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Quantum node swapping

John C Vining, Howard A. Blair

Published Aug 20, 2020• 0 citations
Publisher

Abstract

The focus of this work is the evolution of a quantum network where each node is initialized with a unique data entry encoding classical information such as a serial number. Each node is then probabilistically swapped with one of its immediate neighbors in a specific, but undisclosed order, resulting in a redistribution of entries across the network. In foreseeable practice, Quantum systems prevent the reliable swap of quantum states due to decoherence and imperfect circuit fidelity, but in this network model we require that if each node is measured, all data entries remain unique. Originally motivated by the desire to develop a method which results in all entries only being able to move to their immediate neighbors, we present aspects of the underlying combinatorics, and solutions to either mitigate or potentially minimize the effects of larger travel distances.

DOI
10.1117/12.2568201

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The focus of this work is the evolution of a quantum network where each node is initialized with a unique data entry encoding classical information such as a serial number. Each node is then probabilistically swapped with one of its immediate neighbors in a specific, but undisclosed order, resulting in a redistribution of entries across the network. In foreseeable practice, Quantum systems prevent the reliable swap of quantum states due to decoherence and imperfect circuit fidelity, but in this network model we require that if each node is measured, all data entries remain unique. Originally motivated by the desire to develop a method which results in all entries only being able to move to their immediate neighbors, we present aspects of the underlying combinatorics, and solutions to either mitigate or potentially minimize the effects of larger travel distances.
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We consider a simple model of quantum network, employing qubits (spin-1/2 particles) attached to the nodes of an underlying graph and we study the simplest task, namely information storage (on a single and two qubits), when the graph randomly changes in time. Actually we randomly add edges to an initially disconnected graph according to the Gilbert model characterized by a weighting parameter ex [...] and in an identically and independent way at each time step. We find that by increasing ex the dynamics of relevant quantities like fidelity, entropy or concurrence, gradually transforms from damped to damped oscillatory and finally to purely oscillatory. That leads to the paper [see, Information dissipation in random quantum networks, by U. Farooq and S. Mancini, OSID 21(3), 1450004, 2014]. We also study a system composed by pairs of qubits attached to each node of a linear chain, a model that stems from quantum dot arrays. Here we use the approach of evolution with a stochastic Hamiltonian to describe the noisy effects. We then evaluate the effect of two most common disorders, namely exchange coupling and hyperfine interaction fluctuations, in adiabatic preparation of ground state in such model. We show that the adiabatic ground state preparation is highly robust against these disorders making the chain a good analog simulator. Moreover, we also study the adiabatic information transfer, using singlet-triplet states, across the chain. In contrast to ground state preparation the transfer mechanism is highly affected by disorders. This suggested that for communication tasks across such chains adiabatic evolution is not as effective and quantum quenches would be preferable. That leads to the paper [see, Adiabatic many-body state preparation and information transfer in quantum dot arrays, by U. Farooq, A. Bayat, S. Mancini and S. Bose Phys. Rev. B 91, 134303, 2015]. The present work is organized as follows. In chapter 1, we shall give a survey of the various types of approach which can be employed to analyse the dynamics of open quantum systems that leads to decoherence effects. In chapter 2, we shall give a general description about quantum network and its possible applications. In chapter 3, we shall discuss the problem of quantum state transfer in qubit network and shall give a brief overview of some scheme that enable nearly prefect state transfer. In chapter 4, we shall discuss singlet-triplet networks, that is networks having on each site a pair of (generally entangled) qubit. Then within this framework we propose a model stemming from quantum dot array. There we shall address the problem of ground state preparation and state transfer. Finally we shall describe the inherent entanglement of the ground state of strongly correlated systems can be exploited for both classical and quantum communications. In chapter 5, we shall propose a decoherence model for qubit networks based on edges representing XY interactions randomly added to a disconnected graph accordingly to a suitable probability distribution. In this way we shall describe dissipation of information initially localize in single or two qubits all over the network. In chapter 6 we shall model the noisy effects in the quantum dot array introduced in chapter 4 and investigate their consequences on the preparation of ground state and quantum state transfer mechanism. Finally we shall draw conclusions.
