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arXiv:2005.13513 · Physical Review A

Architecture and noise analysis of continuous-variable quantum gates using two-dimensional cluster states

Mikkel V. Larsen, Jonas Schou Neergaard-Nielsen, Ulrik L. Andersen

Published Oct 19, 2020• 36 citations
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Abstract

Due to its unique scalability potential, continuous-variable quantum optics is a promising platform for large-scale quantum computing. In particular, very large cluster states with a two-dimensional topology that are suitable for universal quantum computing and quantum simulation can be readily generated in a deterministic manner, and routes towards fault tolerance via bosonic quantum error correction are known. In this article we propose a complete measurement-based quantum computing architecture for the implementation of a universal set of gates on the recently generated two-dimensional cluster states [M. V. Larsen et al., Science 366, 369 (2019); W. Asavanant et al., Science 366, 373 (2019)]. We analyze the performance of the various quantum gates that are executed in these cluster states as well as in other two-dimensional cluster states (the bilayer-square lattice and quad-rail lattice cluster states [R. N. Alexander et al., Phys. Rev. A 94, 032327 (2016); N. C. Menicucci, Phys. Rev. A 83, 062314 (2011)]) by estimating and minimizing the associated stochastic noise addition as well as the resulting gate error probability. We compare the four different states and find that, although they all allow for universal computation, the quad-rail lattice cluster state performs better than the other three states, which all exhibit similar performance.

