Quantum error detection (QED) offers a promising pathway to fault tolerance in near-term quantum devices by balancing error suppression with minimal resource overhead. However, its practical utility hinges on optimizing design parameters-such as syndrome measurement frequency-to avoid diminishing returns from detection overhead. In this work, we present a comprehensive framework for fault-tolerant compilation and simulation of quantum algorithms using [[n, n-2, 2]] codes, which enable low-qubit-overhead error detection and a simple nearly fault-tolerant universal set of operations. We demonstrate and analyze our pipeline with a purely statistical interpretation and through the implementation of Grover's search algorithm. Our results are used to answer the question is quantum error detection a worthwhile avenue for early-term fault tolerance, and if so how can we get the most out of it? Simulations under the circuit-level noise model reveal that finding optimal syndrome schedules improves algorithm success probabilities by an average of 6.7x but eventual statistical limits from post-selection in noisy/resource-limited regimes constrain scalability. Furthermore, we propose a simple data-driven approach to predict fault tolerant compilation parameters, such as optimal syndrome schedules, and expected fault tolerant performance gains based on circuit and noise features. These results provide actionable guidelines for implementing QED in early-term quantum experiments and underscore its role as a pragmatic, constant-overhead error mitigation layer for shallow algorithms. To aid in further research, we release all simulation data computed for this work and provide an experimental QED compiler at https://codeqraft.xyz/qed.
Quantum error detection (QED) offers a promising pathway to fault tolerance in near-term quantum devices by balancing error suppression with minimal resource overhead. However, its practical utility hinges on optimizing design parameters-such as syndrome measurement frequency-to avoid diminishing returns from detection overhead. In this work, we present a comprehensive framework for fault-tolerant compilation and simulation of quantum algorithms using [[n, n-2, 2]] codes, which enable low-qubit-overhead error detection and a simple nearly fault-tolerant universal set of operations. We demonstrate and analyze our pipeline with a purely statistical interpretation and through the implementation of Grover's search algorithm. Our results are used to answer the question is quantum error detection a worthwhile avenue for early-term fault tolerance, and if so how can we get the most out of it? Simulations under the circuit-level noise model reveal that finding optimal syndrome schedules improves algorithm success probabilities by an average of 6.7x but eventual statistical limits from post-selection in noisy/resource-limited regimes constrain scalability. Furthermore, we propose a simple data-driven approach to predict fault tolerant compilation parameters, such as optimal syndrome schedules, and expected fault tolerant performance gains based on circuit and noise features. These results provide actionable guidelines for implementing QED in early-term quantum experiments and underscore its role as a pragmatic, constant-overhead error mitigation layer for shallow algorithms. To aid in further research, we release all simulation data computed for this work and provide an experimental QED compiler at https://codeqraft.xyz/qed.
Noisy intermediate-scale quantum (NISQ) processors are entering an early fault-tolerance regime where full quantum error correction carries prohibitive resource costs, yet lightweight error detection can meaningfully improve algorithmic success rates. Existing compilation and error-detection toolchains treat these concerns in isolation, with no principled way to balance detection overhead against success probability under latency constraints. We present an integrated hardware-aware compilation and data-driven quantum error-detection (QED) framework that jointly optimises qubit mapping, SWAP insertion, and syndrome-schedule placement via a noise-weighted cost function and a learned multi-objective scheduler. Simulation experiments on an HPC cluster using GPU-accelerated density-matrix simulation (NVIDIA cuQuantum SDK) across VQE, phase-estimation, and Grover benchmarks, three noise profiles, and circuit sizes of 6-20 qubits (depths 10-160), show that joint co-design raises algorithmic success probability by up to 68 percent (95 percent CI: 60 percent to 76 percent) over SABRE on an 8-qubit VQE instance with post-selection.
