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Quantum walks are the quantum-mechanical analog of random walks, in which a quantum `walker' evolves between initial and final states by traversing the edges of a graph, either in discrete steps from node to node or via continuous evolution…

The realization of a global quantum network capable of supporting secure communication and other quantum information processing (QIP) tasks hinges on the ability to distribute high-fidelity entanglement across long distances while…

A quantum internet holds promise for achieving distributed quantum sensing and large-scale quantum computer networks, as well as quantum communication among arbitrary clients all over the globe. The main building block is efficient…

Demonstrating quantum advantage has been a pressing challenge in the field. Most claimed quantum speedups rely on a subroutine in which classical information can be accessed in a coherent quantum manner, which imposes a crucial constraint…

Quantum computers require quantum logic, something fundamentally different to classical Boolean logic. This difference leads to a greater efficiency of quantum computation over its classical counter-part. In this review we explain the basic…

Quantum networks (QNs) are a promising platform for secure communications, enhanced sensing, and efficient distributed quantum computing. However, due to the fragile nature of quantum states, these networks face significant challenges in…

In general, a quantum circuit is constructed with elementary gates, such as one-qubit gates and CNOT gates. It is possible, however, to speed up the execution time of a given circuit by merging those elementary gates together into larger…

Quantum networks, which enable the transfer of quantum information across long distances, promise to provide exciting benefits and new possibilities in many areas including communication, computation, security, and metrology. These networks…

Quantum computing is presently undergoing rapid development to achieve a significant speedup promised in certain applications. Nonetheless, scaling quantum computers remains a formidable engineering challenge, prompting exploration of…

We present a comprehensive and self-contained simplified review of the quantum computing scheme of Phys. Rev. Lett. 98, 190504 (2007), which features a 2-D nearest neighbor coupled lattice of qubits, a threshold error rate approaching 1%,…

We consider the problem of deciding if a set of quantum one-qudit gates $\mathcal{S}=\{U_1,\ldots,U_n\}$ is universal. We provide the compact form criteria leading to a simple algorithm that allows deciding universality of any given set of…

Random linear network codes can be designed and implemented in a distributed manner, with low computational complexity. However, these codes are classically implemented over finite fields whose size depends on some global network parameters…

Quantum computing is poised to redefine the algorithmic foundations of communication systems. While quantum superposition and entanglement enable quadratic or exponential speedups for specific problems, identifying use cases where these…

With the advantages of high-speed parallel processing, quantum computers can efficiently solve large-scale complex optimization problems in future networks. However, due to the uncertain qubit fidelity and quantum channel noise, distributed…

We present an explicit construction of a relativistic quantum computing architecture using a variational quantum circuit approach that is shown to allow for universal quantum computing. The variational quantum circuit consists of tunable…

Quantum communications bring a paradigm change in internet security by using quantum resources to establish secure keys between parties. Present-day quantum communications networks are mainly point-to-point and use trusted nodes and key…

The field of quantum algorithms is vibrant. Still, there is currently a lack of programming languages for describing quantum computation on a practical scale, i.e., not just at the level of toy problems. We address this issue by introducing…

In this paper we give a polynomial-time quantum algorithm for computing orders of solvable groups. Several other problems, such as testing membership in solvable groups, testing equality of subgroups in a given solvable group, and testing…

A quantum computer consists of a set of quantum bits upon which operations called gates are applied to perform computations. In order to perform quantum algorithms, physicists would like to design arbitrary gates to apply to quantum bits.…

The quantum technology revolution brings with it the promise of a quantum internet. A new -- quantum -- network stack will be needed to account for the fundamentally new properties of quantum entanglement. The first realisations of quantum…