arXiv subjects

Axel Dahlberg

Publications and source records attributed to Axel Dahlberg.

17 recordsLinked to original sources

arXiv2024

Design and demonstration of an operating system for executing applications on quantum network nodes

The goal of future quantum networks is to enable new internet applications that are impossible to achieve using solely classical communication. Up to now, demonstrations of quantum network applications and functionalities on quantum processors have been performed in ad-hoc software that was specific to the experimental setup, programmed to perform one single task (the application experiment) directly into low-level control devices using expertise in experimental physics. Here, we report on the design and implementation of the first architecture capable of executing quantum network applications on quantum processors in platform-independent high-level software. We demonstrate the architecture's capability to execute applications in high-level software, by implementing it as a quantum network operating system -- QNodeOS -- and executing test programs including a delegated computation from a client to a server on two quantum network nodes based on nitrogen-vacancy (NV) centers in diamond. We show how our architecture allows us to maximize the use of quantum network hardware, by multitasking different applications on a quantum network for the first time. Our architecture can be used to execute programs on any quantum processor platform corresponding to our system model, which we illustrate by demonstrating an additional driver for QNodeOS for a trapped-ion quantum network node based on a single $^{40}\text{Ca}^+$ atom. Our architecture lays the groundwork for computer science research in the domain of quantum network programming, and paves the way for the development of software that can bring quantum network technology to society.

quant-ph↗

arXiv2023

Requirements for a processing-node quantum repeater on a real-world fiber grid

We numerically study the distribution of entanglement between the Dutch cities of Delft and Eindhoven realized with a processing-node quantum repeater and determine minimal hardware requirements for verifiable blind quantum computation using color centers and trapped ions. Our results are obtained considering restrictions imposed by a real-world fiber grid and using detailed hardware-specific models. By comparing our results to those we would obtain in idealized settings we show that simplifications lead to a distorted picture of hardware demands, particularly on memory coherence and photon collection. We develop general machinery suitable for studying arbitrary processing-node repeater chains using NetSquid, a discrete-event simulator for quantum networks. This enables us to include time-dependent noise models and simulate repeater protocols with cut-offs, including the required classical control communication. We find minimal hardware requirements by solving an optimization problem using genetic algorithms on a high-performance-computing cluster. Our work provides guidance for further experimental progress, and showcases limitations of studying quantum-repeater requirements in idealized situations.

quant-ph↗

arXiv2022

A Quantum Router Architecture for High-Fidelity Entanglement Flows in Quantum Networks

The past decade has seen tremendous progress in experimentally realizing the building blocks of quantum repeaters. Repeater architectures with multiplexed quantum memories have been proposed to increase entanglement distribution rates, but an open challenge is to maintain entanglement fidelity over long-distance links. Here, we address this with a quantum router architecture comprising many quantum memories connected in a photonic switchboard to broker entanglement flows across quantum networks. We compute the rate and fidelity of entanglement distribution under this architecture using an event-based simulator, finding that the router improves the entanglement fidelity as multiplexing depth increases without a significant drop in the entanglement distribution rate. Specifically, the router permits channel-loss-invariant fidelity, i.e. the same fidelity achievable with lossless links. Furthermore, this scheme automatically prioritizes entanglement flows across the full network without requiring global network information. The proposed architecture uses present-day photonic technology, opening a path to near-term deployable multi-node quantum networks.

quant-ph↗

arXiv2022

Limitations of nearest-neighbour quantum networks

Quantum communication research has in recent years shifted to include multi-partite networks for which questions of quantum network routing naturally emerge. To understand the potential for multi-partite routing, we focus on the most promising architectures for future quantum networks - those connecting nodes close to each other. Nearest-neighbour networks such as rings, lines, and grids, have been studied under different communication scenarios to facilitate the sharing of quantum resources, especially in the presence of bottlenecks. We here analyze the potential of nearest-neighbour quantum networks and identify some serious limitations, by demonstrating that rings and lines cannot overcome common bottleneck communication problems.

quant-ph↗

arXiv2021

NetQASM -- A low-level instruction set architecture for hybrid quantum-classical programs in a quantum internet

