Using an imperfect photonic network to implement random unitaries

Burgwal, Roel; Clements, William R.; Smith, Devin H.; Gates, James C.; Kolthammer, W. Steven; Renema, Jelmer J.; Walmsley, Ian A.

doi:10.1364/oe.25.028236

Cited by 75 publications

(65 citation statements)

References 24 publications

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“…This result seems to contradict previous studies on the spatial tolerance of MZIs in a GridUnitary multiplier [14,15,16]. It was discovered that the central MZIs of the multiplier had a much lower tolerance than those near the edges.…”

Section: Localized Imprecisionsmentioning

confidence: 62%

“…However, the idea of tolerance of a MZI to beamsplitter fabrication imprecision, while related, is not the same as the network sensitivity to localized imprecisions. To elaborate, tolerance is implicitly defined, in references [14,15,16], as roughly the allowable beamsplitter imperfection (deviation from 50:50) that still permits post-fabrication optimization of phaseshifter towards arbitrary unitary matrices. In our prefabrication optimization approach, we take sensitivity to be the deviation from ideal classification accuracy when imprecision is introduced to the MZI with no further reconfiguration.…”

Section: Localized Imprecisionsmentioning

confidence: 99%

“…Neural networks in which quantization happens as part of the training procedure has been demonstrated to have accuracies very near their full precision counterpart, down to even binary weights [49,50]. Analyses has been done on the distribution of the internal phase shift (θ) of MZIs of GridUnitary multipliers when used to implement randomly sampled unitary matrices [15,16,14]. It was shown that the phases are not uniformly distributed spatially.…”

Section: E Quantization Errormentioning

confidence: 99%

“…Therefore, realistic considerations of ONNs require that these imprecisions be taken into account. Previous analyses of the effects of fabrication errors on photonic networks were in the context of post-fabrication optimization of unitary networks [14,15,16]. Our study differs in three main areas.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Design of optical neural networks with component imprecisions

Fang¹,

Manipatruni²,

Wierzynski³

et al. 2019

Opt. Express

137

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For the benefit of designing scalable, fault resistant optical neural networks (ONNs), we investigate the effects architectural designs have on the ONNs' robustness to imprecise components. We train two ONNs -one with a more tunable design (GridNet) and one with better fault tolerance (FFTNet) -to classify handwritten digits. When simulated without any imperfections, GridNet yields a better accuracy (∼ 98%) than FFTNet (∼ 95%). However, under a small amount of error in their photonic components, the more fault tolerant FFTNet overtakes GridNet. We further provide thorough quantitative and qualitative analyses of ONNs' sensitivity to varying levels and types of imprecisions. Our results offer guidelines for the principled design of fault-tolerant ONNs as well as a foundation for further research.Second, rather than optimization towards a specific matrix, the linear operations learned for the classification task is not, a priori, known. As such, our primary figure of merit is the classification accuracy instead of the fidelity between the target unitary matrix and the one learned.Lastly, the aforementioned studies mainly focused on the optimization of the networks after fabrication. The imprecisions introduced generally reduced the expressivity of the network -how well the network can represent arbitrary transformations. Evaluation of this reduction in tunability and mitigating strategies were provided. However, such post-fabrication optimization requires the characterization of every MZI, the number of which scales with the dimension (N ) of the network as N 2 . Protocols for self configuration of imprecise photonic networks have been demonstrated [17,18]. While measurement of MZIs were not necessary in such protocols, each MZI needed to be configured progressively and sequentially. Thus, the same N 2 scaling problem remained. Furthermore, if multiple ONN devices are fabricated, each device, with unique imperfections, has to be optimized separately. The total computational power required, therefore, scales with the number of devices produced.In contrast, we consider the effects of imprecisions introduced after software training of ONNs (Code 1, Ref.[19]), details of which we present in Sec. 3. This pre-fabrication training is more scalable, both in network size and fabrication volume. An ideal ONN (i.e., one with no imprecisions) is trained in software only once and the parameters are transferred to multiple fabricated instances of the network with imprecise components. No subsequent characterization or tuning of devices are necessary. In addition to the benefit of better scalability, fabrication of static MZIs can be made more precise and cost effective compared to re-configurable ones.We evaluate the degradation of ONNs from their ideal performances with increasing imprecision. To understand how such effects can be minimized, we investigate the role that the architectural designs have on ONNs' sensitivity to imprecisions. The results are presented in Sec. 4.1. Specifically, we study the performance of two ONNs i...

