Quantum technology is a rapidly growing field; in the near future, quantum computers may be able to solve computationally complex problems that currently cannot be realistically solved by a classical computer. Digital quantum simulation is one such potential applications. Simulating the behavior of quantum mechanical systems, such as molecules, with a quantum computer is possible in polynomial time. Running the same computation with a classical computer would take an amount of time exponentially scaling with the size of the problem. Being able to obtain error free results of such simulations on a quantum computer could make it possible to obtain more accurate information on, for example, the effects of drugs or the chemical properties of materials. However, at this point quantum computing is in the Noisy intermediate-scale quantum (NISQ) era. The technology in this current era is defined by sensitivity of systems to noise and a limited amount of computing power. Noise can be defined as any unwanted signal, which can cause errors in the calculation results. As of 2026, the size of quantum processors available is from 50 qubits to 1121 qubits. Due to the limited number of physical qubits available, it is not possible to achieve fault tolerance by programming data into error-corrected logical qubits. The use of error mitigation methods, which aim to minimize the impact of error in the computational results, is a promising option to error correction due to no lower limits for the QPU size. The thesis was to conducted as a literature review on the use of different methods to mitigate noise-induced error in the results of digital quantum simulation implented on NISQ-era quantum computers. The methods considered in this thesis are zeronoise extrapolation (ZNE), Clifford data regression (CDR) and probabilistic error cancellation (PEC). The effectiveness of error mitigation methods is examined on the basis of various indicators, such as accuracy compared to theoretical results, and resource requirements by reviewing articles or conference publications on the digital quantum simulation of spin Hamiltonian dynamics. Based on the results of the study, it is possible to conclude that the error mitigation methods examined in the thesis successfully reduced effects of noise from the results of the simulations. On the other hand, there is a trade-off between the use of resources and accuracy: higher accuracy increases the overhead of using mitigation with a certain rate depending on the method. However, the use of error reduction methods is 4 still preferable due to the benefits they provide in obtaining usable results. The best results are obtained by tailoring the selection of methods based on the application and the type of error to be mitigated.
Quantum technology is a rapidly growing field; in the near future, quantum computers may be able to solve computationally complex problems that currently cannot be realistically solved by a classical computer. Digital quantum simulation is one such potential applications. Simulating the behavior of quantum mechanical systems, such as molecules, with a quantum computer is possible in polynomial time. Running the same computation with a classical computer would take an amount of time exponentially scaling with the size of the problem. Being able to obtain error free results of such simulations on a quantum computer could make it possible to obtain more accurate information on, for example, the effects of drugs or the chemical properties of materials. However, at this point quantum computing is in the Noisy intermediate-scale quantum (NISQ) era. The technology in this current era is defined by sensitivity of systems to noise and a limited amount of computing power. Noise can be defined as any unwanted signal, which can cause errors in the calculation results. As of 2026, the size of quantum processors available is from 50 qubits to 1121 qubits. Due to the limited number of physical qubits available, it is not possible to achieve fault tolerance by programming data into error-corrected logical qubits. The use of error mitigation methods, which aim to minimize the impact of error in the computational results, is a promising option to error correction due to no lower limits for the QPU size. The thesis was to conducted as a literature review on the use of different methods to mitigate noise-induced error in the results of digital quantum simulation implented on NISQ-era quantum computers. The methods considered in this thesis are zeronoise extrapolation (ZNE), Clifford data regression (CDR) and probabilistic error cancellation (PEC). The effectiveness of error mitigation methods is examined on the basis of various indicators, such as accuracy compared to theoretical results, and resource requirements by reviewing articles or conference publications on the digital quantum simulation of spin Hamiltonian dynamics. Based on the results of the study, it is possible to conclude that the error mitigation methods examined in the thesis successfully reduced effects of noise from the results of the simulations. On the other hand, there is a trade-off between the use of resources and accuracy: higher accuracy increases the overhead of using mitigation with a certain rate depending on the method. However, the use of error reduction methods is 4 still preferable due to the benefits they provide in obtaining usable results. The best results are obtained by tailoring the selection of methods based on the application and the type of error to be mitigated.
Minimizing the effect of noise is essential for quantum computers. The conventional method to protect qubits against noise is through quantum error correction. However, for current quantum hardware in the so-called noisy intermediate-scale quantum (NISQ) era, noise presents in these systems and is too high for error correction to be beneficial. Quantum error mitigation is a set of alternative methods for minimizing errors, including error extrapolation, probabilistic error cancellation, measurement error mitigation, subspace expansion, symmetry verification, virtual distillation, etc. The requirement for these methods is usually less demanding than error correction. Quantum error mitigation is a promising way of reducing errors on NISQ quantum computers. This paper gives a comprehensive introduction to quantum error mitigation. The state-of-art error mitigation methods are covered and formulated in a general form, which provides a basis for comparing, combining and optimizing different methods in future work.
