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Analysis of practical implementations of quantum operations under realistic noise sources

Mahsa Karimi

Published Sep 8, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.11575/prism/51974

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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.
Quantum computing holds the potential to address problems that are currently considered intractable for classical processors by leveraging quantum mechanical effects for simulation, optimization, and chemistry. Despite recent technological progress, quantum hardware remains in the noisy intermediate-scale regime, where coherence limits, gate imperfections, and readout errors restrict circuit depth and algorithmic reliability. Although first demonstrations of small-scale Quantum Error Correction exist, logical processors with low logical error rates are still distant. In the near term, even error-corrected qubits are expected to operate with residual error, which means that improving calibration and mitigating errors at the physical and circuit level will remain essential for obtaining meaningful results. Established calibration routines and mitigation methods such as Zero-Noise-Extrapolation (ZNE) are valuable, but need to be further improved and more rigorously validated with respect to their underlying assumptions, stability and quantitative benefits. This thesis addresses error reduction techniques on transmon qubits through calibration, gate analysis, and circuit-level mitigation. First, a systematic comparison of two single-qubit amplitude calibration techniques is carried out (cross-point and ping-pong calibration), followed by an analysis of two implementations of a two-qubit gate, based on the cross-resonance interaction. The results show that cross-point calibration offers faster convergence, higher precision and a more favorable signal to noise ratio than ping-pong calibration. Hamiltonian tomography confirms the validity of a reduced model for the cross-resonance interaction, and algorithmic tests reveal that direct and echoed CNOT gates offer complementary advantages depending on the application. Second, the thesis develops and evaluates the method of Inverted-Circuit Zero-Noise-Extrapolation (IC-ZNE). Its main idea consists of measuring the effective error strength of a circuit through inverted circuits. This quantity is then used for extrapolation towards zero noise rather than relying on simple, approximate noise scaling assumptions as in standard ZNE. This approach constitutes a novel and original method. IC-ZNE consistently produces results closer to ideal reference values than standard ZNE. The method achieves up to 77% error reduction in observable error on the tested circuits compared to standard ZNE and simple post processing filters can yield up to 39% reduction in selected cases compared to standard ZNE. Further refinements introduce noise-adaptive circuit scaling strategies that enhance mitigation outcomes without significant additional cost. The performance of these techniques is examined across several circuits and in the context of variational quantum algorithms. Applications to the Quantum Approximate Optimization Algorithm and the Variational Quantum Eigensolver demonstrate that these techniques extend the useful operating regime of current devices, although their effectiveness decreases for very deep circuits or unfavorable variational ansätze. Taken together, the calibration and mitigation techniques investigated and developed in this thesis demonstrate practical routes toward enhancing the reliability of near-term quantum processors. While they cannot replace full fault-tolerant quantum computation, they offer useful and complementary capabilities that support progress toward scalable quantum technologies.
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.
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.
Quantum computing promises to address problems in simulation, optimization, and chemistry, but current hardware operates in the noisy intermediate-scale (NISQ) regime where coherence limits, gate imperfections, and readout errors restrict performance. Improving calibration and mitigating errors therefore remain essential. This thesis analyzes error reduction on superconducting transmon qubits through calibration, gate analysis, and circuit-level mitigation. It compares single-qubit amplitude calibration methods and analyzes two-qubit gates based on the cross-resonance interaction, identifying differences in precision, convergence, and performance. In addition, it develops Inverted-Circuit Zero-Noise-Extrapolation (IC-ZNE) which measures effective error strength using inverted circuits. Compared to standard ZNE, IC-ZNE achieves results closer to ideal values and reduces observable errors. Overall, the presented methods improve the reliability of near-term quantum processors.
