Every day, the world produces about several exabytes (1018) of data at an exponentially growing rate [1]. The need to process such a flow of information, increase the speed of its transmission, as well as the widespread use of artificial intelligence methods require an increase in the computers performance. However, this process has hardware limitations associated with an increase in power consumption, the limits of miniaturization and speed of silicon transistors, as well as the limit of performance growth when parallelizing calculations.

One of the ways to overcome these obstacles is to use optical photonic integrated circuits (PIC) [2] in the design of traditional processors.

Using PIC, ultra-fast execution of vector-matrix operations is carried out, used, for example, in machine learning tasks [3], [4], [5], [6] and modern telecommunication standards. The operation of matrix–vector multiplication is implemented here by passing an ordered set (vector) of optical signals (modes) through a multilayer optical network formed by cascades of planar Mach–Zehnder interferometers (MZI) [7], [8], [9]. Physically, the role of a vector is played by a set of input modes, and the action of a linear matrix operator corresponds to phase shifts and attenuation of the intensities of optical signals at interferometers.

Unlike an electronic computing device that needs to perform m(2n−1) scalar operations during a sequential algorithm for multiplying an (m×n)-matrix by a vector, the PIC performs this action in one clock cycle at the speed of light propagation in the network . Thermal losses are insignificant, which increases the energy efficiency of PIC by several orders of magnitude compared to classical electronics.

The main obstacles to scaling optical networks include manufacturing errors, optical losses, scattering loss due to sidewall roughness, and the finite accuracy of digital-to-analog conversions of control signals into voltages at phase shifters [10]. Over the past decade, a number of works [4], [8], [9], [10], [11], [12] have proposed optical network topologies and algorithms for their optimization that circumvent some of these difficulties.

A planar MZI, which is the basic element of the PIC, can be manufactured using three classes of materials:

optically nonlinear ferroelectric crystals, such as, for example, lithium niobate [13];

silicon-containing thin-film structures, in particular, based on the silicon-on-insulator (SOI) system, as well as silicon nitrides and oxynitrides [14], [15] [see Fig. 1(b)];

quantum-sized thin-film structures, in particular, based on indium phosphide, germanium-silicon solid solutions and other systems [16], [17].

At the same time, the principles of vector-matrix multiplications that can be performed by MZI are universal and do not depend on the specific method of implementation of the device. Therefore, to test the calculations made in the work using a computer experiment, we chose a platform based on lithium niobate as the simplest and most intuitive from the point of view of constructing a numerical model.

In this work, we consider a single MZI (see Fig. 1), the directional couplers of which have splitting errors due to inaccuracy in maintaining the distance between the waveguides and the interaction length. For such an interferometer, using the error vector magnitude (EVM) we obtain two estimates of the calculation accuracy, depending on the splitting error. The first estimate is obtained as a measure of the difference between the transformation matrices implemented by interferometers and is presented in the form of the norm of the difference between two unitary matrices corresponding to ideal and non-ideal interferometers. The second estimate is obtained as a measure of the difference in output intensities. It is shown that in this case the accuracy of the operation depends not only on the errors in the couplers, but also on the parameters of the input signals. This means that the proximity of the transformation matrices does not guarantee the preservation of the proximity of the calculation results.