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arXiv:2306.06397 · Physical Review Applied

Lower-depth programmable linear optical processors

Rui Tang, Ryota Tanomura, Takuo Tanemura, Yoshiaki Nakano

Published Jan 26, 2024• 13 citations
arXivHTMLPDF

Abstract

Programmable linear optical processors (LOPs) can have widespread applications in computing and information processing due to their capabilities of implementing reconfigurable on-chip linear transformations. A conventional LOP that uses a mesh of Mach-Zehnder interferometers (MZIs) requires $2N+3$ stages of phase shifters for $N\ifmmode\times\else\texttimes\fi{}N$ matrices. However, it is beneficial to reduce the number of phase-shifter stages to realize a more compact and lower-loss LOP, especially when long and lossy electro-optic phase shifters are used. In this work, we propose a structure for LOPs that can implement arbitrary matrices as long as they can be realized by previous MZI-based schemes. Through numerical analysis, we further show that the number of phase-shifter stages in the proposed structure can be reduced to $N+2$ and $N+3$ for a large number of random dense matrices and sparse matrices, respectively. This work contributes to the realization of compact, low-loss, and energy-efficient programmable LOPs.

DOI
10.1103/physrevapplied.21.014054

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Programmable linear optical processors (LOPs) can have widespread applications in computing and information processing due to their capabilities of implementing reconfigurable on-chip linear transformations. A conventional LOP that uses a mesh of Mach-Zehnder interferometers (MZIs) requires 2N+32N+32N+3 stages of phase shifters for N\ifmmode×\else\texttimes\fiNN\ifmmode\times\else\texttimes\fi{}NN\ifmmode×\else\texttimes\fiN matrices. However, it is beneficial to reduce the number of phase-shifter stages to realize a more compact and lower-loss LOP, especially when long and lossy electro-optic phase shifters are used. In this work, we propose a structure for LOPs that can implement arbitrary matrices as long as they can be realized by previous MZI-based schemes. Through numerical analysis, we further show that the number of phase-shifter stages in the proposed structure can be reduced to N+2N+2N+2 and N+3N+3N+3 for a large number of random dense matrices and sparse matrices, respectively. This work contributes to the realization of compact, low-loss, and energy-efficient programmable LOPs.
There has been an escalating demand for dynamically reconfigurable photonic structures to implement any linear optical transformation between the input and output ports. Such devices are often constructed as a mesh of reconfigurable Mach-Zehnder interferometers(MZIs). Consequently, the programmed MZIs can redistribute the light to implementarbitrary unitary transformations from an input vector of optical signals to an outputvector of coherent optical modes. These structures have been widely used as a promising hardware platform for fast and energy-efficient matrix multiplications in different applications, such as information processing, machine learning algorithms, neural networks(NNs), etc. Matrix multiplication is an essential but time- and energy-consuming operation in machine learning computations. The computational complexity of NNs necessitates well designed and implemented hardware accelerators for fast and energy-efficient data processing, which allows for scaling the structure to larger NNs in current and upcoming applications. Over the last few years, the considerable progress in silicon photonics has made it possible to fabricate multiport optical interferometric structures with small ootprints and high-power efficiency, which can be exploited as hardware accelerators, thanks to the inherent parallelism of optics. This Ph.D. thesis presents the theoretical and experimental analysis of multiport reconfigurable MZI-based optical processors. The optical processors are meshes of 2×2 reconfigurable MZIs. It is demonstrated how the optical transformation matrix of the optical processors is theoretically decomposed for a given application. The Reck-mesh-based optical processor is experimentally calibrated before programming the device for a given application. Additionally, the thesis includes the theoretical and measurement results of a single layer NN implemented by a 4×4 Reck-mesh-based optical processor. Finally, a novel phase-error- and loss-tolerant multiport field-programmable MZI-based optical processor for optical NNs is proposed. The new structure with a diamond mesh shape makes use of a set of additional MZIs compared to the commonly used Reck (triangular) mesh. The additional MZIs in the Diamond mesh make its topology more symmetric yielding higher phase error- and loss-tolerance, and also provide extra degrees of freedom in the optimization of ONN weight matrix during training. Furthermore, the better classification performance of the Diamond mesh compared to the Reck mesh is associated with the fact that the Diamond mesh is capable of excluding the light intensity that could have degraded the classification accuracy of the implemented ONNs. This is done by means of the tapered-out wave guides of the additional MZIs in the Diamond mesh, while the optimal light intensity is sent to its outputs for better classification. The demonstration of these analyses is significant as it can be used to implement any universal field-programmable photonic device as an optical processor, i.e., optical computational accelerator, which can be experimentally programmed to implement arbitrary linear optical transformation matrix for a given application. Additionally, the presented analytical results in this thesis can be used to enhance the classification performance of ONNs implemented by such structures. As a result of these analyses, the thesis proposes the Diamond-mesh-based optical processor as a promising candidate for large scale ONNs which outperforms the Reck-mesh-based ones in the presence of experimental imperfections
