Recirculating Bricks Mesh Architecture

• Recirculating Bricks Mesh Architecture is a programmable photonic processor built from a 2D array of MZIs arranged in a bricks pattern, enabling multidirectional signal routing and recirculation.
• It achieves efficient optical transformations by reusing a compact region for complex unitary operations, reducing the number of active MZIs by more than a factor of 13 compared to feed-forward meshes.
• The design supports versatile applications in photonic neural networks, quantum photonics, and matrix operations, with integrated calibration and self-stabilization for practical deployment.

Searching arXiv for papers on “recirculating bricks mesh architecture” and closely related uses of “Brick” across photonics and building-data semantics. “Recirculating Bricks Mesh Architecture” denotes, in its explicit and technically precise usage, a programmable photonic processor built from a two-dimensional shifted rectangular, or “bricks,” waveguide mesh of Mach–Zehnder interferometers (MZIs), whose defining property is multidirectional signal propagation with path reuse and recirculation rather than strictly one-way feed-forward transmission (Gosciniak, 20 Apr 2026). In adjacent literatures, the same phrase is either absent or only approximate: building-data papers use Brick to denote an ontology and graph schema rather than a photonic fabric, while modular-construction papers use bricks to denote discrete physical units. This suggests that the term is best treated as domain-specific rather than universal, with programmable photonics providing the clearest exact definition and several other fields providing analogical or partial uses (Vittori et al., 2023).

1. Definition and conceptual scope

In the photonics literature, the architecture is explicitly presented as a programmable recirculating “bricks” mesh architecture for photonic neural networks, quantum photonics, and distillation protocols (Gosciniak, 20 Apr 2026). Its core idea is that a compact planar mesh of programmable interferometric elements can be reused by routing light through the same programmable region multiple times, so that a smaller physical substrate can emulate more complex transformations.

A common misconception is to read the phrase as a building-services term referring to hydronic recirculation loops, return-air recirculation, or a building “mesh” protocol. That reading is not supported by the building-semantics paper “BIM-to-BRICK,” which states that “Recirculating Bricks Mesh Architecture” is not a term the authors use explicitly and that the work does not present a dedicated “recirculating” subsystem architecture in that sense; the closest supported concept is a BRICK-based semantic building graph integrating BIM, IoT, BMS, HVAC, and occupant data (Vittori et al., 2023).

The same caution applies to modular façade systems. The photobioreactor façade paper is highly relevant because it describes a distributed mesh of interconnected “neutralization bricks” with an air circulation system, yet it does not rigorously define a full closed-loop recirculation circuit with return headers, pressure balancing, or flow-balance equations. Its relevance is therefore architectural and analogical rather than terminological (Liu, 9 Mar 2025).

2. Photonic topology and optical model

The photonic recirculating bricks mesh is a two-dimensional lattice of waveguides and MZIs arranged in a shifted rectangular or “bricks” pattern. Its unit cell contains 2 to 4 MZIs, whereas a hexagonal mesh requires 6 MZIs per unit cell; the mesh uses a 3-point interconnection scheme rather than the 4-point connectivity of a regular square mesh, and all ports may serve as inputs or outputs on all four sides of the mesh (Gosciniak, 20 Apr 2026). These properties jointly reduce path length and propagation loss while enlarging routing freedom.

Its recirculating character comes from the fact that light is not constrained to a single pass. Signals may propagate horizontally, vertically, backward, and through loops, so photons can traverse a smaller programmable and tunable component multiple times to simulate a larger, more complex unitary transformation (Gosciniak, 25 May 2026). This distinguishes the architecture from Reck and Clements meshes, whose propagation is essentially one-directional and whose circuit depth scales directly with the implemented unitary.

The local programmable element is the MZI. The architecture employs both symmetric MZIs (sMZIs) and asymmetric MZIs (aMZIs). In the formulation used for the neural-photonics paper, the 50:50 beam splitter and phase shifter are written as

$$U_{BS}=\frac{1}{\sqrt{2}} \begin{bmatrix} 1 & i\ i & 1 \end{bmatrix}, \qquad U_{PS}= \begin{bmatrix} e^{i\phi} & 0\ 0 & 1 \end{bmatrix},$$

and the symmetric MZI takes the factored form

$$U_{sMZI}= i e^{i(\phi_1+\phi_2)/2} \begin{bmatrix} \cos\!\left(\frac{\phi_1-\phi_2}{2}\right) & \sin\!\left(\frac{\phi_1-\phi_2}{2}\right)\ -\sin\!\left(\frac{\phi_1-\phi_2}{2}\right) & \cos\!\left(\frac{\phi_1-\phi_2}{2}\right) \end{bmatrix}.$$

The differential phase controls effective coupling, while the common phase contributes only a global phase factor (Gosciniak, 20 Apr 2026).

