Abstract
We consider a basic quantum hybrid network model consisting of a number of nodes each holding a qubit, for which the aim is to drive the network to a consensus in the sense that all qubits reach a common state. Projective measurements are applied serving as control means, and the measurement results are exchanged among the nodes via classical communication channels. In this way the quantum-opeartion/classical-communication nature of hybrid quantum networks is captured, although coherent states and joint operations are not taken into consideration in order to facilitate a clear and explicit analysis. We show how to carry out centralized optimal path planning for this network with all-to-all classical communications, in which case the problem becomes a stochastic optimal control problem with a continuous action space. To overcome the computation and communication obstacles facing the centralized solutions, we also develop a distributed Pairwise Qubit Projection (PQP) algorithm, where pairs of nodes meet at a given time and respectively perform measurements at their geometric average. We show that the qubit states are driven to a consensus almost surely along the proposed PQP algorithm, and that the expected qubit density operators converge to the average of the network’s initial values.
Highlights
Consensus seeking over complex networks has played a foundational role in the development of distributed computation and networked control systems[1, 2]
Quantum operations can be performed locally and the outcomes of the measurements are exchanged via classical communications, leading to the so-called local-operation classical-communication (LOCC) networks which have served as protocols for quantum cryptography or potential tools for engineering complex quantum states[15]
This theoretical simplification has neglected the effects of coherent states and joint operations in realistic quantum information processing networks, but the quantum-operation/classical-communication nature of LOCC networks has been preserved and highlighted
Summary
Consensus seeking over complex networks has played a foundational role in the development of distributed computation and networked control systems[1, 2]. We consider a consensus seeking problem over a quantum hybrid network consisting of a number of nodes each holding a qubit, where projective measurements are applied and the measurement results are exchanged. We develop a distributed Pairwise Qubit Projection (PQP) algorithm, where pairs of nodes meet at a given time and respectively perform measurements at their geometric average.
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