Bounds for multi-end communication over quantum networks

Pirandola, Stefano

doi:10.1088/2058-9565/ab3f66

Cited by 48 publications

(47 citation statements)

References 62 publications

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“…and we assume that the map Γ in (16) has no inverse. The connectivity of the objective function and the pairwise connectivity of the quantum computer's hardware are not related, since these connections are represented in different layers [10].…”

Section: Connectivity Of the Objective Function In The Target Statementioning

confidence: 99%

Quantum State Optimization and Computational Pathway Evaluation for Gate-Model Quantum Computers

Gyöngyösi

2020

Sci Rep

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A computational problem fed into a gate-model quantum computer identifies an objective function with a particular computational pathway (objective function connectivity). The solution of the computational problem involves identifying a target objective function value that is the subject to be reached. A bottleneck in a gate-model quantum computer is the requirement of several rounds of quantum state preparations, high-cost run sequences, and multiple rounds of measurements to determine a target (optimal) state of the quantum computer that achieves the target objective function value. Here, we define a method for optimal quantum state determination and computational path evaluation for gate-model quantum computers. We prove a state determination method that finds a target system state for a quantum computer at a given target objective function value. The computational pathway evaluation procedure sets the connectivity of the objective function in the target system state on a fixed hardware architecture of the quantum computer. The proposed solution evolves the target system state without requiring the preparation of intermediate states between the initial and target states of the quantum computer. Our method avoids high-cost system state preparations and expensive running procedures and measurement apparatuses in gate-model quantum computers. The results are convenient for gate-model quantum computations and the near-term quantum devices of the quantum Internet.A computational problem fed into a quantum computer defines an objective function with a particular connectivity (computational pathway) [10]. The solution of this computational problem in the quantum computer involves identifying an objective function with a target value that is subject to be reached. To achieve the target objective function value, the quantum computer must reach a particular system state such that the gate parameters of the unitary operations satisfy the target value. These optimal gate parameter values of the unitary operations of the quantum computer identify the optimal state of the quantum computer. This optimal system state is referred to as the target system state of the quantum computer. Finding the target system state involves multiple measurement rounds and iterations, with high-cost system state preparations 1 , quantum computations, and measurement procedures. Therefore, optimizing the determination procedure of the target system state is essential for gate-model quantum computers.Here, we define a method for state determination and computational path evaluation for gatemodel quantum computers. The aim of state determination is to find a target system state for a quantum computer such that the pre-determined target objective function value is reached. The aim of the computational path evaluation is to find the connectivity of the objective function in the target system state on the fixed hardware architecture [10] of the quantum computer. To resolve these issues, we define a framework that utilizes the theory of kernel methods ...

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Section: Connectivity Of the Objective Function In The Target Statementioning

confidence: 99%

Quantum State Optimization and Computational Pathway Evaluation for Gate-Model Quantum Computers

Gyöngyösi

2020

Sci Rep

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“…Using (20), the probabilistic reduction of entanglement accessibility ratio (PR-EAR) Ω c (Φ c (f )) at a given ratio x, condition c, and probability q is defined as…”