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Section: Localized Imprecisionsmentioning

confidence: 62%

Section: Localized Imprecisionsmentioning

confidence: 99%

Section: E Quantization Errormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Design of optical neural networks with component imprecisions

Fang¹,

Manipatruni²,

Wierzynski³

et al. 2019

Opt. Express

137

View full text Add to dashboard Cite

show abstract

“…For instance, when one clip-to-clip connection 2 To fulfill all the above desiderata, a top-down approach could be to adopt well-established meshes of optical elements for programmable multifunctional nanophotonics hardware [32]. However, their versatility comes at the cost of higher computational resources (should one iteratively adjust their settings according to externally-processed unitary decompositions [31]) or of a less intuitive dependency of the output on the internal components [48,49]. 3 Non-ideal detection efficiency can be counteracted with a control feedback, by sending again a photon to the same decision tree if, in the previous time bin, no photon was collected.…”

Section: Decision Trees As Linear Optical Circuitsmentioning

confidence: 99%

Photonic architecture for reinforcement learning

et al. 2020

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The last decade has seen an unprecedented growth in artificial intelligence and photonic technologies, both of which drive the limits of modern-day computing devices. In line with these recent developments, this work brings together the state of the art of both fields within the framework of reinforcement learning. We present the blueprint for a photonic implementation of an active learning machine incorporating contemporary algorithms such as SARSA, Q-learning, and projective simulation. We numerically investigate its performance within typical reinforcement learning environments, showing that realistic levels of experimental noise can be tolerated or even be beneficial for the learning process. Remarkably, the architecture itself enables mechanisms of abstraction and generalization, two features which are often considered key ingredients for artificial intelligence. The proposed architecture, based on single-photon evolution on a mesh of tunable beamsplitters, is simple, scalable, and a first integration in quantum optical experiments appears to be within the reach of near-term technology.OPEN ACCESS RECEIVED promising features as compared to electronic processors [27][28][29][30]. For instance, nanosecond-scale routing and reconfigurability have already been demonstrated [31][32][33], while encoding information in photons enables decision-making at the speed of light, only limited by the generation and detection rates. Moreover, the use of phase-change materials for in-memory information processing [34] promises to enhance the energy efficiency, since their properties can be modified without continuous external intervention [35,36]. Importantly, since the architecture uses single photons, decision-making is fueled by genuine quantum randomness. This feature marks a fundamental departure from pseudorandom number generation in conventional devices. (ii) The second contribution is the development of a specific variant of PS based on binary decision trees (tree-PS, or t-PS for short), which is closely connected to the standard PS and suitable for the implementation on a photonic circuit. Furthermore, we discuss how this variant enables key features of artificial intelligence, namely abstraction and generalization [37,38].The Article is structured as follows. In section 2 we summarize the theoretical framework of RL, exemplified by three common approaches: SARSA, Q-learning, and PS. In section 3 we describe the blueprint for a fully integrated, photonic RL agent. We then numerically investigate its performance within two standard RL tasks and under realistic experimental imperfections in section 4. Finally, in section 5 we discuss promising features of this architecture within the context of t-PS.

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A survey of approaches for implementing optical neural networks

Fei

et al. 2021

Optics & Laser Technology

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Using an imperfect photonic network to implement random unitaries

Cited by 75 publications

References 24 publications

Design of optical neural networks with component imprecisions

Design of optical neural networks with component imprecisions

Photonic architecture for reinforcement learning

A survey of approaches for implementing optical neural networks

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