Quantum Period Reconstruction of Binary Sequences

Igor E. Shparlinski, Arne Winterhof

Dulte José de Barros, B.G. Dorsch

This paper presents an approach to soft-decision decoding for a (n, k) binary linear block code. This approach achieves near-optimal to optimal performance for any signal-to-noise ratio value. The proposed decoding is based on the reordering of the received symbols according to their reliability measure and can be applied to any binary linear code. The basic idea is to generate a sequence of codewords such that there will be a high probability that the next codeword is closer to the received vector. In this algorithm the information provided by the soft-decisions is used to generate information sets utilized in decoding. A fast procedure checks whether a given set of k positions is an information set. A sequence of codewords is reconstructed using a sequence of information sets. Each codeword reconstructed is compared with the received word and the closest one is selected. Hence, the decoding algorithm is an iterative procedure designed to enhance the performance of the usual soft-decision decoding, since with each iteration of the procedure, real vectors successively closer to the received vector are examined. A high performance stop rule is utilized to reduce the number of generated information sets, stopping the decoding process when a codeword is closest to the received sequence.

Stefan Weigert

Easwar Magesan, Alexandre Cooper, H. Yum +1 more

Quantum systems have shown great promise for precision metrology thanks to advances in their control. This has allowed not only the sensitive estimation of external parameters but also the reconstruction of their temporal profile. In particular, quantum control techniques and orthogonal function theory have been applied to the reconstruction of the complete profiles of time-varying magnetic fields. Here, we provide a detailed theoretical analysis of the reconstruction method based on the Walsh functions, highlighting the relationship between the orthonormal Walsh basis, sensitivity of field reconstructions, data compression techniques, and dynamical decoupling theory. Specifically, we show how properties of the Walsh basis and a detailed sensitivity analysis of the reconstruction protocol provide a method to characterize the error between the reconstructed and true fields. In addition, we prove various results about the negligibility function on binary sequences which lead to data compression techniques in the Walsh basis and a more resource-efficient reconstruction protocol. The negligibility proves a fruitful concept to unify the information content of Walsh functions and their dynamical decoupling power, which makes the reconstruction method robust against noise.

Alexander Miessen, Pauline J. Ollitrault, Francesco Tacchino +1 more

N. E. Bonesteel, Robert Cipri, Daniel Zeuch