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Register a new userConsensus for Quantum Networks: From Symmetry to Gossip Iterations
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This paper extends the consensus framework, widely studied in the literature on distributed computing and control algorithms, to networks of quantum systems. We define consensus situations on the basis of invariance and symmetry properties, finding four different probabilistic generalizations of classical consensus states. We then extend the gossip consensus algorithm to the quantum setting and prove its convergence properties, showing how it converges to symmetric states while preserving the expectation of permutation-invariant global observables.
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Different techniques to speed up quantum adiabatic processes are currently being explored for applications in atomic, molecular and optical physics, such as transport, cooling and expansions, wavepacket splitting, or internal state control. Here we examine the capabilities of superadiabatic iterations to produce a sequence of shortcuts to adiabaticity. The general formalism is worked out as well as examples for population inversion in a two-level system.
Approximate Counting refers to the problem where we are given query access to a function $f : [N] to {0,1}$, and we wish to estimate $K = #{x : f(x) = 1}$ to within a factor of $1+epsilon$ (with high probability), while minimizing the number of queries. In the quantum setting, Approximate Counting can be done with $Oleft(minleft(sqrt{N/epsilon}, sqrt{N/K}/epsilonright)right)$ queries. It has recently been shown that this can be achieved by a simple algorithm that only uses Grover iterations; however the algorithm performs these iterations adaptively. Motivated by concerns of computational simplicity, we consider algorithms that use Grover iterations with limited adaptivity. We show that algorithms using only nonadaptive Grover iterations can achieve $Oleft(sqrt{N/epsilon}right)$ query complexity, which is tight.
Our objective was to design a quantum repeater capable of achieving one million entangled pairs per second over a distance of 1000km. We failed, but not by much. In this letter we will describe the series of developments that permitted us to approach our goal. We will describe a mechanism that permits the creation of entanglement between two qubits, connected by fibre, with probability arbitrarily close to one and in constant time. This mechanism may be extended to ensure that the entanglement has high fidelity without compromising these properties. Finally, we describe how this may be used to construct a quantum repeater that is capable of creating a linear quantum network connecting two distant qubits with high fidelity. The creation rate is shown to be a function of the maximum distance between two adjacent quantum repeaters.
Enabled by rapidly developing quantum technologies, it is possible to network quantum systems at a much larger scale in the near future. To deal with non-Markovian dynamics that is prevalent in solid-state devices, we propose a general transfer function based framework for modeling linear quantum networks, in which signal flow graphs are applied to characterize the network topology by flow of quantum signals. We define a noncommutative ring $mathbb{D}$ and use its elements to construct Hamiltonians, transformations and transfer functions for both active and passive systems. The signal flow graph obtained for direct and indirect coherent quantum feedback systems clearly show the feedback loop via bidirectional signal flows. Importantly, the transfer function from input to output field is derived for non-Markovian quantum systems with colored inputs, from which the Markovian input-output relation can be easily obtained as a limiting case. Moreover, the transfer function possesses a symmetry structure that is analogous to the well-know scattering transformation in sd picture. Finally, we show that these transfer functions can be integrated to build complex feedback networks via interconnections, serial products and feedback, which may include either direct or indirect coherent feedback loops, and transfer functions between quantum signal nodes can be calculated by the Riegles matrix gain rule. The theory paves the way for modeling, analyzing and synthesizing non-Markovian linear quantum feedback networks in the frequency-domain.
The following notes are based on lectures delivered at the research school Modeling and Control of Open Quantum Systems (Mod{e}lisation et contr^{o}le des syst`{e}mes quantiques ouverts) at CIRM, Marseille, 16-20 April, 2018, as part of the Trimester textit{Measurement and Control of Quantum Systems: Theory and Experiments} organized at Institut Henri Poincar{e}, Paris, France. The aim is to introduce quantum filtering to an audience with a background in either quantum theory or classical filtering.
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