Section: Probabilistic Reduction Of Entanglement Accessibility Ratiomentioning

confidence: 99%

Entanglement accessibility measures for the quantum Internet

Gyöngyösi

Imre

2020

Quantum Inf Process

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We define metrics and measures to characterize the ratio of accessible quantum entanglement for complex network failures in the quantum Internet. A complex network failure models a situation in the quantum Internet in which a set of quantum nodes and a set of entangled connections become unavailable. A complex failure can cover a quantum memory failure, a physical link failure, an eavesdropping activity, or any other random physical failure scenario. Here, we define the terms entanglement accessibility ratio, cumulative probability of entanglement accessibility ratio, probabilistic reduction of entanglement accessibility ratio, domain entanglement accessibility ratio, and occurrence coefficient. The proposed methods can be applied to an arbitrary topology quantum network to extract relevant statistics and to handle the quantum network failure scenarios in the quantum Internet. IntroductionAs quantum computers evolves significantly [1-10], there arises a fundamental need for a communication network that provides unconditionally secure communication and all the network functions of the traditional internet. This network structure is the quantum Internet [11][12][13][14][15]22]. The availability of quantum entanglement is a crucial aspect in any global-scale quantum Internet. The quantum Internet refers to a set of connected heterogeneous quantum communication networks realized by quantum nodes and channels (such as optical fibers or wireless optical quantum channels in the physical layer) [16,[59][60][61][62][63][64]. The quantum Internet also integrates a set of classical auxiliary communication channels to transmit auxiliary classical side-information between the quantum nodes. The quantum Internet is modeled as a global-scale quantum communication network composed of quantum subnetworks and networking components. The core network of the quantum Internet is assumed to be an entangled network structure [15,20,21,24,25,27,28,[39][40][41][42][43][44][45][46][47], which is a communication network in which the quantum nodes are connected by entangled connections. An entangled connection refers to a shared entangled system (i.e., a Bell state for qubit systems to connect two quantum nodes) between the quantum nodes. In an unentangled network structure, the quantum nodes are not necessarily connected by entanglement [16,78], and the communication between the nodes is realized in a point-to-point setting. This setting does not allow quantum communication over arbitrary distances, and an unentangled network structure can mostly be used for establishing a point-to-point quantum key distribution (QKD) [70,103] between the quantum nodes. These short distances can be extended to longer distances by the utilization of free-space quantum channels [15,70]. However, this solution is auxiliary, since it can be used only at some specific points of the unentangled network structure. Therefore, it does not represent an adequate and fundamental answer to the problem of long-distance quantum communication. Consequently, in an unentangl...

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“…In order to generalize these results to teleportation‐covariant networks, we first introduce some notions from graph theory . Let us describe an arbitrary quantum network

scriptN

as an undirected graph with nodes or points P and edges E .…”

Section: Preliminary Notionsmentioning

confidence: 99%

“…Finally, ref. [36] further extended the study to quantum communication networks with multiple senders and receivers. Using this theory, it is possible to write an upper bound for the total number of qubits that an ensemble of senders can transmit to an ensemble of receivers in terms of the relative entropy of entanglement (REE), defined as…”

Section: Preliminary Notionsmentioning

confidence: 99%

“…[32]) In order to generalize these results to teleportation-covariant networks, we first introduce some notions from graph theory. [34][35][36] Let us describe an arbitrary quantum network  as an undirected graph with nodes or points P and edges E. Two points, x and y, are connected by an edge (x, y) ∈ E if and only if there is a corresponding quantum channel  xy between the two. Each point p has a local register of quantum systems over which LOs are performed and optimized on the basis of two-way CCs with the other nodes.…”

Section: Preliminary Notionsmentioning

confidence: 99%

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Exploring the Limitations of Quantum Networking through Butterfly‐Based Networks

2019

Self Cite

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The classical and quantum networking regimes of the butterfly network and a group of larger networks constructed with butterfly network blocks are investigated. By considering simultaneous multicasts from a set of senders to a set of receivers, the corresponding rates for transmitting classical and quantum information through the networks are analyzed. More precisely, achievable rates (i.e., lower bounds) for classical communication are compared with upper bounds for quantum communication, quantifying the performance gap between the rates for networks connected by identity, depolarizing, and erasure channels. For each network considered, a range is observed over which the classical rate non‐trivially exceeds the quantum capacity. It is found that, by adding butterfly blocks in parallel, the difference between transmitted bits and qubits can be increased up to one extra bit per receiver in the case of perfect transmission (identity channels). The aim is to provide a quantitative analysis of those network configurations which are particularly disadvantageous for quantum networking, when compared to classical communication. By clarifying the performance of these “negative cases,” some guidance on how quantum networks should be built is also provided.

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Bounds for multi-end communication over quantum networks

Cited by 48 publications

References 62 publications

Quantum State Optimization and Computational Pathway Evaluation for Gate-Model Quantum Computers

Quantum State Optimization and Computational Pathway Evaluation for Gate-Model Quantum Computers

Entanglement accessibility measures for the quantum Internet

Exploring the Limitations of Quantum Networking through Butterfly‐Based Networks

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