DOI
10.1103/physreva.102.042608

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Due to its unique scalability potential, continuous-variable quantum optics is a promising platform for large-scale quantum computing. In particular, very large cluster states with a two-dimensional topology that are suitable for universal quantum computing and quantum simulation can be readily generated in a deterministic manner, and routes towards fault tolerance via bosonic quantum error correction are known. In this article we propose a complete measurement-based quantum computing architecture for the implementation of a universal set of gates on the recently generated two-dimensional cluster states [M. V. Larsen et al., Science 366, 369 (2019); W. Asavanant et al., Science 366, 373 (2019)]. We analyze the performance of the various quantum gates that are executed in these cluster states as well as in other two-dimensional cluster states (the bilayer-square lattice and quad-rail lattice cluster states [R. N. Alexander et al., Phys. Rev. A 94, 032327 (2016); N. C. Menicucci, Phys. Rev. A 83, 062314 (2011)]) by estimating and minimizing the associated stochastic noise addition as well as the resulting gate error probability. We compare the four different states and find that, although they all allow for universal computation, the quad-rail lattice cluster state performs better than the other three states, which all exhibit similar performance.
Continuous-variable measurement-based quantum computation, which requires deterministically generated large-scale cluster states, is a promising candidate for practical, scalable, universal, and fault-tolerant quantum computation. In this work, based on our compact and scalable scheme of generating a two-dimensional spatiotemporal cluster state, a complete architecture including cluster state preparation, gate implementations, and error correction, is proposed. First, a scheme for generating two-dimensional large-scale continuous-variable cluster state by multiplexing both the temporal and spatial domains is proposed. Then, the corresponding gate implementations by gate teleportation are discussed and the actual gate noise from the generated cluster state is considered. After that, the quantum error correction can be further achieved by utilizing the square-lattice Gottesman-Kitaev-Preskill (GKP) code. Finally, a fault-tolerant quantum computation can be realized by introducing bias into the square-lattice GKP code (to protect against phase-flip errors) and concatenating a repetition code (to handle the residual bit-flip errors), with a squeezing threshold of 12.3 dB. Our work provides a possible option for a complete fault-tolerant quantum computation architecture in the future.
Continuous-variable measurement-based quantum computation on cluster states has in recent years shown great potential for scalable, universal, and fault-tolerant quantum computation when combined with the Gottesman-Kitaev-Preskill (GKP) code and quantum error correction.However, no complete fault-tolerant architecture exists that includes everything from cluster-state generation with finite squeezing to gate implementations with realistic noise and error correction.In this work, we propose a simple architecture for the preparation of a cluster state in three dimensions in which gates can be efficiently implemented by gate teleportation.To accommodate scalability, we propose architectures that allow both spatial and temporal multiplexing, with the temporally encoded version requiring as little as two squeezed light sources.Because of its three-dimensional structure, the architecture supports topological qubit error correction, while GKP error correction is efficiently realized within the architecture by teleportation.To validate fault tolerance, the architecture is simulated using surface-GKP codes, including noise from GKP states as well as gate noise caused by finite squeezing in the cluster state.We find a fault-tolerant squeezing threshold of 12.7 dB, with room for further improvement.
Continuous-variable measurement-based quantum computation on cluster states has in recent years shown great potential for scalable, universal, and fault-tolerant quantum computation when combined with the Gottesman-Kitaev-Preskill (GKP) code and quantum error correction. However, no complete fault-tolerant architecture exists that includes everything from cluster-state generation with finite squeezing to gate implementations with realistic noise and error correction. In this work, we propose a simple architecture for the preparation of a cluster state in three dimensions in which gates can be efficiently implemented by gate teleportation. To accommodate scalability, we propose architectures that allow both spatial and temporal multiplexing, with the temporally encoded version requiring as little as two squeezed light sources. Because of its three-dimensional structure, the architecture supports topological qubit error correction, while GKP error correction is efficiently realized within the architecture by teleportation. To validate fault tolerance, the architecture is simulated using surface-GKP codes, including noise from GKP states as well as gate noise caused by finite squeezing in the cluster state. We find a fault-tolerant squeezing threshold of 12.7 dB, with room for further improvement.Received 11 January 2021Revised 18 May 2021Accepted 23 July 2021DOI:https://doi.org/10.1103/PRXQuantum.2.030325Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasMeasurement-based quantum computingOptical quantum information processingQuantum information processing with continuous variablesQuantum InformationAtomic, Molecular & Optical
Entanglement is the key resource for measurement-based quantum computing. It is stored in quantum states known as cluster states, which are prepared offline and enable quantum computing by means of purely local measurements. Universal quantum computing requires cluster states that are both large and possess (at least) a two-dimensional topology. Continuous-variable cluster states-based on bosonic modes rather than qubits-have previously been generated on a scale exceeding one million modes, but only in one dimension. Here, we report generation of a large-scale two-dimensional continuous-variable cluster state. Its structure consists of a 5- by 1240-site square lattice that was tailored to our highly scalable time-multiplexed experimental platform. It is compatible with Bosonic error-correcting codes that, with higher squeezing, enable fault-tolerant quantum computation.
We consider measurement-based quantum computation that uses scalable continuous-variable cluster states with a one-dimensional topology. The physical resource, known here as the dual-rail quantum wire, can be generated using temporally multiplexed offline squeezing and linear optics or by using a single optical parametric oscillator. We focus on an important class of quantum gates, specifically Gaussian unitaries that act on single quantum modes (qumodes), which gives universal quantum computation when supplemented with multi-qumode operations and photon-counting measurements. The dual-rail wire supports two routes for applying single-qumode Gaussian unitaries: The first is to use traditional one-dimensional quantum-wire cluster-state measurement protocols. The second takes advantage of the dual-rail quantum wire in order to apply unitaries by measuring pairs of qumodes called macronodes. We analyze and compare these methods in terms of the suitability for implementing single-qumode Gaussian measurement-based quantum computation.
Optical continuous-variable cluster states (CVCSs) in combination with Gottesman-Kitaev-Preskill (GKP) qubits enable fault-tolerant quantum computation so long as these resources are of high enough quality. Previous studies concluded that a particular CVCS, the quad rail lattice (QRL), exhibits a lower GKP gate-error rate than others do. We show in this work that many other experimentally accessible CVCSs also achieve this level of performance by identifying operational equivalences to the QRL. Under this equivalence, the GKP Clifford gate set for each CVCS maps straightforwardly from that of the QRL, inheriting its noise properties. Furthermore, each cluster state has at its heart a balanced four-splitter---the four-mode extension to a balanced beam splitter. We classify all four-splitters, show they form a single equivalence class under SWAP and parity operators, and give a construction of any four-splitter with linear optics, thus extending the toolbox for theoretical and experimental cluster-state design and analysis.