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  1. Abstract

    We investigate the ground states of spin models defined on networks that we imprint (e.g., non-complex random networks like Erdos–Renyi, or complex networks like Watts–Strogatz, and Barabasi–Albert), and their response to decohering processes which we model with network attacks. We quantify the complexity of these ground states, and their response to the attacks, by calculating distributions of network measures of an emergent network whose link weights are the pairwise mutual information between spins. We focus on attacks which projectively measure spins. We find that the emergent networks in the ground state do not satisfy the usual criteria for complexity, and their average properties are captured well by a single dimensionless parameter in the Hamiltonian. While the response of classical networks to attacks is well-studied, where classical complex networks are known to be more robust to random attacks than random networks, we find counter-intuitive results for our quantum networks. We find that the ground states for Hamiltonians defined on different classes of imprinted networks respond similarly to all our attacks, and the attacks rescale the average properties of the emergent network by a constant factor. Mean field theory explains these results for relatively dense networks, but we also find the simple rescaling behavior away from the regime of validity of mean field theory. Our calculations indicate that complex spin networks are not more robust to projective measurement attacks, and presumably also other quantum attacks, than non-complex spin networks, in contrast to the classical case. Understanding the response of the spin networks to decoherence and attacks will have applications in understanding the physics of open quantum systems, and in designing robust complex quantum systems—possibly even a robust quantum internet in the long run—that is maximally resistant to decoherence.

     
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  2. Abstract

    Quantum annealing is a powerful alternative model of quantum computing, which can succeed in the presence of environmental noise even without error correction. However, despite great effort, no conclusive demonstration of a quantum speedup (relative to state of the art classical algorithms) has been shown for these systems, and rigorous theoretical proofs of a quantum advantage (such as the adiabatic formulation of Grover’s search problem) generally rely on exponential precision in at least some aspects of the system, an unphysical resource guaranteed to be scrambled by experimental uncertainties and random noise. In this work, we propose a new variant of quantum annealing, called RFQA, which can maintain a scalable quantum speedup in the face of noise and modest control precision. Specifically, we consider a modification of flux qubit-based quantum annealing which includes low-frequency oscillations in the directions of the transverse field terms as the system evolves. We show that this method produces a quantum speedup for finding ground states in the Grover problem and quantum random energy model, and thus should be widely applicable to other hard optimization problems which can be formulated as quantum spin glasses. Further, we explore three realistic noise channels and show that the speedup from RFQA is resilient to 1/f-like local potential fluctuations and local heating from interaction with a sufficiently low temperature bath. Another noise channel, bath-assisted quantum cooling transitions, actually accelerates the algorithm and may outweigh the negative effects of the others. We also detail how RFQA may be implemented experimentally with current technology.

     
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