We introduce NetQASM, a low-level instruction set architecture for quantum internet applications. NetQASM is a universal, platform-independent and extendable instruction set with support for local quantum gates, powerful classical logic and quantum networking operations for remote entanglement generation. Furthermore, NetQASM allows for close integration of classical logic and communication at the application layer with quantum operations at the physical layer. This enables quantum network applications to be programmed in high-level platform-independent software, which is not possible using any other QASM variants. We implement NetQASM in a series of tools to write, parse, encode and run NetQASM code, which are available online. Our tools include a higher-level SDK in Python, which allows an easy way of programming applications for a quantum internet. Our SDK can be used at home by making use of our existing quantum simulators, NetSquid and SimulaQron, and will also provide a public interface to hardware released on a future iteration of Quantum Network Explorer.

quant-ph↗

arXiv2021

NetSquid, a NETwork Simulator for QUantum Information using Discrete events

In order to bring quantum networks into the real world, we would like to determine the requirements of quantum network protocols including the underlying quantum hardware. Because detailed architecture proposals are generally too complex for mathematical analysis, it is natural to employ numerical simulation. Here we introduce NetSquid, the NETwork Simulator for QUantum Information using Discrete events, a discrete-event based platform for simulating all aspects of quantum networks and modular quantum computing systems, ranging from the physical layer and its control plane up to the application level. We study several use cases to showcase NetSquid's power, including detailed physical layer simulations of repeater chains based on nitrogen vacancy centres in diamond as well as atomic ensembles. We also study the control plane of a quantum switch beyond its analytically known regime, and showcase NetSquid's ability to investigate large networks by simulating entanglement distribution over a chain of up to one thousand nodes.

quant-ph↗

arXiv2020

Designing a Quantum Network Protocol

The second quantum revolution brings with it the promise of a quantum internet. As the first quantum network hardware prototypes near completion new challenges emerge. A functional network is more than just the physical hardware, yet work on scalable quantum network systems is in its infancy. In this paper we present a quantum network protocol designed to enable end-to-end quantum communication in the face of the new fundamental and technical challenges brought by quantum mechanics. We develop a quantum data plane protocol that enables end-to-end quantum communication and can serve as a building block for more complex services. One of the key challenges in near-term quantum technology is decoherence -- the gradual decay of quantum information -- which imposes extremely stringent limits on storage times. Our protocol is designed to be efficient in the face of short quantum memory lifetimes. We demonstrate this using a simulator for quantum networks and show that the protocol is able to deliver its service even in the face of significant losses due to decoherence. Finally, we conclude by showing that the protocol remains functional on the extremely resource limited hardware that is being developed today underlining the timeliness of this work.

cs.NI↗

arXiv2020

Transforming graph states to Bell-pairs is NP-Complete

Critical to the construction of large scale quantum networks, i.e. a quantum internet, is the development of fast algorithms for managing entanglement present in the network. One fundamental building block for a quantum internet is the distribution of Bell pairs between distant nodes in the network. Here we focus on the problem of transforming multipartite entangled states into the tensor product of bipartite Bell pairs between specific nodes using only a certain class of local operations and classical communication. In particular we study the problem of deciding whether a given graph state, and in general a stabilizer state, can be transformed into a set of Bell pairs on specific vertices using only single-qubit Clifford operations, single-qubit Pauli measurements and classical communication. We prove that this problem is NP-Complete.

quant-ph↗

arXiv2020

QuAlg -- A symbolic algebra package for quantum information

We introduce QuAlg, an open-source symbolic algebra package for quantum information. QuAlg supports working with qubit-states, qudit-states, fock-states and even wave-functions in infinite dimenional Hilbert spaces. States can have amplitudes which are pure complex numbers or more complicated symbolic expressions involving for example delta-distributions. These symbolic expressions can be automatically simplified and integrated. Furthermore, arbitrary operators can be defined, even transformations between different Hilbert spaces. Operators can be applied to states or used to defined measurement operators.

quant-ph↗

arXiv2020

Mapping graph state orbits under local complementation

Graph states, and the entanglement they posses, are central to modern quantum computing and communications architectures. Local complementation---the graph operation that links all local-Clifford equivalent graph states---allows us to classify all stabiliser states by their entanglement. Here, we study the structure of the orbits generated by local complementation, mapping them up to 9 qubits and revealing a rich hidden structure. We provide programs to compute these orbits, along with our data for each of the 587 orbits up to 9 qubits and a means to visualise them. We find direct links between the connectivity of certain orbits with the entanglement properties of their component graph states. Furthermore, we observe the correlations between graph-theoretical orbit properties, such as diameter and colourability, with Schmidt measure and preparation complexity and suggest potential applications. It is well known that graph theory and quantum entanglement have strong interplay---our exploration deepens this relationship, providing new tools with which to probe the nature of entanglement.

