Infinite families of cyclic and negacyclic codes supporting 3-designs

Interplay between coding theory and combinatorial $t$-designs has been a hot topic for many years for combinatorialists and coding theorists. Some infinite families of cyclic codes supporting infinite families of $3$-designs have been constructed in the past 50 years. However, no infinite family of negacyclic codes supporting an infinite family of $3$-designs has been reported in the literature. This is the main motivation of this paper. Let $q=p^m$, where $p$ is an odd prime and $m \geq 2$ is an integer. The objective of this paper is to present an infinite family of cyclic codes over \gf(q) supporting an infinite family of $3$-designs and two infinite families of negacyclic codes over \gf(q^2) supporting two infinite families of $3$-designs. The parameters and the weight distributions of these codes are determined. The subfield subcodes of these negacyclic codes over \gf(q) are studied. Three infinite families of almost MDS codes are also presented. A constacyclic code over GF($4$) supporting a $4$-design and six open problems are also presented in this paper

S-QGPU: Shared Quantum Gate Processing Unit for Distributed Quantum Computing

We propose a distributed quantum computing (DQC) architecture in which individual small-sized quantum computers are connected to a shared quantum gate processing unit (S-QGPU). The S-QGPU comprises a collection of hybrid two-qubit gate modules for remote gate operations. In contrast to conventional DQC systems, where each quantum computer is equipped with dedicated communication qubits, S-QGPU effectively pools the resources (e.g., the communication qubits) together for remote gate operations, and thus significantly reduces the cost of not only the local quantum computers but also the overall distributed system. Moreover, S-QGPU's shared resources for remote gate operations enable efficient resource utilization. When not all computing qubits in the system require simultaneous remote gate operations, S-QGPU-based DQC architecture demands fewer communication qubits, further decreasing the overall cost. Alternatively, with the same number of communication qubits, it can support a larger number of simultaneous remote gate operations more efficiently, especially when these operations occur in a burst mode.Comment: 8 pages, 6 figure