With the development of quantum computing devices, we are approaching to the dawn of a new generation of high-performance quantum hardware architectures. Quantum computers can be built using a variety of technologies, and with very different stacks of quantum architectures. The differences revolves around the technological complexity of realising qubits and their interconnections, on the construction of quantum memories for multi-qubit structures, and their interface with quantum processors. However, one of the most significant technological challenges is that of distributing the entanglement in the quantum graphs that define the network architectures of Quantum Processing Units (QPUs), in which interactions between pairs of qubits are constrained by fixed quantum networks with partially or fully connected nodes. In this context, architecture-restricted Quantum Network Coding (QNC) for the implementation of QPUs in quantum computers is a very relevant research topic in the field of quantum hardware to be implemented by the Quantum Software Layer of the stack of such Quantum Computers.
In this repository, a new and very recently published QNC technique, known as Quantum Linear Network Coding (QLNC), was used. Quantum circuits (QCs) implemented based on the QLNC technique allows to distribute entanglement based on QCs whose depth can be limited by simple lattice properties, leading to a constant of modest size for many reasonable choices in various architectures. This technique also overcomes the problem of multiple unicast or multiple multicast of each cluster in the network. The QLNC protocol is more versatile than other QNC protocols, as it starts from the idea of quantization clustering by mapping classical network topologies onto quantum networks, encoded on the basis of logical CCs.
CCs that allow the distribution of discrete-variable interleaved states were designed, simulated and implemented on IBM quantum computers using the QLNC technique for 5-qubit L-type and T-type configurations, and quantum architectures such as Butterfly Quantum Networks (6 qubits) and GHZ (12 qubits) were simulated on the IBM Qiskit platform. This technique can be extended to any QPU without any limitation of network architecture or quantum network connections. Moreover, it presents a specialised formalism, which is different and more efficient than the formalism with stabilising states. Based on the results obtained, using different quantum information techniques, comparisons of the QLNC technique with the Measurement-based Quantum Coding on Cluster States (MQNC) technique were made, which systematically favour, in all aspects considered, the QLNC technique.
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