Quantum computing is entering a transitional regime between noisy intermediate-scale quantum (NISQ) processing and early fault-tolerant quantum computation (FTQC), in which increasingly capable hardware is beginning to support repeated syndrome measurements, partial error correction, and logical-qubit operations, while residual physical and logical errors remain non-negligible. In this regime, error suppression, error mitigation, and quantum error correction are increasingly better viewed as complementary layers of a unified error-reduction strategy rather than as separate approaches, with each acting at a different stage of the quantum computation to improve simulation reliability. Thus, in this review, we provide a practical and forward-looking overview of the principal hardware error sources and the corresponding error suppression and mitigation methods for reducing their impact across the current NISQ-FTQC transition. We discuss hardware-aware circuit design, coherent-error suppression, readout mitigation, noise extrapolation, classical inference, and software-supported workflows, with particular emphasis on their implementation on actual quantum processors. We further examine how error mitigation techniques can be adapted to encoded and logical-qubit settings so that they can operate alongside quantum error correction to suppress residual logical errors and improve the accuracy of computation in the early fault-tolerant regime.
Quantum computation is expected to have significant practical applications. The main problem in quantum computing is susceptibility to noise. Quantum error correction was developed to allow large-scale applications of quantum computing by achieving fault tolerance. However, as large-scale fault-tolerant quantum computation is not available, the question of applications of near-term hardware remains important. Current noisy intermediate-scale (NISQ) quantum devices can be used for small applications or as testbeds for larger applications; noise suppression techniques are of significant importance to their applicability. This thesis addresses noise suppression via quantum error mitigation (QEM) and quantum error correction (QEC) for near-term applications. The work aims to improve the understanding of noise-suppression techniques and their performance for exploring the physical systems of interest. The results presented in this thesis are divided into QEM and QEC chapters. The majority of the work is focused on QEM. The main interest of this thesis is the application of QEM to Hamiltonian simulations. Two simulation methods: the Trotter method and a quantum signal processing-based method, are explored. Both simulation methods, enhanced by zero-noise extrapolation, are employed to simulate the transverse-field Ising model. The obtained numerical results are promising, as the QEM allows a good recovery of noiseless values in low-noise shallow circuits, even with fixed sampling resources. A further result obtained in the QEM domain is a definition of a mitigation technique based on optimal measurement (in a metrological sense). The presentation includes analytical calculations of implementation costs and error propagation, as well as a numerical application to Hamiltonian simulation, yielding promising results: noise suppression by several orders of magnitude. The QEC part of the thesis explores its application in quantum metrology. The focus is on parameter sensing in many-body Hamiltonians. The results are purely analytical and extend a known lemma to m-local homogeneous Pauli Hamiltonian parameter sensing. This allows discussion of the scaling achieved for sensing the Hamiltonian parameters with respect to the code properties. The results in this thesis establish applications of QEM and QEC in selected near-term applications, quantify their performance, and discuss caveats and potential future applications. This thesis presents a theoretical and numerical study with implications for future experimental implementations. The relative success of the QEM and QEC shown in this thesis relies on tailoring the techniques to a chosen problem, highlighting the importance of technique adaptation in near-term applications.
Quantum computing promises to revolutionize several scientific and technological domains through fundamentally new ways of processing information. Among its most compelling applications is digital quantum simulation, where quantum computers are used to replicate the behavior of other quantum systems. This could enable the study of problems that are otherwise intractable on classical computers, transforming fields such as quantum chemistry, condensed matter physics, and materials science. Despite this potential, realizations of practical quantum advantage for relevant problems are hindered by imperfections of current devices. This also affects quantum hardware based on superconducting circuits which is among the most advanced and scalable platforms. The envisaged long-term solution of fault-tolerant quantum computers that correct their own errors remains out of reach mainly due to the associated qubit number overhead. As a result, the field has developed strategies that combine quantum and classical resources, exploit hardware-native operations, and employ error mitigation techniques to extract meaningful results from noisy data. This doctoral thesis contributes to this broader effort by exploring methods for advancing quantum simulation across the full computational stack, including hardware-level innovations, refined techniques for noise modeling and error mitigation, and algorithmic improvements enabled by efficient measurement processing.
The pursuit of high-fidelity digital quantum simulation is fundamentally constrained by the inevitable presence of noise in current and near-term quantum processors. While quantum error correction ultimately promises fault-tolerance, its substantial qubit overhead renders it impractical for the noisy intermediate-scale quantum (NISQ) era. This research addresses the critical gap between hardware imperfections and simulation accuracy by designing systematic, resource-efficient machine learning (ML) error-mitigation protocols tailored specifically for digital quantum simulation. Unlike generic error-suppression methods, our approach exploits the unique structural properties of simulated quantum dynamics—including time-translation invariance, locality of interactions, and conserved quantities—to inform the training of lightweight neural networks and Gaussian process regressors. We develop a hybrid framework that combines randomized compiling with data-driven noise-inversion models, enabling real-time estimation and subtraction of both coherent and incoherent errors without exponential sampling overhead. Through extensive numerical benchmarks on spin-chain and Fermi-Hubbard models, we demonstrate that our ML protocols achieve up to an order-of-magnitude reduction in infidelity compared to standard probabilistic error cancellation and zero-noise extrapolation, while requiring fewer calibration circuits. Furthermore, we introduce an adaptive online learning scheme that continuously refines the mitigation model during the simulation runtime, automatically adjusting to time-dependent drift in hardware noise. Our results establish a practical pathway toward scalable, high-accuracy quantum simulations on existing devices, with implications for condensed matter physics, quantum chemistry, and the development of quantum advantage benchmarks.
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.