Implementation of distillation protocols using a recirculating bricks mesh network

Abstract: General-purpose programmable photonic processors provide a flexible foundation for integrating various functionalities within a single chip. A two-dimensional bricks waveguide mesh of Mach Zehnder interferometers has been demonstrated to possess considerable potential in the domain of photonic neural networks and quantum signal processing. In this article, we propose an expansion of the available applications of recirculating bricks mesh architecture to distillation protocols necessary for quantum signal processing. These protocols are essential for the heralding of the output of single photons, which is characterized by a reduced distinguishability error rate. The demonstration will be made of a single programmable optical system's ability to realize various distillation protocols with reduced computational resource costs. The present study will concentrate on cascaded quantum interferometers and Fourier transform-based schemes. It will demonstrate that the bricks mesh can implement such schemes, which are unattainable using feed-forward networks, without the need for complex out-of-plane integration. The propagation of the signal in any direction, along with the utilization of all ports as both input and output, facilitates the execution of such transformations with minimal optical depth of the circuit and in time scales shorter than the decoherence time.

• The paper introduces a recirculating bricks mesh network that achieves up to a twofold enhancement in reconfiguration and reduced optical losses versus traditional feed-forward architectures.
• The paper shows a twofold reduction in network depth for photon distillation, yielding a 2.2x improvement in photon indistinguishability.
• The paper leverages a QFT-based design to decrease circuit elements, supporting scalable, fault-tolerant photonic quantum computing.

Recirculating "Bricks" Mesh Networks for Photonic Distillation Protocols

Photonic Mesh Architectures and Quantum Information Processing

The integration of programmable photonic processors has led to substantial advances in scalable quantum signal processing, specifically in the generation and manipulation of multiphoton states essential for photonic quantum computing. Traditional architectures for unitary transformations, such as triangular (Reck) and rectangular (Clements) mesh networks, are constrained by unidirectional signal flow and resultant limitations in circuit versatility and reconfigurability. This paper introduces the recirculating "bricks" mesh network, a two-dimensional lattice of MZIs, as an alternative with improved scalability, reconfigurability, and reduced optical losses compared to conventional feed-forward architectures.

The recirculating "bricks" mesh achieves higher reconfiguration performance—attaining up to 12 distinct filter configurations with only 25 MZIs, a twofold enhancement relative to regular square meshes—by leveraging its compact interconnection scheme and the capacity for bidirectional signal propagation. The reduction of optical path length directly yields lower propagation losses and a minimized circuit footprint, crucial for maintaining photon indistinguishability and operational fidelity within the decoherence time.

Distillation Protocols in Programmable Photonic Systems

Distillation protocols constitute a pivotal technique for purification of photon states, enhancing indistinguishability to suppress logical errors in photonic quantum computation. Conventional feed-forward networks require complex, multilayered arrangements of beam splitters and phase shifters for such protocols, thereby increasing optical depth and resource consumption. The recirculating "bricks" mesh architecture circumvents these constraints, implementing distillation gates and cascaded HOM interferometers with fewer layers and reduced circuit complexity. Notably, for two-photon distillation, the paper demonstrates a reduction from two MZI layers in feed-forward networks to a single layer in the recirculating mesh, resulting in a twofold decrease in network depth and propagation losses.

The paper provides quantitative evidence: the distillation gate achieves a 2.2x reduction in indistinguishability error post-distillation. Furthermore, in a tree-configured protocol for purifying multiphoton states, the circuit depth is reduced from three layers (four beam splitters) in feed-forward configurations to one or two layers in the bricks mesh, thus suppressing losses and improving heralding efficiency.

Multiphoton Interference and Quantum Fourier Transform Implementation

Suppressing computational resource costs in multiphoton interference protocols is addressed via the implementation of Quantum Fourier Transform (QFT) interferometers. Fourier-based suppression laws (zero-transmission laws) ensure that for fully indistinguishable input states, specific output configurations are eliminated, efficiently filtering the photon state space and facilitating benchmarking of genuine n-photon indistinguishability. The recirculating bricks mesh leverages symmetries in the QFT, reducing required beam splitters and phase shifters to $O(m/2 \log_2 m)$ for $m$ modes, compared to $O(m^2)$ for conventional decompositions.

Barak and Ben-Aryeh's quantum fast Fourier transform (qFFT) scheme, rooted in the Cooley-Tukey algorithm, is directly translatable onto the bricks mesh architecture, achieving significant reductions in circuit elements. For example, a two-qubit DFT necessitates four pairs of beam splitters and phase shifters in the bricks mesh versus six in feed-forward meshes; a three-qubit DFT with eight modes requires twelve pairs versus twenty-eight. The two-dimensional integration available in the bricks mesh eliminates the need for out-of-plane interconnects, facilitating planar fabrication and minimizing losses.

Practical and Theoretical Implications

The recirculating "bricks" mesh network represents a robust platform for photonic quantum technologies, providing practical benefits in reduced hardware footprint, minimized insertion loss, and programmability for diverse quantum protocols. Its compatibility with advanced monitoring and auto-stabilization strategies (e.g., Wheatstone bridge feedback loops using TCOs) enhances stability and compensates for thermal drift and fabrication tolerances in real time.

From a theoretical perspective, the bricks mesh enables the efficient realization of unitary transformations previously unattainable in feed-forward architectures, supporting advanced distillation schemes and multiphoton interference protocols across all possible symmetries. This positions the architecture for scalable fault-tolerant photonic quantum computation and high-fidelity quantum state engineering. Speculatively, the bricks mesh's versatility and efficiency may enable novel hybrid approaches in photonic neural networks and quantum machine learning, leveraging dynamic reconfigurability and rapid information processing.

Conclusion

This work establishes that recirculating "bricks" mesh networks provide a highly efficient and configurable substrate for implementing photonic distillation protocols, cascaded HOM interferometers, and QFT-based multiphoton interference schemes. The architecture delivers strong numerical results in reducing network depth, optical losses, and resource requirements compared to feed-forward meshes. Its capacity for universal reconfigurability and planar integration addresses fundamental scalability and loss challenges, strengthening the foundation for advanced photonic quantum processors and heralded quantum information protocols (2605.25911).