This thesis is concerned with fault-tolerant quantum information processing using quantum error-correcting codes. It contains two major pieces of work. The first is a study of coherent noise in the context of stabilizer error-correcting codes. The second is a proposed scheme for a universal set of fault-tolerant logical gates in a particular code family built out of the 3D toric code. Chapter 1 provides an introduction to quantum computation and fault tolerance. Many basic concepts in error-correcting codes are defined. Special attention is paid to the set of code properties that are most likely to determine how easily a given fault-tolerant scheme might be implemented on a physical device. These include the fault-tolerant noise threshold and the overhead. In Chapters 2 and 3 we study the effectiveness of quantum error correction against coherent noise. Coherent errors (for example, unitary noise) can interfere constructively, so that in some cases the average infidelity of a quantum circuit subjected to coherent errors may increase quadratically with the circuit size; in contrast, when errors are incoherent (for example, depolarizing noise), the average infidelity increases at worst linearly with circuit size. We consider the performance of quantum stabilizer codes against a noise model in which a unitary rotation is applied to each qubit, where the axes and angles of rotation are nearly the same for all qubits. In Chapter 2 we introduce coherent noise and incoherent noise and a number of methods that are useful for the study of coherent noise. We study the repetition code as a basic example, and we also study a correlated noise model. In Chapter 3 we show that for the toric code subject to such independent coherent noise, and for minimal-weight decoding, the logical channel after error correction becomes increasingly incoherent as the length of the code increases, provided the noise strength decays inversely with the code distance. A similar conclusion holds for weakly correlated coherent noise. Our methods can also be used for analyzing the performance of other codes and fault-tolerant protocols against coherent noise. However, our result does not show that the coherence of the logical channel is suppressed in the more physically relevant case where the noise strength is held constant as the code block grows, and we recount the difficulties that prevented us from extending the result to that case. Nevertheless our work supports the idea that fault-tolerant quantum computing schemes will work effectively against coherent noise, providing encouraging news for quantum hardware builders who worry about the damaging effects of control errors and coherent interactions with the environment. Chapter 4 is connected to another aspect of fault tolerance, fault-tolerant logical gates. The toric code is a promising candidate for fault-tolerant quantum computation because of its high threshold and low-weight stabilizers. A universal gate set in the toric code generally requires magic state distillation, which can incur a significant qubit overhead. In this work we construct an error-correcting code in three dimensions based on the toric code that features a fault-tolerant T gate with no magic state distillation required. We further describe a subsystem version of our code which supports a universal set of fault-tolerant gates. This code can be converted into the stabilizer version using gauge-fixing. We also argue that our code can be converted to a (2+1)-D protocol, where a 2D lattice undergoes a measurement-based protocol over time. In this way, a fault-tolerant logical T gate can be realized in a 2D toric code structure.
The transition from noisy intermediate-scale quantum (NISQ) processors to large-scale fault-tolerant machines requires more than incremental improvements in physical qubit fidelity. While advances in quantum error correction (QEC) theory continue to lower the theoretical overhead of quantum computing, much of this research remains abstracted from the physical realities of qubit implementations. This disconnect often results in hardware-agnostic designs that are inefficient or impractical to build. In this dissertation, I identify three primary gaps between theoretical QEC research and practical hardware: (1) the high levels of noise and temporal instability in experimental devices that impede scalable QEC; (2) the prohibitively large qubit and time costs of useful algorithms, driven largely by the limitations of the standard surface code; and (3) the failure of current resource estimates to account for hardware-level constraints, such as limited connectivity and the complexity of implementing non-local operations. To bridge these gaps, I propose a holistic, cross-stack approach where the error correction protocols and the physical hardware are designed in concert. By developing realistic device models and hardware-aware solutions at the lowest levels of the software stack, we can accelerate the path toward functional fault-tolerance. I present my work across three research thrusts: first, leveraging codesign to mitigate hardware-specific noise and reduce physical error rates; second, developing software tools for fault-tolerant quantum computers to reduce the space-time overhead of the QEC layer; and third, proposing two novel hardware-aware QEC architectures that provide practical, high-performance routes to scalable quantum computation.