Session N53: Quantum Networks: Theory, Protocols and Applications

Data Center Quantum Networks: From Experiment to System

Scaling up quantum computers will require interconnecting small quantum computer nodes into larger multicomputer systems that can collaborate to solve large problems.  This scaling requires fast, robust, high-fidelity creation of inter-node entanglement.  Brilliant experiments have shown that the basic technology works; the next stage in evolution is to move from experiment to system.

Progressing to system requires solving many classic (but not always classical) computer engineering problems: efficient design of photonic switching networks,  fair and reliable allocation of resources, distributed control, tolerance of both errors and hardware failures, interoperability of heterogeneous technologies built by different organizations, and compilation of application programs for execution on multicomputers.

I will present our testbed network, which begins with spontaneous parametric down conversion (SPDC) entanglement sources and switched photon measurement nodes and will eventually include nodes with memory and ultimately connect full quantum computers.  Our approach includes open access to specifications and source code for the interconnect protocols, with the long-term goal of influencing standards for quantum networking equipment.   

Entanglement Routing Techniques for Quantum Communication Networks

Entanglement routing on quantum communication networks consists of choosing the optimal sequence of local entanglements to combine through swapping operations to establish end-to-end entanglement between a source and a destination node on a quantum network. Similar to classical network routing, a quantum routing protocol uses network information to choose the best paths to satisfy a set of end-to-end entanglement requests. However, in addition to network state information, a quantum routing protocol must also take into account the requested entanglement fidelity, the probabilistic nature of swapping operations, and the short coherence times of bi-partite entangled states when conducting path selection and path recovery. In this work, we formally define the entanglement routing problem, and analyze and categorize the main approaches to address it, drawing comparisons to and inspiration from classical network routing strategies where applicable. We draw comparisons between well-studied routing strategies, including reactive, proactive, opportunistic, and virtual routing for quantum networks. Assessment of relevant algorithms, protocol designs, and published studies provide network engineers with guidelines for efficient designs of intermediate-scale quantum networks.   

Entangled State Quantum Pulse Position Modulation for Communication Security

We present the Quantum Pulse Position Modulation (QPPM) protocol, which is an entanglement-based communications format approach designed to enhance the security of pulse position modulation (PPM) in optical communications. QPPM interleaves states from two-mode entangled light with thermal noise states resulting in a data transmission method that is stealthy and secure. We have calculated various quantum-information theoretic bounds, namely the Helstrom bound and the quantum Chernoff bound, for correctly decoding the transmitted symbols at the receiver. These bounds were computed numerically using a two-mode squeezed vacuum state to carry data, interleaved with a thermal state. A passive eavesdropper's inability to discriminate one half of a two-mode squeezed vacuum state from a thermal state renders them ineffective at identifying the presence of an active communication channel.   

Nonclassicality in Quantum Communication Networks

Quantum communication networks are rapidly being developed and applied, however, there is still much to understand about the operational advantages that quantum networks actually provide. In this work, we introduce nonclassicality as a quantifier of quantum advantage, which generalizes standard Bell nonlocality to signaling systems. To this end, we apply a black-box framework for characterizing communication networks in terms of their communication resources and causal structure. We devise operational tests that quantify a network's performance against a given task. We derive a connection between a class of operational tests and the network's ability to simulate a given behavior. Finally, we apply our nonclassicality framework to demonstrate explicit quantum advantages across a wide range of quantum network topologies and resource configurations. To obtain our main results, we develop a resource-theoretic quantum circuit model for simulating general communication networks assisted by quantum resources. Using quantum hardware-compatible variational optimization techniques, we optimize these simulations over the set of free operations. We first demonstrate in bipartite signaling systems that quantum communication, entanglement-assisted classical communication, and entanglement-assisted quantum communication resources can all demonstrate explicit advantages over classical communication resources. We then extend our techniques to showcase quantum advantages in multiaccess networks, broadcast networks, and multipoint communication networks. Overall, the described operational tests can be used to help certify and verify resources in quantum networks. We also identify distributed computing advantages where quantum resources are able to perform distributed computational tasks with greater success than classical resources. Finally, our work demonstrates a class of variational quantum networking protocols that can automatically establish protocols such as dense-coding or key distribution on uncharacterized network devices where the quality of the protocol is characterized operationally by the simulation error.   