Quantum integrated photonics requires large-scale linear optical circuitry, and for many applications, it is desirable to have a universally programmable circuit, able to implement an arbitrary unitary transformation on a number of modes. This has been achieved using the Reck scheme, consisting of a network of Mach–Zehnder interferometers containing a variable phase shifter in one path as well as an external phase shifter after each Mach–Zehnder. It subsequently became apparent that with symmetric Mach–Zehnders containing a phase shifter in both paths, the external phase shifters are redundant, resulting in a more compact circuit. The rectangular Clements scheme improves on the Reck scheme in terms of circuit depth, but it has been thought that an external phase-shifter was necessary after each Mach–Zehnder. Here, we show that the Clements scheme can be realized using symmetric Mach–Zehnders, requiring only a small number of external phase-shifters that do not contribute to the depth of the circuit. This will result in a significant saving in the length of these devices, allowing more complex circuits to fit onto a photonic chip, and reducing the propagation losses associated with these circuits. We also discuss how similar savings can be made to alternative schemes, which have robustness to imbalanced beam-splitters.
Universal linear optical (ULO) circuit is a versatile device that plays a fundamental role in quantum computation, optical machine learning, and MIMO processing for optical communications. The design of the ULO, i.e., a universal multiport interferometer, was initially proposed by Reck et al. in 1994 [1] and improved in terms of circuit depth and robustness to optical losses by Clements et al. in 2016 [2]. Recently, a further compactified circuit design was proposed Bell and Walmsley [3]. In Bell's scheme, the circuit layout consists of a network of symmetric Mach-Zehnder interferometers (MZI) with two variable phase shifters in each arm. The design significantly reduces the whole device length compared to the conventional designs, where the circuit consists of a network of asymmetric MZIs, each of which has a phase shifter in one arm and an external phase shifter outside of itself. This downsizing becomes significantly important toward the realization of large-scale ULOs in the limited chip area, particularly when each phase shifter is long or when the spacing between phase shifters cannot be made small. This time we experimentally demonstrate that Bell's scheme can express arbitrary unitary matrices as well as Clements' scheme.
We demonstrate a novel mesh of Mach-Zehnder interferometers (MZIs) for programmable optical processors. We thoroughly analyze the benefits and drawbacks of previously known meshes and compare our newly proposed mesh with these prior architectures, highlighting its unique features and advantages. The proposed mesh, referred to as Bokun mesh, is an architecture that merges the attributes of the prior topologies Diamond and Clements. Similar to Diamond, Bokun provides diagonal paths passing through every individual MZI enabling direct phase monitoring. However, unlike Diamond and similar to Clements, Bokun maintains a minimum optical depth leading to better scalability. Providing the monitoring option, Bokun's programming is faster improving the total energy efficiency of the processor. The performance of Bokun mesh enabled by an optimal optical depth is also more resilient to the loss and fabrication imperfections compared to architectures with longer depth such as Reck and Diamond. Employing an efficient programming scheme, the proposed architecture improves energy efficiency by 83% maintaining the same computation accuracy for weight matrix changes at 2 kHz.
Programmable linear optical interferometers are a core primitive in optical signal processing, quantum information processing, and photonic computing. Existing photonic-integrated implementations realize arbitrary MMM-mode unitaries using Mach--Zehnder-interferometer meshes whose footprint and accumulated loss scale with O(M2)O(M^2)O(M2) optical components. Here we analyze and experimentally demonstrate a programmable architecture for implementing linear optical transformations directly on spatially tiled free-space {\em pixel modes} using multi-plane light conversion (MPLC). In this architecture, MMM spatial modes arranged on a transverse lattice undergo a unitary transformation and are mapped to MMM output modes of identical geometry through a sequence of programmable phase masks separated by free-space propagation segments. Numerical simulations show that arbitrary MMM-mode unitaries can be compiled to a desired high fidelity using a number of phase planes that scales approximately linearly with MMM. Using a spatial-light-modulator-based MPLC, we experimentally demonstrate programmable interferometers acting on up to 161616 spatial pixel modes, including tunable beamsplitters, Hadamard unitaries, spatial permutations, and partial unitaries on select subsets of modes. These results establish MPLC-based pixel-mode interferometers as a promising architecture for programmable linear optics with applications in classical and quantum optical interconnects, photonic switching, and quantum information processing.