Photonic-computing error correction through optical en-/decoder calibrations

TL;DR

This work addresses the pervasive analog errors in photonic matrix-vector multipliers (PMVMPs) by introducing a general, hardware-free error-correction scheme that offsets the optical en-/decoders with complex factors. By engineering 2N complex degrees of freedom through encoder amplitude scaling $|\

Abstract

Photonic processors have emerged as an attractive platform for fast and energy-efficient matrix-vector multiplication. However, they are susceptible to error due to their analog nature. Here, we present an error-correction technique that implements a correction offset to the optical en-/decoders of photonic processors. Our proposed method is general-purpose, does not require introducing any additional components to the photonic network, and can address errors stemming from unbalanced losses, 50/50 beamsplitter deviations, digital-to-analog conversion inaccuracies, and any unknown sources. In particular, we show that our method is highly effective in mitigating unbalanced-loss errors, a problem that has not previously been addressed by any error-correction technique. Using this approach, we achieve over 90% error reduction in large triangular meshes, overcoming a key obstacle to highly accurate photonic processors for information processing.

Figures (5)

• Figure 1: Schematic representation of a photonic matrix-vector multiplication processor consisting of an optical splitting tree that distributes the input laser source to an optical encoder, a photonic mesh, and an optical decoder. Vector data is encoded from digital information onto optical fields defined by the encoder mapping. The output optical vector is converted back into digital data defined by the decoder mapping. The en-/decoder mappings are shown here as black "$\ast$" representing voltage/current pairs as discrete points for simplicity. Scaling these mappings along the amplitude axis and shifting them along the phase axis corresponds to applying a complex factor $\eta$ to each in/output, providing 2N complex degrees of freedom for error correction.
• Figure 2: Example of a Mach-Zehnder modulator for encoding complex input data ($x_i=A_ie^{i\varphi_i}$) and its conversion mappings to tuning voltages ($V_1$ and $V_2$). (a) The amplitude is encoded from the difference in tuning voltages mapped by the solid line. Rescaling this mapping to the dashed line implements a correction factor of $|\eta_i|$ in amplitude (a correction factor of $|\eta_i|=0.8$ is chosen for illustrative purposes). (b) The phase is encoded from the sum of the tuning voltages mapped by the solid line. Shifting this mapping to the dashed line corresponds to adding a constant phase shift of, $\Delta\varphi_i$, to the encoded phase, $\varphi_i$.
• Figure 3: Example of a homodyne detection scheme for decoding, where the output data, $y_j$, is extracted by interfering with an oscillating reference signal (local oscillator), thus measuring the quadratures of the signal from the differences in photocurrents. Scaling of both the real and imaginary axes by some factor corresponds to implementing an amplitude correction factor exemplified here as $|\eta_j'|=0.5$. Implementing phase corrections can also be achieved by rotation of the complex plane.
• Figure 4: (a) The average matrix error for a $N=32$ universal multiport interferometer for the triangular mesh (red) or rectangular mesh (blue) with no error corrections (solid line), with error correction on either the encoder or decoder (dashed line) and with error correction on both the encoder and decoder (dotted line). (b-c) The normalized average correction factor amplitude for each input port for the triangular and rectangular mesh with a 0.2 dB unit-cell loss using both input and output correction. A small $N=4$ triangular and rectangular mesh is shown in each figure for conceptual clarity. The matrix error and correction factor have been averaged across $10^5$ Haar-random unitary matrices as a function of a constant loss of each unit cell in the mesh. The unit-cell loss is the only non-ideality in this simulation, and the non-ideal matrix has been normalized to account for the overall loss $\hat{U}\to \hat{U}/||\hat{U}||$. Note that the symmetric nature of the meshes leads to effectively the same performance for correcting on either the encoder or the decoder.
• Figure 5: The average relative matrix error reduction for various non-idealities such as unbalanced losses in a triangular mesh (red), unbalanced losses in a rectangular mesh (blue), DAC errors (magenta), 50/50 beam splitter deviations (green), and Gaussian-distributed errors in matrix elements (yellow). To account for overall losses, the non-ideal matrices have been normalized $\hat{U}\to \hat{U}/||\hat{U}||$. The matrix errors are averaged over $10^3\times 256/N$ Haar-random unitary matrices.