Architecturally, the claimed benefit is not merely universality but efficiency. Compared with feed-forward rectangular and triangular meshes, the bricks architecture is described as having significantly reduced optical depth, and the number of active MZIs required for arbitrary linear transformations is reported to be reduced by more than a factor of 13 (Gosciniak, 20 Apr 2026).

3. Neural-network and linear-operator realizations

Within photonic neural networks, the mesh functions as the optical interference unit (OIU) for matrix-vector multiplication and hosts the nonlinear optical function unit (NOFU) for activation. The paper writes neural computation in McCulloch–Pitts form as

$$z_j=\sigma\!\left(\sum_i w_{ij}x_i\right), \qquad y_j=\sum_i w_{ij}x_i,$$

with optical amplitudes and phases carrying the inputs and MZI settings encoding the weights (Gosciniak, 20 Apr 2026).

A notable architectural claim is that the same physical mesh can be reprogrammed as a crossbar network, optical interference circuit with variable structure, FIR filter, IIR filter, or matrix operator subject to Singular Value Decomposition. The SVD factorization is written as

$W = U \Sigma V^{\dagger},$

with the two unitary factors implemented by programmable interferometer meshes and the diagonal factor implemented by optical attenuators (Gosciniak, 20 Apr 2026). The same work also presents binary-tree layers and diagonal-line layers as alternative organizations of the unitary factors, both compatible with layer-by-layer power optimization.

The crossbar interpretation is especially important because it departs from the usual $O(N^2)$ hardware growth of feed-forward meshes. Standard feed-forward $N\times N$ unitary meshes require exactly

$\frac{N(N-1)}{2}$

MZIs, whereas the paper claims that in the proposed recirculating bricks topology the total number of MZI units scales with $N$ for the relevant topology considered (Gosciniak, 20 Apr 2026). This is a strong architectural claim rather than a general theorem for all workloads.

The architecture also changes where nonlinearities may be inserted. Instead of treating the NOFU as a separate photonic layer, the paper states that nonlinear activation can be realized within any vertical lines of the mesh. The nonlinearities explicitly mentioned are saturable absorption and optical bistability (Gosciniak, 20 Apr 2026). A plausible implication is that the architecture supports more heterogeneous computational graphs than strictly layered photonic neural networks.

4. Quantum photonics and distillation protocols

For quantum photonics, the same mesh is proposed as a programmable linear-optical processor for boson sampling, photon indistinguishability metrology, and temporal-mode processing through loops (Gosciniak, 1 Apr 2026). In the standard operator language used there,

$a_i^\dagger \to \sum_{j=1}^{m} U_{ij} a_j^\dagger,$

and multi-photon transition probabilities are governed by permanents:

$$P_{S,V}=\frac{|\mathrm{Per}(U_{S,V})|^2}{S_1!\cdots S_m!\,V_1!\cdots V_m!}.$$

The architecture is presented as especially attractive because detection can occur on all sides of the mesh, increasing accessible mode usage without requiring a monolithic feed-forward interferometer (Gosciniak, 1 Apr 2026).

The resource comparisons are central. For $$U_{sMZI}= i e^{i(\phi_1+\phi_2)/2} \begin{bmatrix} \cos\!\left(\frac{\phi_1-\phi_2}{2}\right) & \sin\!\left(\frac{\phi_1-\phi_2}{2}\right)\ -\sin\!\left(\frac{\phi_1-\phi_2}{2}\right) & \cos\!\left(\frac{\phi_1-\phi_2}{2}\right) \end{bmatrix}.$$0 modes, the paper describes a bricks mesh with 10 horizontal symmetric MZIs, 28 vertical modified MZIs, and 38 MZIs total, compared with approximately 496 MZIs in a comparable feed-forward architecture. For $$U_{sMZI}= i e^{i(\phi_1+\phi_2)/2} \begin{bmatrix} \cos\!\left(\frac{\phi_1-\phi_2}{2}\right) & \sin\!\left(\frac{\phi_1-\phi_2}{2}\right)\ -\sin\!\left(\frac{\phi_1-\phi_2}{2}\right) & \cos\!\left(\frac{\phi_1-\phi_2}{2}\right) \end{bmatrix}.$$1 modes, it gives 21 horizontal symmetric MZIs, 42 vertical modified MZIs, and 63 MZIs total, compared with 946 MZIs in a feed-forward realization (Gosciniak, 1 Apr 2026). The same work also argues that temporal modes can be handled with programmed loops; the minimum cavity size is 4 BULs, and with $$U_{sMZI}= i e^{i(\phi_1+\phi_2)/2} \begin{bmatrix} \cos\!\left(\frac{\phi_1-\phi_2}{2}\right) & \sin\!\left(\frac{\phi_1-\phi_2}{2}\right)\ -\sin\!\left(\frac{\phi_1-\phi_2}{2}\right) & \cos\!\left(\frac{\phi_1-\phi_2}{2}\right) \end{bmatrix}.$$2 the corresponding round-trip time is about 30 ps, yielding a spectral period of about 34 GHz (Gosciniak, 1 Apr 2026).

