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Welcome to the first issue of the Journal on Selected Areas in Information Theory (JSAIT) focusing on Deep Learning: Mathematical Foundations and Applications to Information Science.

I would like to warmly welcome our readers to this inaugural special issue of JSAIT, the Information Theory Society’s first new journal since the IRE Transactions on Information Theory launched in 1953. The society’s desire to expand its technical scope, incubate new research directions, catalyze connections with other disciplines, and highlight new and emerging applications formed the impetus for the new journal.

Quantum stabilizer codes constructed from sparse matrices have good performance and can be efficiently decoded by belief propagation (BP). A conventional BP decoding algorithm treats binary stabilizer codes as additive codes over GF(4). This algorithm has a relatively complex process of handling check-node messages, which incurs higher decoding complexity. Moreover, BP decoding of a stabilizer code usually suffers a performance loss due to the many short cycles in the underlying Tanner graph.

One of the main problems in quantum information systems is the presence of errors due to noise, and for this reason quantum error-correcting codes (QECCs) play a key role. While most of the known codes are designed for correcting generic errors, i.e., errors represented by arbitrary combinations of Pauli X, Y and Z operators, in this paper we investigate the design of stabilizer QECC able to correct a given number eg of generic Pauli errors, plus eZ Pauli errors of a specified type, e.g., Z errors.

Quantum state discrimination (QSD) is a key enabler in quantum sensing and networking, for which we envision the utility of non-coherent quantum states such as photon-added coherent states (PACSs). This paper addresses the problem of discriminating between two noisy PACSs. First, we provide representation of PACSs affected by thermal noise during state preparation in terms of Fock basis and quasi-probability distributions. Then, we demonstrate that the use of PACSs instead of coherent states can significantly reduce the error probability in QSD.

We continue the study of the quantum channel version of Shannon's zero-error capacity problem. We generalize the celebrated Haemers bound to noncommutative graphs (obtained from quantum channels). We prove basic properties of this bound, such as additivity under the direct sum and submultiplicativity under the tensor product. The Haemers bound upper bounds the Shannon capacity of noncommutative graphs, and we show that it can outperform other known upper bounds, including noncommutative analogues of the Lovász theta function (Duan-Severini-Winter, �鶹��ýAV Trans.

In order to perform universal fault-tolerant quantum computation, one needs to implement a logical non-Clifford gate. Consequently, it is important to understand codes that implement such gates transversally. In this paper, we adopt an algebraic approach to characterize all stabilizer codes for which transversal $T$ and $T^{\dagger }$ gates preserve the codespace. Our Heisenberg perspective reduces this question to a finite geometry problem that translates to the design of certain classical codes.

Secret and perfect randomness is an essential resource in cryptography. Yet, it is not even clear that such exists. It is well known that the tools of classical computer science do not allow us to create secret and perfect randomness from a single weak public source. Quantum physics, on the other hand, allows for such a process, even in the most paranoid cryptographic sense termed “device-independent quantum cryptography”.

Restricted Boltzmann Machines trained with different numbers of iterations were used to provide a large diverse set of energy functions each containing many local valleys (LVs). They were used to confirm the property of the D-Wave quantum annealer (QA) to find potentially important LVs in the energy functions of Markov Random Fields that may be missed by classical searches. Even after a prohibitively long classical search by simulated annealing (SA), as many as 30-50% of the QA-found LVs remained not found by the SA.