Despite rapid advances in quantum hardware, noise remains a central obstacle to deploying quantum algorithms on near-term devices. In particular, random coherent errors that accumulate during circuit execution constitute a dominant and fundamentally challenging noise source. We introduce a noise-resilient framework for Quantum Signal Processing (QSP) that mitigates such coherent errors without increasing circuit depth or ancillary qubit requirements. Our approach uses ensembles of noisy QSP circuits combined with measurement-level averaging to suppress random phase errors in Z rotations. Building on this framework, we develop robust QSP algorithms for implementing polynomial functions of Hermitian matrices and for estimating observables, with applications to Hamiltonian simulation, quantum linear systems, and ground-state preparation. We analyze the trade-off between approximation error and hardware noise, which is essential for practical implementation under the stringent depth and coherence constraints of current quantum hardware. Our results establish a practical pathway for integrating error mitigation seamlessly into algorithmic design, advancing the development of robust quantum computing, and enabling the discovery of scientific applications with near- and mid-term quantum devices.
Despite rapid advances in quantum hardware, noise remains a central obstacle to deploying quantum algorithms on near-term devices. In particular, random coherent errors that accumulate during circuit execution constitute a dominant and fundamentally challenging noise source. We introduce a noise-resilient framework for Quantum Signal Processing (QSP) that mitigates such coherent errors without increasing circuit depth or ancillary qubit requirements. Our approach uses ensembles of noisy QSP circuits combined with measurement-level averaging to suppress random phase errors in Z rotations. Building on this framework, we develop robust QSP algorithms for implementing polynomial functions of Hermitian matrices and for estimating observables, with applications to Hamiltonian simulation, quantum linear systems, and ground-state preparation. We analyze the trade-off between approximation error and hardware noise, which is essential for practical implementation under the stringent depth and coherence constraints of current quantum hardware. Our results establish a practical pathway for integrating error mitigation seamlessly into algorithmic design, advancing the development of robust quantum computing, and enabling the discovery of scientific applications with near- and mid-term quantum devices.
Measurement overhead and hardware noise present fundamental obstacles to the practical realization of quantum algorithms on near-term quantum devices. In many quantum applications, the dominant computational cost arises from repeated measurements needed to extract accurate information and from handling noise effects. This dissertation develops a unified framework for efficient measurement and error mitigation in quantum algorithms.In this work, measurement is treated as a controllable and designable component across hardware, algorithmic, and statistical levels, rather than as a fixed final step. By tailoring measurement schemes and estimators, we show that substantial reductions in measurement cost can be achieved without sacrificing accuracy. This approach is developed and validated across multiple settings, from hardware-level randomized measurement implementations to algorithm-level molecular energy estimation.At the hardware level, we investigate randomized measurement schemes based on photonic metasurfaces. We find that the device itself naturally realizes the required family of measurement bases without repeated active optical reconfiguration, providing an efficient platform for randomized measurements. We analyze the effect of realistic measurement noise and develop calibration-based error mitigation techniques that suppress noise-induced bias. Numerical studies show that this approach enables accurate estimation of state properties under realistic measurement noise.At the algorithmic level, we investigate measurement-efficient quantum eigen solvers through the Non-Orthogonal Quantum Eigensolver (NOQE). We develop a detailed implementation framework for NOQE, including circuit construction and simplification, analysis of measurement complexity, and resource estimation. Building on this understanding, we incorporate randomized measurements as an alternative to standard Hadamard-test-based schemes and develop shadow-tomography-enhanced variants of NOQE that significantly reduce circuit complexity and qubit requirements while maintaining favorable sample complexity. Shadow-based error mitigation methods, including shadow distillation, further improve robustness against noise.Finally, we investigate a more fundamental redesign of the NOQE measurement task by reformulating matrix-element estimation as a quantum amplitude estimation problem. By integrating iterative quantum amplitude estimation into the NOQE framework, we replace the original incoherent sampling-based estimation with coherent information accumulation through amplitude amplification and achieve near-Heisenberg scaling in measurement complexity, improving on the standard sampling-based methods. Numerical results for molecular energy estimation demonstrate that this approach reaches chemical accuracy with fewer queries than the original NOQE.Overall, this dissertation shows that measurement overhead is not a fixed limitation, but a resource bottleneck that can be identified and reduced at multiple levels in quantum applications. Across the settings studied here, improvements are achieved at different layers, including hardware-aware randomized measurements, algorithm-level redesign of measurement protocols, estimator-level error mitigation, and statistical improvements based on coherent information accumulation. Taken together, these results provide a unified framework for understanding and reducing measurement cost under realistic noise, and offer practical guidance for the design of quantum algorithms on near-term quantum devices.
The Quantum Approximate Optimization Algorithm (QAOA) is a leading candidate for solving combinatorial optimization problems on near-term quantum hardware. However, its practical deployment remains severely limited by hardware-induced noise and decoherence. In the absence of full fault tolerance, Quantum Error Mitigation (QEM) techniques offer a viable approach to enhance QAOA performance on noisy intermediate-scale quantum (NISQ) devices. In this work, we present a unified classification of QEM strategies specifically tailored for QAOA, systematically categorized into preprocessing, during execution, and post-processing phases. We further classify QAOA deployment settings—such as hardware-constrained devices, stochastic noise-dominated environments, and dense graphs problem—and recommend appropriate QEM techniques for each. A comparative analysis highlights the trade-offs among mitigation accuracy, resource overhead, and robustness to different noise types. By synthesizing recent advances and identifying open challenges, our paper provides both a comprehensive survey and a practical framework for designing robust, noise-resilient QAOA pipelines on near-term quantum platforms.