Requirements for Deterministic Quantum Teleportation over Metropolitan and Long-Distance Backbone

We investigate high-level parameter trade-offs in the requirements for performing quantum teleportation deterministically with an average fidelity exceeding the classical bound of 2/3 on both metropolitan-scale and long-distance quantum networks. In particular, we examine the interplay between the coherence time of quantum memory, the rate and fidelity at which entanglement can be generated. We do so for two different scenarios: one where the to-be-teleported state needs to be stored in memory until the required entanglement is established, and one where this is not the case. Using both simplified analytical models and an extensive simulation framework implemented using NetSquid, a discrete-event simulator for quantum networks, and using baseline parameters based on the state of the art of networked ion traps and atomic-ensemble memories, we identify the requirements imposed on the metropolitan link by the long-distance setup to enable quantum teleportation. Our work sheds light on the trade-offs between different hardware improvements that could be made in order to realize quantum teleportation in deployed quantum networks.   

Time-Constrained Local Quantum State Discrimination

We investigate the task of quantum state discrimination using local operations and simultaneous classical or quantum communication (LOSCC and LOSQC) between the parties, which may be seen as types of `cross communication.' This problem is motivated by time-sensitive cryptographic protocols like quantum position verification (QPV), but also by a gap in our basic understanding of the interplay between quantum mechanics, locality, and communication. We present substantial progress on closing this gap. We prove necessary and sufficient conditions for a set of states to be perfectly discriminated using LOSCC or LOSQC. We characterize the product ensembles of a qubit and qudit that are LOSCC discriminable. We identify the minimal product state ensemble that is LOSQC but not LOSCC discriminable and use it to prove an arbitrary gap in discrimination power between the two models. For other ensembles, even quantum communication is not strong enough, and we present a trace distance uncertainty relation for product ensembles that provides general non-trivial error bounds for state discrimination with LOSQC.   

Classical and Quantum Distributed Algorithms for the Survivable Network Design Problem

We develop distributed classical and quantum approaches for the survivable network design problem (SNDP), also sometimes called the generalized Steiner problem. This generalizes many difficult graph problems of interest, such as the traveling salesman problem, the Steiner tree problem, and the k-connected network problem, among others. In the distributed settings that we consider, no classical or quantum algorithms had been formulated to the best of our knowledge. We describe algorithms that are heuristics for the general problem but give concrete approximation bounds under certain parameterizations of the SNDP, which in particular hold for the three aforementioned problems that SNDP generalizes. We use a classical algorithmic framework first studied by (Goemans & Bertsimas, 1993, Mathematical Programming, 60, 145–166) and provide a distributed implementation thereof. Notably, we obtain asymptotic quantum speedups by leveraging quantum shortest path computations in this framework, generalizing recent work of (Kerger, Bernal Neira, Izquierdo, & Rieffel, 2023,

Algorithms, 16, 332), which raises the question of whether there is a separation between the classical and quantum models for the problems considered.   

On Fidelity-Preserving Entanglement Purification Protocols

Entanglement purification protocols (EPPs) are crucial to suppress inevitable noise in quantum entanglement, and therefore it is important to understand their fundamental limits. Here, we introduce the fidelity-preserving (FP) property for EPPs where the output fidelity is at least as high as the highest input fidelity. This property is desirable for near-term quantum networks and distributed quantum computing architectures with probabilistic entanglement generation and noisy quantum memories. We examine the entire family of n-to-1 bilocal Clifford EPPs (BiCEPs) for Bell diagonal states (BDS), prove the necessary and sufficient condition of FP for biCEPs, and conclude that an FP biCEP for arbitrary BDS does not exist. We also prove a second no-go theorem – even with fidelity information (FI), biCEP can only achieve trivial FP for arbitrary BDS. As a direct corollary, we show that biCEP still cannot be FP without FI, and can only be trivially FP with FI, even with an arbitrary number of pure Bell pairs as catalyst. Finally, we demonstrate that the recurrence protocol satisfies a relaxed version of FP when the input fidelity has an upper bound below unity for Werner states, while the allowed fidelity region inevitably shrinks for higher upper bound. Our results provide fundamental insights on EPPs and quantum information processing (QIP) beyond the independent and identically distributed (i.i.d.) setting, and also reveal the practical limitations of integrating EPPs into real-world QIP architectures.   

