Universal linear manipulation via routing and projective measurements

Overview

Multiport interferometers are essential components in classical and quantum photonics, used for tasks ranging from optical neural networks to boson sampling. Traditionally, these devices are designed to be universal, meaning they can implement any unitary transformation in an N-dimensional Hilbert space. However, such designs (like the Reck or Clements schemes) require a large number of Mach-Zehnder interferometers (MZIs) and detectors, which increases the physical footprint, power consumption, and susceptibility to losses.

The Routing Approach

This paper introduces 'routing' and 'multi-routing' schemes that leverage the fact that, in many photonic applications, detectors do not need to operate simultaneously. By using a single detector (or fewer detectors than the total number of modes) and performing multiple projective measurements over sequential time intervals, the authors show that the same unitary transformations can be achieved with a drastically reduced number of MZIs.

For a system with N modes, universal schemes require N(N-1)/2 MZIs. The proposed routing schemes reduce this requirement to N-1 MZIs. The authors provide a constructive algorithm for these architectures, demonstrating that by configuring the phases of these fewer components, one can route specific input states to a reference output mode, effectively mimicking the behavior of a full universal interferometer.

This work provides a framework for optimizing photonic hardware by trading temporal resources for spatial ones. By minimizing the number of MZIs and detectors, these schemes are inherently more robust against unbalanced coupling losses and reduce the complexity of control systems. This is particularly advantageous for large-scale photonic circuits where the 'cost' of physical components—in terms of space, power, and fabrication yield—is a significant bottleneck. The generalization to multi-photon states for scattershot boson sampling further extends the utility of these designs to quantum information processing tasks.