quant-ph↗

arXiv2019

Distributed Routing in a Quantum Internet

We develop new routing algorithms for a quantum network with noisy quantum devices such that each can store a small number of qubits. We thereby consider two models for the operation of such a network. The first is a continuous model, in which entanglement between a subset of the nodes is produced continuously in the background. This can in principle allows the rapid creation of entanglement between more distant nodes using the already pre-generated entanglement pairs in the network. The second is an on-demand model, where entanglement production does not commence before a request is made. Our objective is to find protocols, that minimise the latency of the network to serve a request to create entanglement between two distant nodes in the network. We propose three routing algorithms and analytically show that as expected when there is only a single request in the network, then employing them on the continuous model yields a lower latency than on the on-demand one. We study the performance of the routing algorithms in a ring, grid, and recursively generated network topologies. We also give an analytical upper bound on the number of entanglement swap operations the nodes need to perform for routing entangled links between a source and a destination yielding a lower bound on the end to end fidelity of the shared entangled state. We proceed to study the case of multiple concurrent requests and show that in some of the scenarios the on-demand model can outperform the continuous one. Using numerical simulations on ring and grid networks we also study the behaviour of the latency of all the routing algorithms. We observe that the proposed routing algorithms behave far better than the existing classical greedy routing algorithm. The simulations also help to understand the advantages and disadvantages of different types of continuous models for different types of demands.

quant-ph↗

arXiv2019

Counting single-qubit Clifford equivalent graph states is #P-Complete

Graph states, which include for example Bell states, GHZ states and cluster states, form a well-known class of quantum states with applications ranging from quantum networks to error-correction. Deciding whether two graph states are equivalent up to single-qubit Clifford operations is known to be decidable in polynomial time and have been studied both in the context of producing certain required states in a quantum network but also in relation to stabilizer codes. The reason for the latter this is that single-qubit Clifford equivalent graph states exactly corresponds to equivalent stabilizer codes. We here consider the computational complexity of, given a graph state |G>, counting the number of graph states, single-qubit Clifford equivalent to |G>. We show that this problem is #P-Complete. To prove our main result we make use of the notion of isotropic systems in graph theory. We review the definition of isotropic systems and point out their strong relation to graph states. We believe that these isotropic systems can be useful beyond the results presented in this paper.

quant-ph↗

arXiv2019

The complexity of the vertex-minor problem

A graph H is a vertex-minor of a graph G if it can be reached from G by the successive application of local complementations and vertex deletions. Vertex-minors have been the subject of intense study in graph theory over the last decades and have found applications in other fields such as quantum information theory. Therefore it is natural to consider the computational complexity of deciding whether a given graph G has a vertex-minor isomorphic to another graph H, which was previously unknown. Here we prove that this decision problem is NP-complete, even when restricting H, G to be circle graphs, a class of graphs that has a natural relation to vertex-minors.

math.CO↗

arXiv2019

A Link Layer Protocol for Quantum Networks

Quantum communication brings radically new capabilities that are provably impossible to attain in any classical network. Here, we take the first step from a physics experiment to a fully fledged quantum internet system. We propose a functional allocation of a quantum network stack and construct the first physical and link layer protocols that turn ad-hoc physics experiments producing heralded entanglement between quantum processors into a well-defined and robust service. This lays the groundwork for designing and implementing scalable control and application protocols in platform-independent software. To design our protocol, we identify use cases, as well as fundamental and technological design considerations of quantum network hardware, illustrated by considering the state-of-the-art quantum processor platform available to us (Nitrogen-Vacancy (NV) centers in diamond). Using a purpose built discrete-event simulator for quantum networks, we examine the robustness and performance of our protocol using extensive simulations on a super-computing cluster. We perform a full implementation of our protocol, where we successfully validate the physical simulation model against data gathered from the NV hardware. We first observe that our protocol is robust even in a regime of exaggerated losses of classical control messages with only little impact on the performance of the system.We proceed to study the performance of our protocols for 169 distinct simulation scenarios, including tradeoffs between traditional performance metrics such as throughput and the quality of entanglement. Finally, we initiate the study of quantum network scheduling strategies to optimize protocol performance for different use cases.

