Low-Depth Photonic Quantum Computing

• Low-depth photonic quantum computing is an approach that minimizes sequential optical operations to reduce photon loss and maintain quantum coherence.
• It integrates advanced hardware, such as deterministic photon sources and monolithically integrated circuits, to achieve compact, scalable quantum architectures.
• Innovative protocols including fusion-based and measurement-based schemes, along with optimized error correction, enable fault-tolerant and efficient quantum computation.

Low-depth photonic quantum computing refers to architectures, protocols, and devices enabling quantum computation with optical photons in circuits or networks that require a minimal number of sequential optical operations (“depth”). Reducing optical depth is essential to minimize loss accumulation, maintain photon indistinguishability, suppress decoherence, and reduce resource overheads. The field integrates advances in hardware (e.g., deterministic and multiplexed photon sources, integrated circuits, high-efficiency detectors), architectures (e.g., fusion-based models, cluster state generation, circuit-model and measurement-based schemes), and error-corrected protocols that operate efficiently even with realistic device imperfections.

1. Circuit Depth in Photonic Quantum Computing

Circuit depth in photonic quantum computing quantifies the number of sequential optical operations (layers of gates, beamsplitters, phase shifters, measurements, or fusions) a photon undergoes from preparation to final measurement. Low-depth circuits are desirable because:

• Photonic loss per element (propagation, switching, coupling) accumulates multiplicatively with depth, rapidly degrading multi-photon quantum interference.
• Limited depth enables larger, more scalable quantum computations before photon loss or decoherence destroys quantum advantage.
• Many error-correcting schemes, resource multiplexing strategies, and practical device designs benefit from shallower circuits.

Architectures are evaluated on their ability to implement universal quantum operations with constant or sublinear depth scaling relative to the number of qubits/modes, and on how well they suppress loss and errors as depth increases.

2. Hardware Approaches Enabling Low Depth

Recent progress in integrated photonic hardware and quantum emitter engineering has focused on reducing the optical depth per computation through a combination of material advances and system integration:

• Deterministic Photon Sources and Time-Bin Encoding: Quantum dot-based deterministic sources produce time-bin-encoded photons on demand, supporting the parallel construction of cluster states and deterministic linear cluster generation with minimal depth per photonic qubit (Chan et al., 22 Jul 2025). Such sources sharply reduce resource overheads compared to probabilistic spontaneous parametric processes, which usually must be multiplexed with deep switching networks (Sayem, 2023).
• Monolithically Integrated Photonic Circuits: Silicon photonics platforms have demonstrated complete modules—sources, manipulation, fusion, routing, and detection—on a single chip, achieving single-qubit state preparation and measurement fidelities of $99.98\% \pm 0.01\%$, Hong-Ou-Mandel interference between independent sources at $99.50\% \pm 0.25\%$, and two-qubit fusion fidelities at $99.22\% \pm 0.12\%$ (Alexander et al., 26 Apr 2024). Low optical depth arises naturally as qubits can be initialized, manipulated, and measured within a compact circuit.
• Passive, Switchless Networks: Architectures constructed solely from passive linear optics (beamsplitters, phase shifters, filters) without fast switch networks drastically reduce insertion loss and circuit complexity, supporting above-threshold photonic qubit generation and error correction in continuous-variable (CV) cluster state processors (Renault et al., 17 Dec 2024).
• Low-Depth Mesh Architectures for Linear Transformation: Compact beam-splitter meshes arranged in “circular” or partially mixing topologies can implement arbitrary (including nonunitary) transfer matrices with depth $D = N + 2$ for $N$ modes, as opposed to double or higher per conventional multimode mixing blocks. This compactness aids scalability and compatibility with planar fabrication (Fldzhyan et al., 1 Aug 2024).
• Unitary-Sum Matrix Decomposition: By representing a general nonunitary matrix $W$ as a sum of two unitaries, $W = \frac{1}{2}(U D V^\dagger + U D^* V^\dagger)$, parallel circuits can halve the depth versus the classic singular value decomposition (SVD)-based approach while maintaining analytical programmability (Fldzhyan et al., 27 Apr 2025).
• Optimized Switch and Mux Networks: Generalized Mach-Zehnder interferometer (GMZI) networks achieve permutation/multiplexing tasks with only one or two layers of active switching for $N$-to-$M$ routing, minimizing loss and error per photonic operation (Bartolucci et al., 2021).

