We investigate the optimal selection of high-fidelity quantum links that can preserve fragile quantum states during information transmission. However, uniformly estimating the fidelities of all links becomes prohibitively costly in large-scale networks with numerous noisy connections. To overcome this limitation, we recast link selection and fidelity inference as an optimal-action discovery task within a reinforcement learning framework. Subsequently, we propose an algorithm termed Epsilon-Greedy Quantum Link Selection (EGreedyQLiS). This algorithm effectively identifies the optimal link among numerous quantum links and provides accurate fidelity estimates with a low consumption of quantum resources. EGreedyQLiS infers link fidelities using observations obtained from a standard network benchmarking procedure and greedily optimizes link selection during the fidelity estimation procedure. This optimization strategy concentrates quantum resources on estimating high-fidelity links, thereby providing accurate fidelity estimation for these links. The results of extensive simulations demonstrate that EGreedyQLiS exceeds existing approaches in optimal link identification with reduced quantum resource overhead.

Quantum burst error correction codes (QBECCs) are of great importance to deal with the memory effect in quantum channels. As the most important family of QBECCs, quantum cyclic codes (QCCs) play a vital role in the correction of burst errors. In this work, we characterize the burst error correction ability of QCCs constructed from the Calderbank-Shor-Steane (CSS) and the Hermitian constructions. We determine the burst error correction limit of QCCs and quantum Reed-Solomon codes with algorithms in polynomial-time complexities. As a result, lots of QBECCs saturating the quantum Reiger bound are obtained. We show that quantum Reed-Solomon codes have better burst error correction abilities than the previous results. At last, we give the quantum error-trapping decoder (QETD) of QCCs for decoding burst errors. The decoder runs in linear time and can decode both degenerate and nondegenerate burst errors. What’s more, the numerical results show that QETD can decode much more degenerate burst errors than the nondegenerate ones.

Quantum networks are an actively researched and promising field, aiming to achieve efficient quantum information transmission by interconnecting quantum nodes. In large-scale quantum networks, end-to-end throughput is a critical factor that affects the overall performance of the network. The maximum flow problem, extensively studied in classical network theory, identifies a set of paths between the source and destination nodes that maximizes the total flow. This study extends the maximum flow problem to quantum networks, focusing on coordinating multiple paths for multi-path quantum communication. We propose a Quantum Multi-Path Communication Protocol (QMCP) that employs maximum flow theory to allocate transmission resources across multiple nodes efficiently, thus maximizing the total transmission capacity from the source to the destination. Our evaluation demonstrates that QMCP significantly enhances end-to-end throughput in quantum networks.

In the problem of conditional disclosure of secrets (CDS), two parties, Alice and Bob, each has an input and shares a common secret. Their goal is to reveal the secret to a third party, Carol, as efficiently as possible, only if the inputs of Alice and Bob satisfy a certain functional relation$f$. To prevent leakage of the secret to Carol when the input combination is unqualified, both Alice and Bob introduce noise. This work aims to determine the noise capacity, defined as the maximum number of secret bits that can be securely revealed to Carol, normalized by the total number of independent noise bits held jointly by Alice and Bob. Our contributions are twofold. First, we establish the necessary and sufficient conditions under which the CDS noise capacity attains its maximum value of 1. Second, in addition to the above best-case scenarios, we derive an upper bound on the linear noise capacity for any CDS instance. In particular, this upper bound is equal to$(\rho-1)(d-1) /(\rho d-1)$, where$\rho$is the covering parameter of the graph representation of$f$, and$d$is the number of unqualified edges in residing unqualified path.

We closely study N-sum boxes and their transfer matrices. Recently formulated as an abstraction for linear computations over quantum network, such a box allows for tools from quantum information processing to be applied on classical computational problems. We investigate (k, N + t)-sum boxes, which are generalized version of the N-sum boxes, and propose a general construction of their transfer matrices. Seen in this light, an N-sum box is a special case when k = N and t = 0.