Quantum computation promises asymptotic speedups over classical algorithms, but realizing these advantages requires overcoming the noisiness of quantum hardware. Although fault-tolerant error correction can allow for reliable quantum computation even using unreliable components, the resource overheads required can substantially erode the asymptotic performance gains. This dissertation focuses on constructing and optimizing fault-tolerant procedures with lower overhead than previous methods were capable of. We present new frameworks for fault-tolerant syndrome extraction using flag gadgets with exponentially reduced ancilla requirements, explicit measurement schedules that achieve asymptotically fewer measurements than stabilizer generators, and a general method for making arbitrary Clifford circuits fault tolerant. In addition, we optimize surface code measurement schedules in the presence of constraints imposed by fabrication defects to reduce logical error rate. Together, these results advance low-overhead fault tolerance and improve performance in resource-constrained and near-term quantum computing settings.
Quantum computers have the potential to solve several interesting problems in polynomial \ntime for which no polynomial time classical algorithms have been found. However, \none of the major challenges in building quantum devices is that quantum systems are very \nsensitive to noise arising from undesired interactions with the environment. Noise can lead \nto errors which can corrupt the results of the computation. Quantum error correction is \none way to mitigate the effects of noise arising in quantum devices. \nWith a plethora of quantum error correcting codes that can be used in various settings, \none of the main challenges of quantum error correction is understanding how well various \ncodes perform under more realistic noise models that can be observed in experiments. \nThis thesis proposes a new decoding algorithm which can optimize threshold values of \nerror correcting codes under different noise models. The algorithm can be applied to \nany Markovian noise model. Further, it is shown that for certain noise models, logical \nClifford corrections can further improve a code's threshold value if the code obeys certain \nsymmetries. \n \nSince gates and measurements cannot in general be performed with perfect precision, \nthe operations required to perform quantum error correction can introduce more errors \ninto the system thus negating the benefits of error correction. Fault-tolerant quantum \ncomputing is a way to perform quantum error correction with imperfect operations while \nretaining the ability to suppress errors as long as the noise is below a code's threshold. \nOne of the main challenges in performing fault-tolerant error correction is the high resource \nrequirements that are needed to obtain very low logical noise rates. With the use of \nflag qubits, this thesis develops new fault-tolerant error correction protocols that are applicable \nto arbitrary distance codes. Various code families are shown to satisfy the requirements \nof flag fault-tolerant error correction. We also provide circuits using a constant number of \nqubits for these codes. It is shown that the proposed flag fault-tolerant method uses fewer \nqubits than previous fault-tolerant error correction protocols. \n \nIt is often the case that the noise afflicting a quantum device cannot be fully characterized. \nFurther, even with some knowledge of the noise, it can be very challenging to use \nanalytic decoding methods to improve the performance of a fault-tolerant scheme. This \nthesis presents decoding schemes using several state of the art machine learning techniques \nwith a focus on fault-tolerant quantum error correction in regimes that are relevant to near \nterm experiments. It is shown that even in low noise rate regimes and with no knowledge \nof the noise, noise can be further suppressed for small distance codes. Limitations of machine \nlearning decoders as well as the classical resources required to perform active error \ncorrection are discussed. \n \nIn many cases, gate times can be much shorter than typical measurement times of \nquantum states. Further, classical decoding of the syndrome information used in quantum \nerror correction to compute recovery operators can also be much slower than gate times. \nFor these reasons, schemes where error correction can be implemented in a frame (known \nas the Pauli frame) have been developed to avoid active error correction. In this thesis, we \ngeneralize previous Pauli frame schemes and show how Clifford frame error correction can \nbe implemented with minimal overhead. Clifford frame error correction is necessary if the \nlogical component of recovery operators were chosen from the Clifford group, but could \nalso be used in randomized benchmarking schemes.
