Matrix Optimization on Universal Unitary Photonic Devices

Pai, Sunil; Bartlett, Ben; Solgaard, Olav; Miller, David A. B.

doi:10.1103/physrevapplied.11.064044

Cited by 136 publications

(110 citation statements)

References 36 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: 60%

“…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%

“…(33)), the general trend of lower variance near the center of GridUnitary multipliers is evident. This is claimed to translates to a lower tolerance for error [14].…”

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 4 more Smart Citations

Design of optical neural networks with component imprecisions

Fang¹,

Manipatruni²,

Wierzynski³

et al. 2019

Opt. Express

158

100

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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: 60%

Section: Localized Imprecisionsmentioning

confidence: 99%

Section: E Quantization Errormentioning

confidence: 99%

“…(33)), the general trend of lower variance near the center of GridUnitary multipliers is evident. This is claimed to translates to a lower tolerance for error [14].…”

Section: E Quantization Errormentioning

confidence: 99%

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

158

100

View full text Add to dashboard Cite

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Optical Implementation of 2 × 2 Universal Unitary Matrix Transformations

Macho

Pérez

Capmany

2021

Laser & Photonics Reviews

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Unitary operations are a specific class of linear transformations that have become an essential ingredient for the realization of classical and quantum information processing. The ability of implementing any n-dimensional unitary signal transformation by using a reconfigurable optical hardware has recently led to the pioneering concept of programmable linear optical processor, whose basic building block (BB) must be correctly designed to guarantee that the whole system is able to perform n × n universal (i.e., arbitrary) unitary matrix transformations. Here, it is demonstrated that the present architectures of the BB do not fulfil the universal unitary property (at least) in 2 × 2 optical processors, limiting the number of unitary matrix transformations that may be generated. Aiming to solve this fundamental constraint, the theoretical tools required to analyze and design 2 × 2 universal unitary optical circuits and their corresponding BBs are presented. The consequences of this mathematical framework are explored, obtaining a simple route to implement different BB architectures, all of them guaranteeing a true universal unitary functionality in the resulting 2 × 2 optical processors. These findings may pave the way to revisit the design of high-dimensional unitary optical processors, unleashing the potential of programmable integrated photonics technology.

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Analog Programmable‐Photonic Computation

Macho‐Ortiz,

Pérez‐López,

Azaña

et al. 2023

Laser & Photonics Reviews

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Digital electronics is a technological cornerstone in this modern society that has covered the increasing demand for computing power during the last decades thanks to a periodic doubling of transistor density in integrated circuits. Currently, such scaling law is reaching its fundamental limit, leading to the emergence of a large gamut of applications that cannot be supported by digital electronics, specifically, those that involve real‐time multi‐data processing, e.g., medical diagnostic imaging, robotic control, and autonomous driving, among others. In this scenario, an analog computing approach implemented in a real‐time reconfigurable nonelectronic hardware such as programmable integrated photonics (PIP) can be more efficient than digital electronics to perform these emerging applications. However, actual analog computing models such as quantum and neuromorphic computation were not conceived to extract the unique benefits of PIP (and integrated photonics in general). Here, the foundations of a new computation theory are presented, termed Analog Programmable‐Photonic Computation (APC), explicitly designed to unleash the full potential of PIP technology. Interestingly, APC enables overcoming basic theoretical and technological limitations of existing computational models and can be implemented in other technologies (e.g., in electronics, acoustics or using metamaterials), consequently exhibiting the potential to spark a ground‐breaking impact on the information society.

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Matrix Optimization on Universal Unitary Photonic Devices

Cited by 136 publications

References 36 publications

Design of optical neural networks with component imprecisions

Design of optical neural networks with component imprecisions

Optical Implementation of 2 × 2 Universal Unitary Matrix Transformations

Analog Programmable‐Photonic Computation

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