A Quantum Algorithm for Network Reliability
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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 ♯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/ϵ) gate operations and O(E) qubits, where V and E are the number of nodes and edges in the graph and ϵ 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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