A Quantum Algorithm for Network Reliability

• URL: http://arxiv.org/abs/2203.10201v1
• Date: Sat, 19 Mar 2022 00:26:52 GMT
• Title: A Quantum Algorithm for Network Reliability
• Authors: Stefan Pabst and Yunseong Nam
• Abstract summary: We present an explicit, circuit-level implementation of a quantum algorithm that computes $R$. Our algorithm requires $O(EV/epsilon)$ gate operations and $O(E)$bits, where $V$ and $E$ are the number nodes and edges.
• Score: 0.033842793760651545
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Building a network that is resilient to a component failure is vital. Our access to electricity and telecommunications or the internet of things all hinge on an uninterrupted service provided by a robust network. Calculating the network reliability $R$ is $\sharp$P-complete and intractable to calculate exactly for medium and large networks. Here, we present an explicit, circuit-level implementation of a quantum algorithm that computes $R$. Our algorithm requires $O(EV/\epsilon)$ gate operations and $O(E)$ qubits, where $V$ and $E$ are the number of nodes and edges in the graph and $\epsilon$ is the uncertainty in the reliability estimation. This constitutes a significant polynomial speedup over the best classical approaches currently known. We further provide quantum gate counts, relevant for both pre-fault-tolerant and fault-tolerant regimes, sufficient to compute $R$.

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