Quantum information transfer presents significant challenges due to the fragility of quantum states and the potential for decoherence. Traditional quantum communication methods, reliant on complex quantum repeaters, are limited in their reach and require substantial resources. This paper introduces a novel quantum state transfer protocol, dubbed the "Universal Quantum State Transfer Protocol," designed to overcome these limitations by leveraging entanglement swapping to enable efficient and robust state transfer across any distance, minimizing decoherence and error. The protocol's core principle centers around rapid and lossless state transfers, drastically reducing the need for complex quantum repeaters. This work explores the implementation of a unique entanglement swapping mechanism to achieve this goal, demonstrating its potential to revolutionize quantum communication. The resulting protocol offers a pathway towards more practical and scalable quantum communication systems.
In the practical context of quantum networks, the most reliable method of transmitting quantum information is via teleportation because quantum states are highly sensitive. However, teleportation consumes a shared maximally entangled state. Two parties Alice and Bob located at separate nodes that wish to reestablish their shared entanglement will not send entangled qubits directly to achieve this goal, but rather employ a more efficient mechanism that ensures minimal time resources. In this paper, we present a quantum routing scheme that exploits entanglement swapping to reestablish consumed entanglement. It improves and generalizes previous work on the subject and reduces the entanglement distribution time by a factor of 4 k in an arbitrary scale quantum network, where N = 4 k - 1 is a required number of quantum nodes located between source and destination. In addition, k is the greatest positive integer considered by Alice or Bob, such that afterwards they choose N quantum switches.
Quantum networks, leveraging the unique properties of quantum mechanics, hold immense promise for secure communication and distributed quantum computation. Traditional quantum networks suffer from inherent limitations in scalability and data distribution. This paper presents a novel self-organizing quantum network architecture, designed to efficiently distribute quantum data across a network using dynamic state adjustment mechanisms. We propose a mechanism where nodes automatically configure their quantum states based on incoming data, fostering a self-configuring network topology. This contrasts sharply with static network designs, offering improved performance and adaptability. The core mechanism emphasizes the dynamic adjustment of quantum states, addressing a critical bottleneck in current quantum network research. This research explores the potential of this approach to enable efficient data routing and exploration of novel network topologies. The resulting network architecture demonstrates enhanced data distribution capabilities and opens avenues for practical applications in quantum information processing.
Quantum network communication is challenging, as the no-cloning theorem in the quantum regime makes many classical techniques inapplicable; in particular, the direct transmission of qubit states over long distances is infeasible due to unrecoverable errors. For the long-distance communication of unknown quantum states, the only viable communication approach (assuming local operations and classical communications) is the teleportation of quantum states, which requires a prior distribution of the entangled pairs (EPs) of qubits. The establishment of EPs across remote nodes can incur significant latency due to the low probability of success of the underlying physical processes. The focus of our work is to develop efficient techniques that minimize EP generation latency. Prior works have focused on selecting entanglementpaths; in contrast, we selectentanglement swapping trees—a more accurate representation of the entanglement generation structure. We develop a dynamic programming algorithm to select an optimal swapping tree for a single pair of nodes, under the given capacity and fidelity constraints. For the general setting, we develop an efficient iterative algorithm to compute a set of swapping trees. We present simulation results, which show that our solutions outperform the prior approaches by an order of magnitude and are viable for long-distance entanglement generation.
Environmental noise is a prevalent issue that hinders the widespread adoption of quantum technologies. Standard practice to mitigate noise involves minimizing the coupling between a quantum system and its environment, which is usually modeled in the Markovian regime. By moving slightly beyond this regime into the weak non-Markovian regime, we can achieve an effective coupling that is multiple orders of magnitude smaller by exploiting the environmental memory effect. To demonstrate this effect, we simulate state swapping in a Markovian and non-Markovian environment between two modes: a cavity mode initialized as a vacuum state and an atomic motional mode initialized as a displaced squeezed coherent state. To measure the quality of state swapping between environments, we calculate and compare their corresponding multi-mode fidelity for Gaussian states. We find that a non-Markovian environment has superior state swapping fidelity across the following parameters: mean phonon number, cavity decay rate, and vibrational frequency of the atomic motional mode. The fidelity is near-unit for a non-Markovian environment within the parameter ranges mentioned in the results. These results could enable enhanced quantum information exchange between a network and chain of cavity-atom nodes and contribute toward a more prevalent adoption of quantum technologies.