as the precision increases. Here, we show that by realizing belief states as non-orthogonal quantum states, we can bound the statistical complexity of the quantum machine, and that the model distortion can be exponentially suppressed. We further show that the same decoder admits a low-qubit quantum realization, and provide a construction method for the corresponding quantum transducer. Under the assumption that the process is contractive, which holds for any decodable code, we show that the error from this truncation is also upper-bounded by a constant over long streams.