quant-ph↗

arXiv2018

SimulaQron - A simulator for developing quantum internet software

We introduce a simulator for a quantum internet with the specific goal to support software development. A quantum internet consists of local quantum processors, which are interconnected by quantum communication channels that enable the transmission of qubits between the different processors. While many simulators exist for local quantum processors, there is presently no simulator for a quantum internet tailored towards software development. Quantum internet protocols require both classical as well as quantum information to be exchanged between the network nodes, next to the execution of gates and measurements on a local quantum processor. This requires quantum internet software to integrate classical communication programming practises with novel quantum ones. SimulaQron is built to enable application development and explore software engineering practises for a quantum internet. SimulaQron can be run on one or more classical computers to simulate local quantum processors, which are transparently connected in the background to enable the transmission of qubits or the generation of entanglement between remote processors. Application software can access the simulated local quantum processors to execute local quantum instructions and measurements, but also to transmit qubits to remote nodes in the network. SimulaQron features a modular design that performs a distributed simulation based on any existing simulation of a quantum computer capable of integrating with Python. Programming libraries for Python and C are provided to facilitate application development.

quant-ph↗

arXiv2018

How to transform graph states using single-qubit operations: computational complexity and algorithms

Graph states are ubiquitous in quantum information with diverse applications ranging from quantum network protocols to measurement based quantum computing. Here we consider the question whether one graph (source) state can be transformed into another graph (target) state, using a specific set of quantum operations (LC+LPM+CC): single-qubit Clifford operations (LC), single-qubit Pauli measurements (LPM) and classical communication (CC) between sites holding the individual qubits. We first show that deciding whether a graph state |G> can be transformed into another graph state |G'> using LC+LPM+CC is NP-Complete, even if |G'> is restricted to be the GHZ-state. However, we also provide efficient algorithms for two situations of practical interest: 1. |G> has Schmidt-rank width one and |G'> is a GHZ-state. The Schmidt-rank width is an entanglement measure of quantum states, meaning this algorithm is efficient if the original state has little entanglement. Our algorithm has runtime O(|V(G')||V(G)|^3), and is also efficient in practice even on small instances as further showcased by a freely available software implementation. 2. |G> is in a certain class of states with unbounded Schmidt-rank width, and |G'> is a GHZ-state of a constant size. Here the runtime is O(poly(|V(G)|)), showing that more efficient algorithms can in principle be found even for states holding a large amount of entanglement, as long as the output state has constant size. Our results make use of the insight that deciding whether a graph state |G> can be transformed to another graph state |G'> is equivalent to a known decision problem in graph theory, namely the problem of deciding whether a graph G' is a vertex-minor of a graph G. Many of the technical tools developed to obtain our results may be of independent interest.

quant-ph↗

arXiv2018

Transforming graph states using single-qubit operations

Stabilizer states form an important class of states in quantum information, and are of central importance in quantum error correction. Here, we provide an algorithm for deciding whether one stabilizer (target) state can be obtained from another stabilizer (source) state by single-qubit Clifford operations (LC), single-qubit Pauli measurements (LPM), and classical communication (CC) between sites holding the individual qubits. What's more, we provide a recipe to obtain the sequence of LC+LPM+CC operations which prepare the desired target state from the source state, and show how these operations can be applied in parallel to reach the target state in constant time. Our algorithm has applications in quantum networks, quantum computing, and can also serve as a design tool - for example, to find transformations between quantum error correcting codes. We provide a software implementation of our algorithm that makes this tool easier to apply. A key insight leading to our algorithm is to show that the problem is equivalent to one in graph theory, which is to decide whether some graph G' is a vertex-minor of another graph G. Here we show that the vertex-minor problem can be solved in time O(|G|^3) where |G| is the size of the graph G, whenever the rank-width of G and the size of G' are bounded. Our algorithm is based on techniques by Courcelle for solving fixed parameter tractable problems, where here the relevant fixed parameter is the rank width. The second half of this paper serves as an accessible but far from exhausting introduction to these concepts, that could be useful for many other problems in quantum information.

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