Braided interferometer mesh for robust photonic matrix-vector multiplications with non-ideal components

TL;DR

This work tackles robust photonic matrix-vector multiplications by introducing the braid interferometer mesh, a symmetry-enhanced architecture designed to maintain high fidelity under realistic non-idealities. The study uses backpropagation-based optimization to approximate arbitrary unitaries $U_0$ in a common framework, comparing braid against Clements and Fldzhyan under ideal, then progressively non-ideal conditions. Key findings show the braid architecture offers superior robustness, especially as the interferometer size grows, exhibiting balanced path losses and reduced depth that mitigate the impact of component imperfections such as insertion loss, imbalances, and crosstalk. The results suggest braid as a strong candidate for scalable photonic neuromorphic computing and related quantum applications, with footprint and loss profiles becoming comparable to existing designs thanks to advances in crossing technology.

Abstract

Matrix-vector multiplications (MVMs) are essential for a wide range of applications, particularly in modern machine learning and quantum computing. In photonics, there is growing interest in developing architectures capable of performing linear operations with high speed, low latency, and minimal loss. Traditional interferometric photonic architectures, such as the Clements design, have been extensively used for MVM operations. However, as these architectures scale, improving stability and robustness becomes critical. In this paper, we introduce a novel photonic braid interferometer architecture that outperforms both the Clements and Fldzhyan designs in these aspects. Using numerical simulations, we evaluate the performance of these architectures under ideal conditions and systematically introduce non-idealities such as insertion losses, beam splitter imbalances, and crosstalk. The results demonstrate that the braid architecture offers superior robustness due to its symmetrical design and reduced layer count. Further analysis shows that the braid architecture is particularly advantageous in large-scale implementations, delivering better performance as the size of the interferometer increases. We also assess the footprint and total insertion losses of each architecture. Although waveguide crossings in the braid architecture slightly increase the footprint and insertion loss, recent advances in crossing technology significantly minimize these effects. Our study suggests that the braid architecture is a robust solution for photonic neuromorphic computing, maintaining high fidelity in realistic conditions where imperfections are inevitable.

Figures (7)

• Figure 1: Schematics of the three interferometer architectures under analysis for a 6x6 matrix. (a) Clements architecture clements_optimal_2016, with highlights of Type 1, Type 2, and $D$ layers. (b) Fldzhyan architecture fldzhyan_optimal_2020, offering improved fabrication tolerance. (c) Our proposed braid architecture.
• Figure 2: $\mathrm{Error} = 1-\mathrm{fidelity}$ in logarithmic scale of ideal components with 0 dB insertion loss, 0 dB imbalance, and -1000 dB crosstalk of the Clements clements_optimal_2016, Fldzhyan fldzhyan_optimal_2020 and braid architectures. The box plot of the best out of 5 repetitions across 1000 random unitary matrices is shown. The whiskers represent the minimum and maximum values, and the points indicate the sample density. A lower value of error indicates better performance.
• Figure 3: Fidelity results showing the median and interquartile range for different beam splitter non-idealities. These results are calculated based on the highest fidelities obtained from five initial conditions, for 1000 square matrices of size $N$=8. (a) All beam splitters have the same losses. (b) Gaussian truncated distribution of beam splitters insertion losses with an average of 0.5 dB. (c) All beam splitters have the same imbalance. (d) Gaussian distribution of imbalance. Clements and Braid have an average imbalance of 0 dB, while Fldzhyan has average imbalance of -3.5 dB.
• Figure 4: Fidelity braid results showing the median and interquartile range for different crossing non-idealities. These results are calculated based on the highest fidelities obtained from five initial conditions, for 1000 square matrices of size $N$=8. (a) All crossings have the same losses. (b) Gaussian truncated distribution of crossing insertion losses with an average of 0.2 dB. (c) All crossings have the same crosstalk. (d) Gaussian distribution of crosstalk with an average of -35 dB
• Figure 5: Fidelity results for different phase shifter non-idealities. These results are calculated based on the highest fidelities obtained from five initial conditions, for 1000 square matrices of size $N$=8. (a) All phase shifters have the same losses. (b) Gaussian truncated distribution of phase shifter insertion losses with an average of 1 dB.