Abstract Quantum signal processing (QSP) is a powerful toolbox for the design of quantum algorithms and can lead to asymptotically optimal computational costs. Its realization on noisy quantum computers without fault tolerance, however, is challenging because it requires a deep quantum circuit in general. We propose a strategy to run an entire QSP protocol on noisy quantum hardware by carefully reducing overhead costs at each step. To illustrate the approach, we consider the application of Hamiltonian simulation for which QSP implements a polynomial approximation of the time evolution operator. We test the protocol by running the algorithm on the Quantinuum H1-1 trapped-ion quantum computer powered by Honeywell. In particular, we compute the time dependence of bipartite entanglement entropies for Ising spin chains and find good agreements with exact numerical simulations. To make the best use of the device, we determine optimal experimental parameters by using a simplified error model for the hardware and numerically studying the trade-off between Hamiltonian simulation time, polynomial degree, and total accuracy. Our results are the first step in the experimental realization of QSP-based quantum algorithms.
Abstract: Quantum signal processing (QSP) provides a mathematically economical mechanism for transforming the spectral information of a block-encoded operator through carefully phased single-qubit rotations. Photonic quantum computing, meanwhile, offers high-bandwidth operation, network compatibility and substantial room-temperature functionality, yet remains constrained by optical loss, probabilistic state preparation, finite squeezing, detector imperfections and the resource overhead of logical error correction. This paper develops an integrated analytical framework that connects QSP polynomial synthesis to fault-tolerant photonic execution and to a broader construct termed quantum-enhanced scientific intelligence: the reliable extraction of predictive, explanatory and decision-relevant knowledge from complex scientific operators and data. The study adopts a theory-building and model-based research design. It combines block encoding, QSP and quantum singular-value transformation with open-system dynamics, logical-error modelling, constrained multi-objective optimization and risk-adjusted outcome scoring. The proposed QSP-FTSI framework treats algorithmic approximation error, photonic component quality, decoder performance, logical reliability, resource intensity, uncertainty calibration and scientific utility as coupled rather than independent variables. An illustrative normalized model yields a baseline benefit index of 7.942, a composite risk index of 2.640 and a risk-adjusted score of 6.358 on a ten-point scale; an improved low-loss, high-QEC scenario reaches 7.858, whereas a stressed configuration falls to 3.754. These values are demonstrations, not experimental findings. The principal contribution is a publication-ready mathematical architecture for evaluating when QSP-enabled photonic systems can support scientifically meaningful simulation, inverse modelling, spectral filtering and inference under explicit fault-tolerance and reproducibility constraints. The framework also identifies measurable pathways for experimental validation, hardware–algorithm co-design and responsible scientific deployment. Keywords quantum signal processing; quantum singular-value transformation; fault-tolerant photonic computing; block encoding; Gottesman–Kitaev–Preskill codes; fusion-based quantum computation; logical error suppression; Hamiltonian simulation; scientific machine learning; quantum-enhanced inference; photonic integrated circuits; spectral transformation; quantum error correction; risk-adjusted scientific intelligence; hardware–algorithm co-design
Accurately estimating observables on noisy quantum devices remains a central challenge for near-term quantum algorithms. While quantum error mitigation techniques can reduce noise-induced bias, they often rely on unverifiable assumptions about the circuit noise, and cannot guarantee the magnitude of residual bias error. Here, rather than using classical resources to mitigate a noisy quantum circuit execution, we propose a hybrid algorithm that uses quantum resources to improve the accuracy of approximate classical Pauli-path simulation. Our protocol, Quantum Enhanced Pauli Propagation (QuEPP), uses Clifford perturbation theory (CPT) to construct a classically simulable ensemble of Clifford circuits from the low-order terms in CPT, which directly provide the approximate classical Pauli-path simulation of the target circuit. Noisy quantum expectation values of this ensemble are then used to infer a global rescaling factor that corrects quantum execution of the target circuit, providing higher-order contributions absent from the truncated low-order classical simulation. This approach requires no noise characterization, applies to arbitrary circuits, and provides a provable route to asymptotically unbiased estimates. Using IBM Heron hardware, we demonstrate QuEPP on 2D random mirror circuits of up to 49 qubits and circuit depth 80, as well as Trotterized Hamiltonian evolution, showing consistent improvements beyond classical CPT and unmitigated quantum results. QuEPP offers a simple, scalable, and model-free framework for enabling accurate quantum computation in the pre-fault-tolerant era.
The Quantum Approximate Optimization Algorithm (QAOA) is widely regarded as a promising near-term quantum algorithm for addressing hard combinatorial optimization problems on Noisy Intermediate-Scale Quantum (NISQ) devices; however, its real-world effectiveness is severely constrained by hardware noise, including gate infidelities, decoherence, and measurement errors. This work explores an error mitigation–driven approach to enhance the performance and robustness of QAOA without altering its algorithmic structure or requiring fault-tolerant quantum resources. Measurement error mitigation and zero-noise extrapolation are incorporated into the execution and post-processing stages of QAOA circuits and evaluated using the Minimum Vertex Cover problem as a representative benchmark. Performance is assessed through approximation ratios, solution stability, and noise sensitivity across multiple circuit depths. The results indicate that error mitigation not only improves approximation accuracy but also stabilizes output distributions and delays performance degradation at increased circuit depths. Additionally, the mitigated executions demonstrate better consistency across repeated runs, highlighting improved resilience to stochastic noise. These findings emphasize that lightweight and hardware-efficient error mitigation techniques can significantly extend the practical usability of QAOA on current NISQ hardware, providing a scalable and realistic pathway for executing quantum optimization algorithms more reliably in near-term quantum computing environments.