Reconfigurable devices which can implement arbitrary unitary operations are crucial for photonic quantum computation, optical neural networks, and boson sampling. Here, we address the problem of, using multiport interferometers, approximating with a given infidelity any pure-state preparation and any unitary operation. By means of numerical calculations, we show that pure states, in any dimension
d, can be prepared with infidelity $\ensuremath{\le}{10}^{\ensuremath{-}15}$ with three layers of
d-dimensional Fourier transforms and three layers of configurable phase shifters. We also present numerical evidence that
d+1 layers of
d-dimensional Fourier transforms and
d+2 layers of configurable phase shifters can produce any unitary operation with infidelity $\ensuremath{\le}{10}^{\ensuremath{-}14}$. The conclusions are achieved by numerical simulations in the range from
d=3 to
d=10. These results are interesting in light of the recent availability of multicore fiber-integrated multiport interferometers.
Reconfigurable devices capable to implement any unitary operation with a given fidelity are crucial for photonic universal quantum computation, optical neural networks, and boson sampling. Here, we address the problems of approximating with a given infidelity any unitary operation and any pure state using multi-port interferometers, which are of current interest due to the recent availability of multi-core fiber integrated multi-port interferometers. We show that any pure state, in any dimension
d, can be prepared with infidelity
≤10−15 with
3~layers of
d-dimensional Fourier transforms and
3~layers of configurable phase shifters. In contrast, the schemes in [Phys. Rev. Lett. \textbf{73}, 58 (1994) and Optica \textbf{3}, 1460 (2016)], require optical depth
2(d−1). We also present numerical evidence that
d+1~layers of
d-dimensional Fourier transforms and
d+2~layers of configurable phase shifters can produce any unitary with infidelity
≤10−14, while the scheme in [Phys. Rev. Lett. \textbf{124}, 010501 (2020)] only achieves an infidelity in the order of
10−7 for block-diagonal unitary transformations
Universal multiport interferometers (UMIs) have emerged as a key tool for performing arbitrary linear transformations on optical modes, enabling precise control over the state of light in essential applications of classical and quantum information processing such as neural networks and boson sampling. While UMI architectures based on Mach–Zehnder interferometer networks are well established, alternative approaches that involve interleaving fixed multichannel mixing layers and phase masks have recently gained interest due to their high robustness to losses and fabrication errors. However, these approaches currently lack optimal analytical methods to compute design parameters with a low optical depth. In this work, we introduce a constructive decomposition of unitary matrices using a sequence of 2 N +5 phase masks interleaved with 2 N +4 discrete Fourier transform matrices. This decomposition can be leveraged to design universal interferometers based on phase masks and multimode interference couplers, implementing a discrete Fourier transform, offering an analytical alternative to conventional numerical-optimization-based designs and reducing by a factor of 3 the previous best-known analytical methods.