Quantum routing with fast reversals

We present methods for implementing arbitrary permutations of qubits under interaction constraints. Our protocols make use of previous methods for rapidly reversing the order of qubits along a path. Given nearest-neighbor interactions on a path of length n, we show that there exists a constant ϵ≈0.034 such that the quantum routing time is at most (1−ϵ)n, whereas any swap-based protocol needs at least time n−1. This represents the first known quantum advantage over swap-based routing methods and also gives improved quantum routing times for realistic architectures such as grids. Furthermore, we show that our algorithm approaches a quantum routing time of 2n/3 in expectation for uniformly random permutations, whereas swap-based protocols require time n asymptotically. Additionally, we consider sparse permutations that route k≤n qubits and give algorithms with quantum routing time at most n/3+O(k2) on paths and at most 2r/3+O(k2) on general graphs with radius r.

Neural approximation-based adaptive variable impedance control of robots

Variable impedance control improves compliance and robustness in robot-environment interaction through variation of the desired stiffness and the desired damping. This paper proposes neural approximation-based variable impedance controllers for robots in robot-environment interaction. Constraints on variable impedance parameters are given to ensure the exponential stability of the desired first- and second-order variable impedance dynamics. Adaptive neural network controllers are proposed to ensure the achievement of the desired first- and second-order variable impedance dynamics through convergence of variable impedance errors. In the neural networks, deadzone modifications are utilized to enhance robustness by turning off adaptation when auxiliary tracking errors enter the constructed small neighbourhoods of zero. The proposed variable impedance control methods in this paper guarantee the stability and achievement of the desired variable impedance dynamics. Theoretical analysis and simulation results validate the effectiveness of the proposed variable impedance control methods.