Unitary entanglement construction in hierarchical networks

Bapat, Aniruddha; Eldredge, Zachary; Garrison, James R.; Deshpande, Abhinav; Chong, Frederic T.; Gorshkov, Alexey V.

doi:10.1103/physreva.98.062328

Cited by 10 publications

(14 citation statements)

References 60 publications

(79 reference statements)

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“…In contrast to Ref. [14], where architectures are evaluated assuming that only unitary operations are permitted, our results apply to the more general setting that allows nonunitary operations.…”

Section: Introductionmentioning

confidence: 83%

“…In this framework, vertex degrees and total graph edge weights represent required ancilla overheads, justifying their use as cost functions in Ref. [14].…”

Section: Physical Modelmentioning

confidence: 99%

“…In Appendix B, we have done this for the complete, star, and grid graphs, as well as the hierarchical products and hierarchies presented in Ref. [14]. In particular, we compare hierarchies to d-dimensional grids and show that, for some parameters, hierarchies have lower rainbow time and lower total edge weight than grids, making them promising architectures for quantum computing.…”

Section: Rainbow Times and Isoperimetric Numbermentioning

confidence: 99%

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Entanglement bounds on the performance of quantum computing architectures

Eldredge

Zhou

Bapat

et al. 2020

Phys. Rev. Research

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There are many possible architectures of qubit connectivity that designers of future quantum computers will need to choose between. However, the process of evaluating a particular connectivity graph's performance as a quantum architecture can be difficult. In this paper, we show that a quantity known as the isoperimetric number establishes a lower bound on the time required to create highly entangled states. This metric we propose counts resources based on the use of two-qubit unitary operations, while allowing for arbitrarily fast measurements and classical feedback. We use this metric to evaluate the hierarchical architecture proposed by A. Bapat et al. [Phys. Rev. A 98, 062328 (2018)] and find it to be a promising alternative to the conventional grid architecture. We also show that the lower bound that this metric places on the creation time of highly entangled states can be saturated with a constructive protocol, up to a factor logarithmic in the number of qubits.

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Section: Introductionmentioning

confidence: 83%

“…In this framework, vertex degrees and total graph edge weights represent required ancilla overheads, justifying their use as cost functions in Ref. [14].…”

Section: Physical Modelmentioning

confidence: 99%

Section: Rainbow Times and Isoperimetric Numbermentioning

confidence: 99%

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Entanglement bounds on the performance of quantum computing architectures

Eldredge

Zhou

Bapat

et al. 2020

Phys. Rev. Research

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“…We remark that such a hierarchic arrangement was also implicitly assumed in [51,57]. The features of such hierarchical graphs and their properties in a network structure has recently been analyzed in detail in [98].…”

Section: Hierarchical Regionsmentioning

confidence: 98%

A quantum network stack and protocols for reliable entanglement-based networks

Pirker

Dür

2019

New J. Phys.

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We present a stack model for breaking down the complexity of entanglement-based quantum networks. More specifically, we focus on the structures and architectures of quantum networks and not on concrete physical implementations of network elements. We construct the quantum network stack in a hierarchical manner comprising several layers, similar to the classical network stack, and identify quantum networking devices operating on each of these layers. The layers responsibilities range from establishing point-to-point connectivity, over intra-network graph state generation, to inter-network routing of entanglement. In addition we propose several protocols operating on these layers. In particular, we extend the existing intra-network protocols for generating arbitrary graph states to ensure reliability inside a quantum network, where here reliability refers to the capability to compensate for devices failures. Furthermore, we propose a routing protocol for quantum routers which enables the generation of arbitrary graph states across network boundaries. This protocol, in correspondence with classical routing protocols, can compensate dynamically for failures of routers, or even complete networks, by simply re-routing the given entanglement over alternative paths. We also consider how to connect quantum routers in a hierarchical manner to reduce complexity, as well as reliability issues arising in connecting these quantum networking devices. quantum network shall not be limited to the generation of Bell-pairs only [50][51][52][53], because many interesting applications require multipartite entangled quantum states. Therefore, the ultimate goal of quantum networks should be to enable their clients to share arbitrary entangled states to perform distributed quantum computational tasks. An important subclass of multipartite entangled states are so-called graph states [54], and many protocols in quantum information theory rely on this class of states.Here we consider entanglement-based quantum networks utilizing multipartite entangled states [51-53, 55-57] which are capable of generating arbitrary graph states among clients. In general, we identify three successive phases in entanglement-based quantum networks: dynamic, static, and adaptive. In the dynamic phase, which is the first phase, the quantum network devices utilize the quantum channels to distribute entangled states among each other. Once this phase completes, the quantum network devices share certain entangled quantum states, which results in the static phase. In this phase, the quantum network devices store these entangled states for future requests locally. Finally, in the adaptive phase, the network devices manipulate and adapt the entangled states of the static phase. This might be caused either due to requests of clients in networks, but also due to failures of devices in a quantum network.We follow the approach of [51] where a certain network state is stored in the static phase, and client requests to establish certain target (graph) states in the network ar...

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“…Due to these challenges, as well as developing technology for communicating between different quantum chips [7,75], we expect quantum hardware to scale via a modular approach similar to how a classical computer can be scaled increasing the number of processors not just the size of the processors. Two of the leading quantum technologies, ion trap and superconducting physical qubits, are already beginning to explore this avenue and experimentalists project modularity will be the key to moving forward [3,9,18,22,32,43,44]. One such example for ion traps is shown in Figure 2 where many trapped ion devices are connected via a single central optical switch.…”

Section: Introductionmentioning

confidence: 99%

Time-sliced quantum circuit partitioning for modular architectures

Baker

Duckering

Hoover

et al. 2020

Proceedings of the 17th ACM International Conference on Computing Frontiers

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Current quantum computer designs will not scale. To scale beyond small prototypes, quantum architectures will likely adopt a modular approach with clusters of tightly connected quantum bits and sparser connections between clusters. We exploit this clustering and the statically-known control flow of quantum programs to create tractable partitioning heuristics which map quantum circuits to modular physical machines one time slice at a time. Specifically, we create optimized mappings for each time slice, accounting for the cost to move data from the previous time slice and using a tunable lookahead scheme to reduce the cost to move to future time slices. We compare our approach to a traditional statically-mapped, owner-computes model. Our results show strict improvement over the static mapping baseline. We reduce the non-local communication overhead by 89.8% in the best case and by 60.9% on average. Our techniques, unlike many exact solver methods, are computationally tractable. CCS CONCEPTS• Computer systems organization → Quantum computing; • Software and its engineering → Compilers. ACM Reference Format:

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Unitary entanglement construction in hierarchical networks

Cited by 10 publications

References 60 publications

Entanglement bounds on the performance of quantum computing architectures

Entanglement bounds on the performance of quantum computing architectures

A quantum network stack and protocols for reliable entanglement-based networks

Time-sliced quantum circuit partitioning for modular architectures

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