Motivated by federated learning (FL), secure aggregation (SA) aims to securely compute, as efficiently as possible, the sum of a set of inputs distributed across many users. To understand the impact of network topology, hierarchical secure aggregation (HSA) investigated the communication and secret key generation efficiency in a 3-layer relay network, where clusters of users are connected to the aggregation server through an intermediate layer of relays. Due to the pre-aggregation of the messages at the relays, HSA reduces the communication burden on the relay-to-server links and is able to support a large number of users. However, as the number of users increases, a practical challenge arises from heterogeneous security requirements–for example, users in different clusters may require varying levels of input protection. Motivated by this, we study weakly-secure HSA (WS-HSA) with collusion resilience, where instead of protecting all the inputs from any set of colluding users, only the inputs belonging to a predefined collection of user groups (referred to as security input sets) need to be protected against another predefined collection of user groups (referred to as collusion sets). Since the security input sets and collusion sets can be arbitrarily defined, our formulation offers a flexible framework for addressing heterogeneous security requirements in HSA. We characterize the optimal total key rate, i.e., the total number of independent key symbols required to ensure both server and relay security, for a broad range of parameter configurations. For the remaining cases, we establish lower and upper bounds on the optimal key rate, providing constant-factor gap optimality guarantees.

Quantum low-density parity check (QLDPC) codes have rapidly developed in the field of quantum error correction in recent years. A variety of quantum code families have emerged from numerous research activities. In this paper, we employ concatenated Calderbank-Shor-Steane (CSS) codes, hypergraph product codes, and Bacon-Shor codes to train belief-propagation (BP) and neural BP (NBP) decoders. At the same time, we employ a concatenation scheme in BP and NBP, the amplified construction of CSS codes is realized, and the training of longer length parameter quantum codes is realized. The numerical results show that the concatenated CSS codes demonstrate better error correction performance compared to both hypergraph product codes and Bacon-Shor codes. In addition, the concatenated CSS codes are trained using the concatenation scheme to improve the error correction performance of the decoder.

Ascon algorithm has been selected by NIST for standardization of the lightweight cryptography, that will be used in embedded systems, IoT devices, and other resource-constrained devices. As a lightweight cryptographic algorithm, Ascon implementation requires less computation and memory. However, the current implementations of Ascon algorithms and existing protection schemes are vulnerable to side-channel attacks. In this paper, we propose an IPM (inner product masking) based protection for Ascon implementations. Our new masking scheme can prevent side-channel attacks from successfully retrieving the key, even when the leakage levels are nearly identical. Alternatively, the cost of obtaining the key can increase by several orders of magnitude, making the attack significantly more challenging. The proposed scheme is experimentally validated by porting it into a STM32F407 microcontroller and conducting correlation power analysis (CPA) and template attack (TA) on the collected power traces. The experimental results show that while CPA can successfully retrieve the keys from both the unprotected Ascon implementation and the Boolean-masked Ascon implementation, they fail against the new masking scheme. Although TA attacks can break the new scheme, they require approximately 50 times more data compared to attacking the Boolean mask. This demonstrates that the new masking scheme offers significantly greater security than both the Boolean mask and the unprotected implementations.

In this paper, we utilize a concatenation scheme to construct new families of quantum error correction codes achieving the quantum Gilbert-Varshamov (GV) bound asymptotically. Weconcatenate alternant codes with any linear code achievingthe classical GV bound to construct Calderbank-Shor-Steane (CSS) codes. We show that the concatenated code can achieve the quantum GV bound asymptotically and can approach the Hashing bound for asymmetric Pauli channels. By combing Steane’s enlargement construction of CSS codes, we derive a family of enlarged stabilizer codes achieving the quantum GV bound for enlarged CSS codes asymptotically. Asapplications, we derive two families of fast encodable and decodable CSS codes with parameters$\mathscr {Q}_{1}=[[N,\Omega (\sqrt {N}),\Omega (\sqrt {N})]]$, and$\mathscr {Q}_{2}=[[N,\Omega (N/\log N),\Omega (N/\log N)/\Omega (\log N)]]$. We show that$\mathscr {Q}_{1}$can be encoded very efficiently by circuits of size$O(N)$and depth$O(\sqrt {N})$. For an input error syndrome,$\mathscr {Q}_{1}$can correct any adversarial error of weight up to half the minimum distance bound in$O(N)$time.$\mathscr {Q}_{1}$can also be decoded in parallel in$O(\sqrt {N})$time by using$O(\sqrt {N})$classical processors. For an input error syndrome, we proved that$\mathscr {Q}_{2}$can correct a linear number of${X}$-errors with high probability and an almost linear number of${Z}$-errors in$O(N)$time. Moreover,$\mathscr {Q}_{2}$can be decoded in parallel in$O(\log (N))$time by using$O(N)$classical processors.

