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arXiv:1008.1806 · Physical Review Letters

Parallel State Transfer and Efficient Quantum Routing on Quantum Networks

Christopher Chudzicki, Frederick W. Strauch

Published Dec 22, 2010• 40 citations
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Abstract

We study the routing of quantum information in parallel on multidimensional networks of tunable qubits and oscillators. These theoretical models are inspired by recent experiments in superconducting circuits. We show that perfect parallel state transfer is possible for certain networks of harmonic oscillator modes. We extend this to the distribution of entanglement between every pair of nodes in the network, finding that the routing efficiency of hypercube networks is optimal and robust in the presence of dissipation and finite bandwidth.

DOI
10.1103/physrevlett.105.260501

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We study the routing of quantum information in parallel on multidimensional networks of tunable qubits and oscillators. These theoretical models are inspired by recent experiments in superconducting circuits. We show that perfect parallel state transfer is possible for certain networks of harmonic oscillator modes. We extend this to the distribution of entanglement between every pair of nodes in the network, finding that the routing efficiency of hypercube networks is optimal and robust in the presence of dissipation and finite bandwidth.
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Motivated by the need for quantum computers to communicate between multiple, well separated qubits, we introduce the task of quantum routing for distributing quantum states, and generating entanglement, between these sites. We describe regular families of coupled quantum networks which perfectly route qubits between arbitrary pairs of nodes with a high transmission rate. The ability to route multiple states simultaneously and the regularity of the networks vastly improve the utility of this scheme in comparison to the task of state transfer, leading us to propose an implementation in optical lattices.
The goal in quantum state transfer is to avoid the need to physically transport carriers of quantum information. This is achieved by using a suitably engineered Hamiltonian that induces the transfer of the state of one subsystem to another. A less known generalization of state transfer considers multiple systems such that any pair can exchange quantum information and transfers can take place at any time, starting and stopping independently. This is sometimes called routing of quantum states. State transfer in particular has received a great deal of attention, however the vast majority of results in both state transfer and routing concern qubits transferred in a network of restricted structure. Here we consider routing of single-mode Gaussian states and entanglement through complex networks of quantum harmonic oscillators. We compare a protocol where the transfer is completed in a single step but the effective Hamiltonian only approximately transfers the state with one where the transfer can in principle be perfect but the transfer is done in two steps, and also illustrate the state-dependency of the transfer fidelity. We find that even in a random and homogeneous network, the transfer fidelity still depends on the degree of the nodes for any link density, and that in both random and complex networks it is the community structure that controls the appearance of higher frequency normal modes useful for transfer. Finally, we find that networks of sufficient complexity may have superior routing performance over superficially similar random networks. Our results pave the way for further exploration of the role of community structure in state transfer and related tasks.
We propose a class of qubit networks that admit perfect state transfer of any two-dimensional quantum state in a fixed period of time. We further show that such networks can distribute arbitrary entangled states between two distant parties, and can, by using such systems in parallel, transmit the higher-dimensional systems states across the network. Unlike many other schemes for quantum computation and communication, these networks do not require qubit couplings to be switched on and off. When restricted to NNN-qubit spin networks of identical qubit couplings, we show that 2log3N2\phantom{\rule{0.2em}{0ex}}{\mathrm{log}}_{3}N2log3​N is the maximal perfect communication distance for hypercube geometries. Moreover, if one allows fixed but different couplings between the qubits then perfect state transfer can be achieved over arbitrarily long distances in a linear chain. This paper expands and extends the work done by Christandl et al., Phys. Rev. Lett. 92, 187902 (2004).
Distributed quantum networks are not merely information conduits but intricate systems that embody the principles of quantum mechanics. In our study, we examine the underlying mechanisms of quantum connectivity within a distributed framework by exploring phenomena such as superposition and entanglement and their influence on information propagation. We investigate how these fundamental quantum effects interact with routing strategies that, while inspired by classical methods, must contend with quantum decoherence and measurement uncertainties. By simulating distributed networks of 10, 20, 50 and 100 nodes, we assess the performance of routing mechanisms through metrics that reflect both quantum fidelity and operational efficiency. Our findings reveal that the quantum coherence inherent in entangled states can enhance routing fidelity under specific conditions, yet also introduce challenges such as increased computational overhead and sensitivity to network scale. This work bridges the gap between the underlying principles of quantum systems and practical routing implementations, offering new insights into the design of robust distributed quantum networks.