3. Architectural and Protocol Strategies for Depth Reduction

Low-depth photonic computation requires architectural design choices integrated with error models and protocol planning:

• Fusion-Based Quantum Computing (FBQC): Finite-size photonic resource states are produced and subsequently fused, rather than attempting global cluster state production. This allows for modular architectures, low-connectivity networking, and parallelization of resource state generation and fusions, all leading to shallow computational depth per logical cycle (Chan et al., 22 Jul 2025, Bombin et al., 2021).
• Interleaved Modular and Delay-Line Architectures: By incorporating fiber or on-chip delay lines, a single resource-state generator can be time-multiplexed to contribute to a much larger computational slice, boosting effective qubit numbers without increasing circuit depth. Multi-length delays (1-cycle, $L$-delay, $L^2$-delay) “stretch” fusion graphs in time, enabling four logical distance-35 surface-code qubits per module and tolerating photon loss rates above 2% (Bombin et al., 2021).
• Synthetic Time-Dimensional Encoding: Schemes encoding qubits in time bins circulating in a fiber or resonator allow a single atom or quantum emitter to implement arbitrary quantum gates on many qubits sequentially, with the overall device footprint independent of computational depth. Operations are implemented by teleportation via adaptive measurement and do not require single-photon detectors (Bartlett et al., 2021).
• Measurement-Based Quantum Computing (MBQC) with Depth-Optimized Compilation: Circuit transformations, dynamic programming (DP) optimizations, and advanced rewrites in the ZX-calculus can reduce the number of cluster state measurement layers by over 50%, reusing otherwise “wasted” photons via optimal placement and anchoring of MBQC circuit components (Li et al., 2023, Zilk et al., 2022).

4. Computational Models Exploiting Depth Robustness

Boson sampling, as a restricted model of linear optical quantum computing (LOQC), exemplifies the ability to perform hard computational tasks at low circuit depth:

• Boson Sampling with Arbitrarily Low Purity and Fidelity: In the Boson-sampling paradigm, classical hardness arises from the statistics of multi-photon interference, robust to spectral impurity or partial distinguishability. Provided enough photons are used, with system size $n$ increased, the probability $p_{\text{hard}}$ that sufficiently many photons exhibit quantum interference tends toward one, even with arbitrarily low spectral purity or pairwise fidelity. This enables classically intractable algorithms without the need for high-depth error correction or filtering (Rohde, 2012).
• Measurement-Based and One-Way Models: Universal photonic quantum computing can be implemented with shallow circuits if cluster states are generated “on the fly” and only a finite “active block” of the overall lattice is stored at a time. Resource states are fused and measured in a window of fixed depth (roughly 10–20 layers), reducing the need for deep storage or long delay lines (Morley-Short et al., 2017).

5. Low-Depth Processors, Compilation, and Applications

• Universal Photonic Processors: Integrated multiport interferometers (e.g., 12-mode all-to-all-coupled devices) employ systematic networks of tunable beam splitters and phase shifters, supporting arbitrary unitary operations at low loss and limited depth. Such devices achieve circuit depths set by the number of physical interferometer stages required to implement a given transformation (e.g., 12 layers) and are suitable for Boson sampling, quantum simulation, and gate-based algorithms (Taballione et al., 2020, Maring et al., 2023).
• Variational Quantum Algorithms (VQAs) and Hardware-Efficient Ansatzes: In linear optical systems, VQAs can be matched to the available hardware—encoding qubits in photon spatial modes and using deeply reconfigurable interferometer meshes—so the entire variational circuit consists solely of passive elements and remains shallow (Agresti et al., 19 Aug 2024). Cost functions derived from Hamiltonians (e.g., for integer factorization or quantum chemistry) are evaluated via direct measurement in the computational basis.
• Laser-Written and Femtosecond-Fabricated Chips: Femtosecond laser writing enables rapid, low-loss, three-dimensional integration of photonic quantum logic, yielding two-qubit processors with low-depth gate stacks well suited for small-scale algorithms (e.g., VQE for H₂) with reduced calibration complexity (Skryabin et al., 2022).