The architecture has also been specialized to photon-distillation protocols, particularly cascaded Hong–Ou–Mandel interferometers and Fourier-transform-based schemes (Gosciniak, 25 May 2026). In the HOM case, a standard feed-forward realization of the $$U_{sMZI}= i e^{i(\phi_1+\phi_2)/2} \begin{bmatrix} \cos\!\left(\frac{\phi_1-\phi_2}{2}\right) & \sin\!\left(\frac{\phi_1-\phi_2}{2}\right)\ -\sin\!\left(\frac{\phi_1-\phi_2}{2}\right) & \cos\!\left(\frac{\phi_1-\phi_2}{2}\right) \end{bmatrix}.$$3 purification gate requires two MZI layers, whereas the recirculating bricks mesh realizes the same operation with one MZI layer. For a larger cascaded purification tree, the layer count drops from three layers to two layers, or even one layer in a more compact configuration (Gosciniak, 25 May 2026).

For Fourier-based distillation, the paper uses the quantum Fourier transform and the zero-transmission law. In the 4-mode example, the heralded error is stated as

$$U_{sMZI}= i e^{i(\phi_1+\phi_2)/2} \begin{bmatrix} \cos\!\left(\frac{\phi_1-\phi_2}{2}\right) & \sin\!\left(\frac{\phi_1-\phi_2}{2}\right)\ -\sin\!\left(\frac{\phi_1-\phi_2}{2}\right) & \cos\!\left(\frac{\phi_1-\phi_2}{2}\right) \end{bmatrix}.$$4

and the resource count drops from 6 beam-splitter/phase-shifter pairs in feed-forward meshes to 4 in the recirculating bricks realization. For the 8-mode DFT, the comparison is 12 versus 28 (Gosciniak, 25 May 2026). The paper argues that these schemes are unattainable using feed-forward networks without out-of-plane 3D integration, because arbitrary directional routing and all-side I/O are intrinsic to the bricks mesh.

5. Characterization, self-calibration, and stabilization

Recirculation increases functional flexibility but also complicates calibration. The characterization paper on recirculating waveguide meshes studies this problem for meshes built from tunable basic units (TBUs) implemented as symmetric MZIs (Tao et al., 2024). Each TBU is modeled by an imperfect scattering matrix with beam-splitter parameters, upper and lower arm phases, phase-voltage curves, and group index. The characterization strategy is a staged four-step procedure: first obtain the passive phase difference and phase-voltage curves, then extract group index from free spectral range, then reduce the passive-phase ambiguity to two candidates, and finally optimize a reduced parameter set with Particle Swarm Optimization (Tao et al., 2024).

The method is validated on a mesh with 36 TBUs. Across 10 experiments, 95% of BS-ratio characterization errors are below 1.34%, 95% of $$U_{sMZI}= i e^{i(\phi_1+\phi_2)/2} \begin{bmatrix} \cos\!\left(\frac{\phi_1-\phi_2}{2}\right) & \sin\!\left(\frac{\phi_1-\phi_2}{2}\right)\ -\sin\!\left(\frac{\phi_1-\phi_2}{2}\right) & \cos\!\left(\frac{\phi_1-\phi_2}{2}\right) \end{bmatrix}.$$5 characterization errors are below 0.00267 \pi, 85% of multi-frequency prediction errors are below 0.55 dB, and the average RMSE = 0.34 dB (Tao et al., 2024). Robustness tests further report that even with $$U_{sMZI}= i e^{i(\phi_1+\phi_2)/2} \begin{bmatrix} \cos\!\left(\frac{\phi_1-\phi_2}{2}\right) & \sin\!\left(\frac{\phi_1-\phi_2}{2}\right)\ -\sin\!\left(\frac{\phi_1-\phi_2}{2}\right) & \cos\!\left(\frac{\phi_1-\phi_2}{2}\right) \end{bmatrix}.$$6 the RMSE remains below 1.0 dB, and the method is also tested under inaccurate mesh measurements and insertion-loss uncertainty. The same paper applies the characterized model to 6 different kind of FIR/IRR filters, showing that ideal-assumption programming is inadequate whereas characterization-informed programming recovers the intended responses (Tao et al., 2024).

