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.
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.
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.
Quantum computing offers powerful advantages for simulating quantum many-body systems and for accelerating specific computational tasks beyond classical capabilities, motivating major advances in hardware, control, and error-correction toward scalable and fault-tolerant platforms. Realizing a utility-scale quantum computer requires high-fidelity operations, and hence, the study of hardware errors is of paramount importance. In this thesis, we develop techniques that advance the existing tool sets for analyzing hardware imperfections in quantum operations, thereby enabling a more accurate understanding of how dif-ferent quantum platforms can reach the required fault-tolerance thresholds. In Chapter 3, we study the implementation of two-qubit Controlled-Z (CZ) gates in the solid-state rare-earth platform 171Yb3+:YVO. The chapter compares three different physical routes to en-tangling individual ytterbium ions: direct magnetic dipole–dipole coupling between closely spaced ions, photon scattering mediated by an optical cavity, and heralded gates based on two-photon in-terference, with both cavity-assisted and cavity-free variants. To evaluate these proposals on equal footing, we develop and use theoretical tools for estimating state and gate fidelities in the presence of realistic imperfections. In particular, we apply a perturbative treatment to the magnetic-dipolar gate, while the photon-scattering and photon-interference schemes are analyzed using a combina-tion of existing analytic methods and numerical simulations. This provides a quantitative basis for assessing the feasibility, strengths, and limitations of each mechanism. The comparison shows that the photon-interference-based protocol has the most favorable fidelity scaling with cavity co-operativity, making it the strongest candidate for currently accessible 171Yb3+:YVO parameters. Photon-scattering gates offer the advantage of near-deterministic operation, but this comes at the cost of slower gate times and less favorable cooperativity scaling. The magnetic-dipolar approach, by contrast, gives a fast and deterministic cavity-free gate, but requires ions to be positioned suf-ficiently close together. Although the analysis is carried out for 171Yb3+:YVO as a concrete case study, the techniques used to model, benchmark, and compare these gates are applicable more generally to other solid-state spin-qubit platforms. Motivated by the need for a more systematic treatment of noise in photon-heralded opera-tions, Chapter 4 develops an analytic perturbative method for probabilistic quantum gates between non-interacting emitters. Based on the Zero-Photon-Generation formalism, this method describes light–matter dynamics conditioned on time-integrated photon-detection outcomes and decomposes the resulting conditional map into its ideal contribution and leading noise-dependent corrections. In this way, it produces closed-form expressions for process matrices and effective Pauli error weights, giving a direct link between microscopic hardware imperfections and the noise models used in circuit-level and error-correction descriptions. The method is flexible enough to treat errors from different parts of the experimental architecture, including imperfections in photon emission and optical-control components. We benchmark it on a repeat-until-success CZ gate, where the perturbative results match numerical simulations in the low-error regime, and then use it to study phase-shifter calibration errors as an example of coherent optical-control noise. These results give a physics-informed route for optimizing gate parameters, comparing different imperfections, and constructing effective error models for fault-tolerant quantum computing with hybrid light–matter platforms. Together, these results strengthen the connection between microscopic hardware imperfections and effective error models, providing tools for assessing and optimizing quantum operations on the path toward fault-tolerant quantum computation.
Accurate characterization of coherent and non-Markovian errors remains a central challenge in quantum information processing, as conventional benchmarking techniques typically rely on Markovian and time-independent noise assumptions. In practice, however, quantum devices exhibit both systematic coherent miscalibrations and temporally correlated fluctuations, which complicate error diagnosis and mitigation. Here, we apply a technique based on tangent-space decomposition to characterize such error in single-qubit quantum gates implemented on a trapped ion platform. Small imperfections in a quantum operation are treated as perturbations of the target quantum map, represented as tangent vectors in the space of quantum channels. This formulations enables a natural decomposition of the deviation into three components corresponding to coherent, Markovian and non-Markovian processes.The relative weights of these components provide a quantitative measure of the contribution from each type of error mechanism, directly from a single tomographic snapshot. We experimentally validate this method on a single-qubit gates implemented on a trapped 40Ca+ ion, where control is achieved through laser-driven optical transitions. By analyzing experimentally reconstructed process matrices, expressed in the Pauli Transfer Matrix and Choi representations, we identify and quantify non-Markovian effects arising from controlled injection of slow fluctuations in the experimental environment. We also characterize deterministic coherent miscalibrations using the same technique. This approach provides a physically transparent and experimentally accessible tool for diagnosing complex error sources in quantum control systems.
Quantum error correction (QEC), the lynchpin of fault-tolerant quantum computing (FTQC), is designed and validated against well-behaved Pauli stochastic error models. But in real-world deployment, QEC protocols encounter a vast array of other errors -- coherent and non-Pauli errors -- whose impacts on quantum circuits are vastly different than those of stochastic Pauli errors. The impacts of these errors on QEC and FTQC protocols have been largely unpredictable to date due to exponential classical simulation cost. Here, we show how to accurately and efficiently model the effects of coherent and non-Pauli errors on FTQC, and we study the effects of such errors on syndrome extraction for surface and bivariate bicycle codes, and on magic state cultivation. Our analysis suggests that coherent error can shift fault-tolerance thresholds, increase the space-time cost of magic state cultivation, and can increase logical error rates by an order of magnitude compared to equivalent stochastic errors. These analyses are enabled by a new technique for mapping any Markovian circuit-level error model with sufficiently small error rates onto a detector error model (DEM) for an FTQC circuit. The resulting DEM enables Monte Carlo estimation of logical error rates and noise-adapted decoding, and its parameters can be analytically related to the underlying physical noise parameters to enable approximate strong simulation.
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.
Correlated noise is a critical failure mode in quantum error correction (QEC), yet a gap remains between the stochastic Pauli models used for scalable QEC analyses and the microscopic, non-Markovian descriptions of noise in physical devices. We bridge this gap by introducing Spatiotemporal Pauli Processes (SPPs): the natural multi-time generalization of Pauli channels, joint probability distributions over Pauli faults across space and time, obtained exactly from any noise process, however non-Markovian, under standard Pauli-frame randomization. SPPs thereby provide a single language in which correlated noise can be recast, compared, and extended, compatible with both microscopic open systems modeling and the stabilizer workflow of QEC design and analysis. Our central result is constructive: the multi-time Pauli twirl acts by local contractions on a process tensor network, yielding an explicit classical tensor network whose virtual bonds encode memory, bounded by the environment's Liouville-space dimension. Transfer operator diagnostics link memory spectra to correlation decay, and hidden Markov representations enable efficient sampling of correlated Pauli fault trajectories, mapping microscopically derived noise directly into circuit-level QEC simulation. We demonstrate this with surface code memory and stability benchmarks up to distance 19. A temporal "storm" model with tunable correlation time shows that memory alone, at strictly fixed marginal error rates, systematically erodes the exponential error suppression expected from code distance. A genuinely spatiotemporal quantum cellular automaton bath maps exactly, under system twirling, to a nonlinear probabilistic cellular automaton; tuning its coherent interactions drives the noise into a pseudo-critical regime with critical slowing down and macroscopic error avalanches that reverse surface code distance scaling.