In this paper, we present a new construction of asymmetric quantum codes (AQCs) by combining classical concatenated codes (CCs) with tensor product codes (TPCs), called asymmetric quantum concatenated and tensor product codes (AQCTPCs) which have the following three advantages. First, only the outer codes in AQCTPCs need to satisfy the orthogonal constraint in quantum codes, and any classical linear code can be used for the inner, which makes AQCTPCs very easy to construct. Second, most AQCTPCs are highly degenerate, which means they can correct many more errors than their classical TPC counterparts. Consequently, we construct several families of AQCs with better parameters than known results in the literature. Third, AQCTPCs can be efficiently decoded although they are degenerate, provided that the inner and outer codes are efficiently decodable. In particular, we significantly reduce the inner decoding complexity of TPCs from$\Omega (n_{2}a^{n_{1}})(a>1)$to$O(n_{2})$by considering error degeneracy, where$n_{1}$and$n_{2}$are the block length of the inner code and the outer code, respectively. Furthermore, we generalize our concatenation scheme by using the generalized CCs and TPCs correspondingly.

In practical communication and computation systems, errors occur predominantly in adjacent positions rather than in a random manner. In this paper, we develop a stabilizer formalism for quantum burst error correction codes (QBECC) to combat such error patterns in the quantum regime. Our contributions are as follows. Firstly, we derive an upper bound for the correctable burst errors of QBECCs, the quantum Reiger bound (QRB). Secondly, we propose two constructions of QBECCs: one by heuristic computer search and the other by concatenating two quantum tensor product codes (QTPCs). We obtain several new QBECCs with better parameters than existing codes with the same coding length. Moreover, some of the constructed codes can saturate the quantum Reiger bounds. Finally, we perform numerical experiments for our constructed codes over Markovian correlated depolarizing quantum memory channels, and show that QBECCs indeed outperform standard QECCs in this scenario.

In the works of Maucher et al. (200), Bossert et al. (1999) and GrieBer (2003), the authors presented the equivalence of generalized concatenated codes (GCC codes) and generalized error-location codes (GEL codes). However, they find that there exist several errors. In this work, the authors give several corrections to the work of Maucher et al. (2000) and make some amendments to Theorems 2 and 3 , but without affecting the equivalence of the class of GCC codes and the class of GEL codes. The authors give corrected proofs to the amended Theorems 2 and 3, respectively. Then, they conclude that the class of GCC codes is still equivalent to the class of GEL codes.

In this paper, we construct asymmetric quantum error-correcting codes(AQCs) based on subclasses of Alternant codes. Firstly, We propose a new subclass of Alternant codes which can attain the classical Gilbert-Varshamov bound to construct AQCs. It is shown that when dx= 2, Z-parts of the AQCs can attain the classical Gilbert-Varshamov bound. Then we construct AQCs based on a famous subclass of Alternant codes called Goppa codes. As an illustrative example, we get three [[55, 6, 19/4]], [[55, 10, 19/3]], [[55, 15, 19/2]] AQCs from the well known [55, 16, 19] binary Goppa code. At last, we get asymptotically good binary expansions of asymmetric quantum GRS codes, which are quantum generalizations of Retter's classical results. All the AQCs constructed in this paper are pure.