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 computing is poised to revolutionize computational paradigms by leveraging quantum mechanics principles such as superposition and entanglement.However, the full-scale deployment of quantum applications remains constrained by hardware limitations, including high error rates and quantum decoherence.Quantum Software Engineering (QSE) emerges as a critical field addressing these challenges by optimizing algorithm design, error mitigation, and compiler strategies to enhance fault tolerance.Algorithm design in QSE focuses on developing quantum algorithms that efficiently exploit quantum parallelism while minimizing resource overhead.Key advancements include quantum variational algorithms, hybrid quantum-classical frameworks, and novel quantum heuristics tailored for optimization and cryptographic problems.Error mitigation techniques play a pivotal role in extending quantum circuit reliability without requiring full quantum error correction.Methods such as zero-noise extrapolation, probabilistic error cancellation, and quantum embedding techniques help reduce computational inaccuracies.Additionally, compiler optimization ensures efficient quantum program execution by minimizing gate depth, optimizing qubit mapping, and leveraging noise-adaptive scheduling to enhance quantum hardware performance.This paper explores the synergy between these three pillars of QSE, analyzing their impact on improving the feasibility of fault-tolerant quantum computing.It also examines emerging trends, including AI-driven quantum compilers, adaptive error mitigation techniques, and hardware-aware quantum software development.By bridging the gap between theoretical advancements and practical implementations, QSE provides a structured approach to accelerating quantum computing adoption across domains such as cryptography, materials science, and artificial intelligence.The findings underscore the necessity of interdisciplinary collaboration in developing robust quantum software solutions that maximize computational efficiency while mitigating inherent quantum hardware limitations.
Quantum computers promise to solve computational problems that are inaccessible to classical machines. The reliable execution of large-scale quantum algorithms requires robust operations in the presence of noise. Quantum error correction addresses this challenge by encoding quantum information redundantly across several physical qubits, such that errors can be detected and corrected during a computation. However, no single error-correcting code intrinsically supports an inherently robust, fault-tolerant implementation of all gates needed for universal quantum computing. Moreover, most modern approaches to both quantum error correction and the implementation of universal logical operations on encoded qubits rely on mid-circuit measurements and feed-forward control. These types of operations are technologically demanding, often slow, and prone to high error rates, and they limit the overall success probability of quantum algorithms. In this thesis, we develop fault-tolerant protocols and circuits for quantum error correction and universal logical computation, with an emphasis on implementations compatible with current hardware systems. We first focus on fault-tolerant quantum error correction on small codes. By comparing different protocols, we identify trade-offs between compact circuit constructions and their robustness to noise. We then assess their practical performance by comparing numerical simulations of noisy circuits with experimental data. Beyond the preservation of encoded information, we study how universal logic can be implemented in a fault-tolerant manner on encoded qubits. A central approach considered in this thesis is code switching, in which logical information is transferred between two distinct error-correcting codes that support complementary sets of inherently fault-tolerant logical gates. In combination, these codes give access to a complete universal fault-tolerant logical gate set. In this thesis, we determine conditions that allow us to construct fault-tolerant protocols for code switching. We adapt these protocols to the capabilities of current hardware, thereby enabling the first experimental realization of universal fault-tolerant logic by means of code switching. However, the overall performance of these schemes is limited by slow and noisy mid-circuit measurements. To address this bottleneck, we construct a suite of measurement-free fault-tolerant universal operations that do not require any measurements during the execution of an algorithm. In this framework, error correction and logical operations are implemented coherently as part of the quantum circuit, without mid-circuit measurements or in-sequence classical control. We introduce measurement-free code-switching schemes that can be scaled to arbitrary code distances through concatenation, and which thereby provide, in principle, arbitrarily strong error suppression. We further tailor our approach to the capabilities of current trapped-ion quantum processors. New circuit constructions support the first experimental implementation of a logical quantum algorithm without mid-circuit measurements, demonstrated through Grover's search on three encoded qubits. Together, the results of this thesis expand the toolbox for early fault-tolerant quantum computation. They show how protocols for quantum error correction and universal logical gates can be designed without mid-circuit measurements with realistic hardware constraints in mind, opening new pathways towards universal quantum logic.