Optimizing quantum-repeater placement in a 2D plane

When designing a quantum-repeater network that services a set of end nodes, it needs to be decided how many repeaters are installed and at which locations they are placed. While often the locations where quantum hardware could be installed may be limited by existing infrastructure, we here consider an unconstrained scenario where repeaters can be placed anywhere in a two-dimensional plane, as may be appropriate for, e.g., free-space quantum communication and quantum-sensor networks. Additionally, understanding network design in the unconstrained case can provide a point of reference for network design in the constrained case. We study the optimal placement of repeaters and the dependence of network performance on the number of repeaters in the network. In particular, we investigate how the optimal repeater locations depend on what type of network metric is optimized, the protocols executed by the repeaters, and how good the quantum hardware is. We use the obtained insights to formulate heuristics for the design of quantum networks.   

Device-Independent Randomness Amplification

Successful realization of loophole-free Bell tests has settled an 80-year-long debate and manifested that non-locality is an innate property of quantum physics and could be a useful resource for quantum information processing. Applications envisaged more than three decades ago, non-locality forms a basis for device-independent algorithms, especially suited for quantum key distribution, generating certified randomness or self-verification of untrusted devices. With the body of proof-of-principle experiments and applications growing, one crucial flaw of non-locality-based algorithms remains uncontested to date: the requirement for perfect input randomness to either distribute a secret key or generate new certified random bits. To tackle this problem, a concept of randomness amplification has been put forward, allowing generating stronger randomness out of weak input randomness resource -- a task impossible in classical physics. We implement it under a device-independent framework -- again, not attainable without a quantum system possessing the resource of non-locality. In this work, we combine two recent developments -- a theoretical protocol implementing the concept of randomness amplification with realistic devices and only a two-node system; and the experimental progress enabling executing a loophole-free Bell test with superconducting circuits providing a unique combination of degree of non-locality and bit-rate.   

On noise in swap ASAP repeater chains: exact analytics, distributions and tight approximations

Losses are one of the main bottlenecks for the distribution of entanglement in quantum networks, which can be overcome by the implementation of quantum repeaters. The most basic form of a quantum repeater chain is the swap ASAP repeater chain. In such a repeater chain, elementary links are generated and swapped as soon as two adjacent links have been generated. As each entangled state is waiting to be swapped, decoherence is experienced, lowering the fidelity of the state. Qualitatively understanding the average and the total amount of decoherence is still an open problem however. Here, we analytically investigate the homogeneous case, where we find exact analytic formulae for all moments of the fidelity up to 20 links. We generalize these approaches as well to a global cut-off, allowing for fast optimization of the cut-off. We furthermore find simple approximations that are exponentially tight, and, for up to 10 links, the distribution of the delivered fidelity. We use this to analytically calculate the secret-key rate both with and without binning methods, eliminating the need for simulations. Our methods are based on interpreting repeater chains in terms of enumerating lattice paths, and exploiting tools from analytical combinatorics.   

Towards an extendible hybrid quantum computer in the cloud

In the first release of Quantum Inspire (www.quantum-inspire.com), the main focus was on executing quantum circuits. We will present the architecture and functionality of a new version (2.0) that unlocks hybrid computing using co-located classical servers. A dispatcher orchestrates the execution of both classical and quantum tasks to be run on the system. Via a dedicated connection, these tasks communicate with each other.

 

This setup forms the core of Quantum Inspire. However, the system is extendible both with regard to input and output. As part of the National Program Quantum Technology, new quantum computers are being built and existing ones are upgraded to connect to the platform. Users can write an algorithm once to run it many times on the different computers, with little to no tweaks necessary.

 

The platform is furthermore reachable from different end-user interfaces. Quantum Inspire offers native support via a web application and SDK. Additionally, integration with High-Performance Computing (HPC) centers is also on the roadmap. For this, initial tests are run in collaboration with the Dutch National HPC Center, hosted by Surf.   

Role of syndrome information in scheduling teleportation

Quantum teleportation enables quantum information transmission but requires distribution of entangled resource states. Unfortunately, decoherence, caused by environmental interference during quantum state storage, can degrade quantum states, leading to entanglement loss in the resource state and reduction of the fidelity of the teleported information. In this work, we investigate the use of error correction and error syndrome information in scheduling teleportation at a quantum network node in the presence of multiple teleportation requests and finite rate of remote entanglement distribution. Specifically, we focus on the scenario where stored qubits undergo decoherence over time due to imperfect memories. To protect the qubits from resulting errors, we employ quantum encodings, and the stored qubits undergo repeated error correction, generating error syndromes in each round. These error syndromes can provide additional benefits as they can be used to calculate qubit-specific error likelihoods, which can then be utilized in making better scheduling decisions. By integrating error correction techniques into the scheduling process, our goal is to minimize errors and decoherence effects, thereby enhancing the fidelity and efficiency of teleportation in a quantum network setting.