A complementary line of work emphasizes embedded monitoring and feedback. The neural-photonics paper describes the bricks mesh as an excellent substrate for a monitoring system that measures power in each location of the circuit and then self-calibrates and stabilizes the processor using a Wheatstone bridge arrangement with a calibration-free feedback loop (Gosciniak, 20 Apr 2026). The monitor is said to produce a voltage output directly, avoiding current-to-voltage conversion, and the feedback can drive upstream or downstream actuators to compensate process tolerances and thermal drift in real time. This suggests that practical recirculating meshes are not only optical layouts but also control-intensive cyber-physical systems.

6. Analogous uses beyond photonics

Outside photonics, the phrase becomes approximate and domain-dependent. In building informatics, the closest analogue is a semantically linked, multi-source building graph rather than an optical mesh. “BIM-to-BRICK” presents an automated pipeline that converts BIM, BMS metadata, and occupant-related external data into a single RDF knowledge graph. On the SDE4 building in Singapore, it generated a bidirectional link between a BIM model of 932 instances and data for 17 subjects into 458 BRICK objects and 1219 relationships in 17 seconds (Vittori et al., 2023). A later offline platform for Brick transformation similarly emphasizes a tree-based graph structure, processing approximately 7800 labels, matching approximately 7400 point labels with Brick classes, and leaving approximately 400 unmatched (Teymourzadeh et al., 18 Sep 2025). These works do not define a recirculating bricks mesh architecture explicitly; the supported interpretation is a semantic interoperability fabric built from Brick ontology and graph relations.

A more literal brick-and-circulation analogue appears in the modular photobioreactor façade literature. The façade is composed of “neutralization bricks” containing algae, built-in piping, magnetic connectors, and an air circulation system. The realized prototype used 28 bricks, three types of cells, and four types of pipes in a 3 ft by 5 ft façade; each brick took about 15 hours to print and used less than 0.5 kg of PLA (Liu, 9 Mar 2025). The paper states that one external air pump can transport air to all parts of the façade through the integrated pipeline system. It does not, however, provide a fully quantified recirculating manifold with pressure-drop or flow-balance analysis, so the correspondence to the photonic sense remains partial.

In self-assembly and modular materials, “brick” and “mesh” again denote different objects. In DNA-brick self-assembly, boundary bricks are rigid dimers of two standard brick particles; they lower the nucleation barrier and edge boundary bricks stabilize the final structure, but they are also more aggregation-prone, and the paper concludes that maximizing the total number of boundary bricks is not an optimal strategy (Wayment-Steele et al., 2017). In lunar construction, laser-sintered regolith is used to produce interlocking “H”-shaped female and “+”-shaped male bricks; the measured peak compressive stress is ~1.5 MPa, with strength in the scan direction more than 2× higher than in the thickness direction (McCallum et al., 5 Jun 2025). Neither paper defines a recirculating bricks mesh architecture, but both support the broader idea that discrete brick units can be selectively placed, connected, and reconfigured.

A final computational analogue appears in BrickAnything, which treats brick assemblies as connectivity structures rather than mere coordinate lists. It builds a vertical attachment graph, serializes it as a structure-aware tree tokenization, and adds validity-constrained decoding plus adaptive rollback to improve buildability (Ni et al., 25 May 2026). On the challenging subset, the full system reports CD 0.1299, IoU 0.586, rollback 0.422, stable 83.4%, and valid 100% (Ni et al., 25 May 2026). This does not instantiate a recirculating mesh in the photonic sense, but it does provide an explicit model of repeated local attachment and corrective regeneration. A plausible implication is that the idea of “recirculation” can be generalized, across domains, from literal signal loops to iterative reuse of local structure and selective regeneration.