We propose a scheme to compute Pauli error rates in photonics-based quantum error correction using experimental observables of single photons produced from quantum emitters. We show that first-order coherence measurements and first-order cross correlations, which can be implemented using photon counting, can extract single-photon and entangled single-photon wavefunctions in the presence of imperfections due to photon distinguishability, laser noise, and photon loss. Leveraging this, we show that the wavefunction of any entangled state of noisy photons produced from a single quantum emitter can be expressed in matrix-product-state form and can be used to analytically compute the expectation value of the stabilizer generators of the corresponding entangled state. From this we obtain analytic expressions for the Pauli error probabilities in terms of the photon noise parameters. Furthermore, we calculate Pauli error maps for entangled photons after undergoing Bell- state measurements in terms of these parameters. Our work provides a method to use experimental measurements to determine the required quality of photons produced from quantum emitters for fault-tolerant fusion-based photonics quantum computing.
We propose a scheme to compute Pauli error rates in photonics-based quantum error correction using experimental observables of single photons produced from quantum emitters. We show that first-order coherence measurements and first-order cross correlations, which can be implemented using photon counting, can extract single-photon and entangled single-photon wavefunctions in the presence of imperfections due to photon distinguishability, laser noise, and photon loss. Leveraging this, we show that the wavefunction of any entangled state of noisy photons produced from a single quantum emitter can be expressed in matrix-product-state form and can be used to analytically compute the expectation value of the stabilizer generators of the corresponding entangled state. From this we obtain analytic expressions for the Pauli error probabilities in terms of the photon noise parameters. Furthermore, we calculate Pauli error maps for entangled photons after undergoing Bell- state measurements in terms of these parameters. Our work provides a method to use experimental measurements to determine the required quality of photons produced from quantum emitters for fault-tolerant fusion-based photonics quantum computing.
We develop an analytic perturbative framework that enables the analysis of small Markovian errors in probabilistic, photon-heralded quantum operations between non-interacting emitters. Building on and extending the Zero-Photon-Generation (ZPG) framework, we derive closed-form perturbative solutions that capture both ideal (zero-order) and noisy (low-order) gate dynamics conditioned on time-integrated photon counting. Our framework provides analytic solutions to process matrices and Pauli error weights up to leading order, bridging the gap between detailed physical imperfections of a system and its corresponding abstract Pauli noise models. Moreover, our framework captures imperfections across the full physical system stack, from photon generation to optical manipulation. We benchmark the resulting perturbative predictions on a repeat-until-success CZ gate against numerical simulations, demonstrating accurate modeling of source-induced noise, and then apply the same framework to analyze coherent phase-shifter miscalibrations as a representative example of optical-manipulation errors. The methods developed in this work enable physics-informed parameter tuning to optimize gate designs and develop tailored quantum error correction protocols toward fault-tolerant quantum computing using hybrid light--matter quantum systems.
Fusion-based quantum computation is a promising quantum computing model where small-sized photonic resource states are simultaneously entangled and measured by fusion gates. Such operations can be readily implemented with scalable photonic hardware: resource states can be deterministically generated by quantum emitters and fusions require only shallow linear-optical circuits. Here, we propose fusion-based architectures tailored to the capabilities and noise models in quantum emitters. We show that high tolerance to dominant physical error mechanisms can be achieved, with fault-tolerance thresholds of 8% for photon loss, 4% for photon distinguishability between emitters, and spin noise thresholds well above memory-induced errors for typical spin-photon interfaces. Our construction and analysis provide guidelines for the development of photonic quantum hardware targeting fault-tolerant applications with quantum emitters.
Measurement-based quantum computing relies on the generation of large entangled cluster states that act as a universal resource on which logical circuits can be imprinted and executed through local measurements. A number of strategies for constructing sufficiently large photonic cluster states propose fusing many smaller resource states generated by a series of quantum emitters. However, the fusion process is inherently probabilistic with a 50% success probability in standard guise. A recent proposal has shown that, in the limit of low loss, the probability of achieving successful fusion may be boosted to near unity by redundantly encoding the vertices of linear graph states using Greenberger-Horne-Zeilinger states [Quantum 7, 992 (2023)]. Here we present a protocol for deterministically generating redundantly encoded photonic resource states using single quantum emitters, and study the impact of protocol errors and photonic losses on the generated resource states and type-II photonic fusion. Our work provides a route for efficiently constructing complex entangled photonic qubit states for photonic quantum computing and quantum repeaters.