6. Error Correction, Resource Overheads, and Fault Tolerance

• Hybrid Discrete/Bosonic and Continuous-Variable Protocols: Hybrid encoding combines discrete-variable (DV) and bosonic or continuous-variable (CV) qubit representations to exploit near-deterministic gate operations and near-ballistic (feedforward-free) measurements, reducing total circuit depth. Nearly deterministic hybrid Bell-state measurements and topological error correction support fault-tolerant architectures with loss thresholds exceeding 1% and practical resource overheads (Lee et al., 1 Oct 2025).
• Passive CV Cluster Generation and Magic State Injection: Switchless, all-passive photonic circuits using only linear optical elements, filtering, and homodyne detection can produce physical GKP qubits above the fault-tolerance threshold with $\gtrsim 90\%$ probability when Gaussian cluster squeezing of $12$–$13$ dB is reached. Innovative magic state generation schemes further boost the probability for successful non-Clifford injection without excessive squeezing demand (Renault et al., 17 Dec 2024).
• Switch and Mux Network Optimization: Advanced network designs provide low-loss optical paths for resource state multiplexing and feedforward logic, using abelian group–structured GMZI meshes and temporal “rastering” to achieve high muxing efficiencies and minimal switch depth—even for thousands of heralded source channels per photon generation module (Bartolucci et al., 2021).
• Resource and Error Metrics: Error analysis protocols (including physical error budgets for deterministic sources (Chan et al., 22 Jul 2025), loss thresholds for hybrid and surface-code schemes (Lee et al., 1 Oct 2025, Bombin et al., 2021), and normalized square error or root mean square error for matrix-vector multiplication circuits (Fldzhyan et al., 1 Aug 2024, Fldzhyan et al., 27 Apr 2025)) guide practical bounds on circuit depth, scaling, and feasible computation window.

7. Scalability and Future Directions

Advances in low-depth photonic quantum computing point toward scalable, manufacturable, and fault-tolerant quantum architectures:

• Manufacturability: Standard 300 mm CMOS-compatible photonic foundry processes enable scalable manufacture of all essential modules (sources, switches, gates, detectors) with high fidelity, paving the way for constructing millions of physical qubits on-chip (Alexander et al., 26 Apr 2024).
• Distributed and Modular Quantum Networks: High-fidelity chip-to-chip interconnects ($99.72\% \pm 0.04\%$) and time-multiplexing strategies enable extension from monolithic chips to large modular networks supporting fault-tolerant computation with low latency (Alexander et al., 26 Apr 2024, Bartlett et al., 2021).
• Algorithmic and Compilation Optimizations: Improved MBQC compilers using advanced techniques (ZX-calculus rewrites, component-wise dynamic programming) can halve or further reduce the effective cluster state depth required for a given application, directly decreasing execution time and photonic error exposure (Li et al., 2023, Zilk et al., 2022).
• Broader Applications: Low-depth, compact, and error-tolerant photonic circuits extend beyond universal quantum computing to photonic neural networks, iterative solvers, high-dimensional Boson sampling, quantum machine learning, and optical simulation platforms (Fldzhyan et al., 1 Aug 2024, Agresti et al., 19 Aug 2024).

Collectively, these developments provide a comprehensive blueprint for practical, low-depth photonic quantum computation, offering tractable resource requirements and robustness to error, and supporting both near-term quantum advantage and the longer-term goal of universal, scalable fault-tolerant quantum computing using photons.