This thesis presents the development of resource-efficient photon-distillation schemes designed to produce highly indistinguishable photons, a key requirement for large-scale photonic quantum computing. Although photons do not naturally interact, their indistinguishability enables effective interactions through quantum interference, allowing entanglement generation using only linear optical elements and measurements. In practice, however, photons are never perfectly identical. Small differences introduce decoherence, limiting the scalability and reliability of photonic quantum technologies. Addressing indistinguishability errors is therefore essential for fault-tolerant quantum computing. The thesis first reviews the importance of photon indistinguishability and the need to mitigate related errors. It then examines experimental methods for characterizing imperfections and introduces a general model of imperfect photon states. This model captures indistinguishability errors alongside additional experimental noise from photon loss and multiphoton events. A key insight is that loss and multiphoton noise together can act as an effective source of indistinguishability error. To quantify this effect, the work defines an effective indistinguishability metric, enabling practical evaluation of photon-distillation schemes under realistic conditions. The core theoretical contribution is the development of photon-distillation protocols based on multiphoton Fourier interference. Unlike earlier approaches, these schemes can asymptotically suppress indistinguishability errors to arbitrary levels while requiring only linear scaling in photon resources relative to the desired error reduction. The analysis further suggests that photon distillation, when combined with quantum error correction, can significantly reduce the overall resource overhead for fault-tolerant photonic quantum computing. Experimentally, a three-photon Fourier-based distillation protocol was demonstrated on a high-fidelity photonic processor using a resonantly driven quantum-dot single-photon source. After subtracting excess noise contributions, a 2.2-fold reduction in indistinguishability error was achieved; when excess noise was retained, a 1.2-fold net reduction was observed. These results confirm a clear below-threshold improvement in photon quality. Additional analysis suggests that optimized distillation schemes could reduce the photon cost of a logical qubit by up to a factor of four. The thesis concludes by addressing insertion loss and outlining design strategies and future directions for integrating photon-distillation components into scalable quantum architectures.
The heralded generation of entangled states underpins many photonic quantum technologies. As quantum error correction thresholds are determined by underlying physical noise mechanisms, a detailed and faithful characterization of resource states is required. Non-computational leakage, e.g. more than one photon occupying a dual-rail encoded qubit, is an error not captured by standard forms of state tomography, which postselect on photons remaining in the computational subspace. Here we use the continuous-variable (CV) formalism and first quantized state representation to develop a simulation framework that reconstructs photonic quantum states in the presence of partial distinguishability and resulting non-computational leakage errors. Using these tools, we analyze a variety of Bell state generation circuits and find that the five photon discrete Fourier transform (DFT) Bell state generation scheme [Phys Rev. Lett. 126 23054 (2021)] is most robust to such errors for near-ideal photons. Through characterization of a photonic entangling gate, we demonstrate how leakage errors prevent a modular characterization of concatenated gates using current tomographical procedures. Our work is a necessary step in revealing the true noise models that must be addressed in fault-tolerant photonic quantum computing architectures.
Photonic quantum computers use the bosonic statistics of photons to construct, through quantum interference, the large entangled states required for measurement-based quantum computation. Therefore, any which-way information present in the photons will degrade quantum interference and introduce errors. While quantum error correction can address such errors in principle, it is highly resource-intensive and operates with a low error threshold, requiring numerous high-quality optical components. We experimentally demonstrate scalable, optimal photon distillation as a substantially more resource-efficient strategy to reduce indistinguishability errors in a way that is compatible with fault-tolerant operation. Photon distillation is an intrinsically bosonic, coherent error-mitigation technique which exploits quantum interference to project single photons into purified internal states, thereby reducing indistinguishability errors at both a higher efficiency and higher threshold than quantum error correction. We observe unconditional error reduction (i.e., below-threshold behaviour) consistent with theoretical predictions, even when accounting for noise introduced by the distillation gate, thereby achieving actual net-gain error mitigation under conditions relevant for fault-tolerant quantum computing. We anticipate photon distillation will find uses in large-scale quantum computers. We also expect this work to inspire the search for additional intrinsically bosonic error-reduction strategies, even for fault-tolerant architectures.