Quantum computers promise huge speed-up over conventional computers in crucial problems like chemistry and materials simulations, decryption, and even machine learning. However, any imperfect manipulations of the qubits from which the machines are formed and any interactions with the environment can lead to errors and loss of their quantum properties. This thesis will develop practical schemes for fighting such errors in the quantum hardware and discuss possible applications of such noisy machines. We can protect the quantum information against noise by employing additional qubits and performing quantum error correction, whose experimental implementation has been brought much closer to reality via the recent rapid advance of quantum hardware, but challenges still remain. One example is coherent errors, which can grow much faster than regular errors. In this thesis, we tackle it by improving upon the conventional scheme that transforms it into regular errors using twirling, and also by developing a new scheme called Pauli conjugation that makes use of its coherent properties to our advantage. Implementations of quantum error correction codes also bring about hardware challenges like wiring packing and leakage errors. For the silicon spin qubit platform, these can be overcome by a surface code architecture we develop. It is challenging to use quantum error correction for the applications of near- term quantum hardware due to the constrained qubit count. Instead, we rely on quantum error mitigation to fight noise, which makes use of extra measurements instead of extra qubits. The Fermi-Hubbard variational quantum eigensolver is one of the most promising near-term quantum algorithms, thus we have performed a resource estimation for the task to gauge its feasibility. We then improve and combine the existing error mitigation schemes to boost their performance and thus to enhance the feasibility of near-term quantum algorithms, bringing practical applications of quantum hardware closer to reality.
Quantum computers promise huge speed-up over conventional computers in crucial problems like chemistry and materials simulations, decryption, and even machine learning. However, any imperfect manipulations of the qubits from which the machines are formed and any interactions with the environment can lead to errors and loss of their quantum properties. This thesis will develop practical schemes for fighting such errors in the quantum hardware and discuss possible applications of such noisy machines. We can protect the quantum information against noise by employing additional qubits and performing quantum error correction, whose experimental implementation has been brought much closer to reality via the recent rapid advance of quantum hardware, but challenges still remain. One example is coherent errors, which can grow much faster than regular errors. In this thesis, we tackle it by improving upon the conventional scheme that transforms it into regular errors using twirling, and also by developing a new scheme called Pauli conjugation that makes use of its coherent properties to our advantage. Implementations of quantum error correction codes also bring about hardware challenges like wiring packing and leakage errors. For the silicon spin qubit platform, these can be overcome by a surface code architecture we develop. It is challenging to use quantum error correction for the applications of near- term quantum hardware due to the constrained qubit count. Instead, we rely on quantum error mitigation to fight noise, which makes use of extra measurements instead of extra qubits. The Fermi-Hubbard variational quantum eigensolver is one of the most promising near-term quantum algorithms, thus we have performed a resource estimation for the task to gauge its feasibility. We then improve and combine the existing error mitigation schemes to boost their performance and thus to enhance the feasibility of near-term quantum algorithms, bringing practical applications of quantum hardware closer to reality.
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.
Quantum mechanical problems are among the hardest to simulate and, in some cases, remain intractable even for the most powerful computers. Quantum computing has emerged as a new technological platform to address such challenges, with rapid advances in recent years. Yet, current quantum devices remain noisy and limited in scale. Hence, it is essential to identify classically hard problems of practical interest and tractable with existing quantum devices. Among potential applications, the real-time simulation of quantum systems is one of the most promising to deliver an early, practical quantum advantage. This doctoral thesis is therefore centered around simulating quantum dynamics on quantum devices. We first present an overview of the most relevant quantum algorithms for quantum dynamics, highlighting respective advantages and limitations. Further, we identify relevant problems within quantum dynamics that could benefit from quantum simulation in the near future. Second, we propose a method for benchmarking hardware and error mitigation algorithms that is based on well-understood theoretical results and suffers from no scaling issues. The resulting quality metric is intuitive and transferable to other applications. We successfully implement the scheme on up to 133 qubits, demonstrating coherent evolution up to a two-qubit gate depth of 28, featuring 1396 two-qubit gates, before noise becomes prevalent. Third, we propose a novel variant of probabilistic error amplification to implement open quantum dynamics, relying on characterizing and altering hardware noise to mimic the system-environment interaction under study. Lastly, we present two studies on state preparation and phase classification: first, a hybrid algorithm to prepare ground states of electron-phonon systems; second, a quantum machine learning-based approach to distinguish phases in previously prepared quantum states.
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.
The development of quantum computers requires not only experimental advances, but also theoretical efforts to tackle the bottlenecks and identify potential applications. This thesis addresses some essential elements in each stage of the development of quantum computers, from the currently available hardware to the long-term devices. The critical factor that hinders the quantum hardware from performing perfect operations is the presence of noise, however, it can be overcome by error correction codes. We first consider a large-scale quantum processor with asymmetrical noise and preferably a modular structure. By concatenating the surface code with an error-detecting code, and utilising the information from detection with a customised decoder, we find very high thresholds for the designed devices. The second topic is small error correction codes which are more realistic to be implemented in the near future. A measure `integrity' is introduced to benchmark the performance of quantum memories to demonstrate beneficial error correction, associated with four milestones. We show integrity is closely related with other commonly-used measures and can be easily assessed by experimentalists. This framework is then studied in detail in the context of an ion-trap quantum device implemented with the seven qubit code. We present a protocol based on detailed sequences of crystal-reconfiguration operations and stabiliser mappings to perform a full error correction cycle. Realistic error models and parameters from reported works are also given. While experimental efforts continue to battle against the noise, some hybrid quantum-classical algorithms have been developed to be implemented on the near-term noisy devices. The variational algorithm is one of the hybrid algorithms that have been widely applied to simulations of condensed matter physics and quantum chemistry. In the next chapter, we introduce a variational quantum compiler to automatically search for the encoding circuits of small error correction codes. By tailoring the ansatz to optimise the circuit for particular hardware systems, we show some novel circuits discovered with the compiler. The final chapter applies the variational algorithm to solve linear algebra problems including linear systems of equations and matrix-vector multiplications. We show that the linear algebra problems can be solved with near-term devices, with circuit depth linear to the condition number and super-linear to the number of qubits.
Quantum computation is an exciting and rapidly developing paradigm of computing, which has the potential to improve or accelerate numerous important applications ranging from cryptography to drug discovery. Inspired by these prospects, researchers and engineers across the world have, in recent years, made tremendous advances in building programmable quantum devices. Nevertheless, the size and error rates in state-of-the-art quantum computers are still several orders of magnitude away from those required to achieve computational speedups using existing quantum algorithms. These developments, along with their limitations, motivate us to consider two important questions: First, are there any useful applications in which current or near-term quantum devices can outperform classical computers? Second, can we develop efficient error-correction schemes to suppress the error rates in near-term quantum devices? In this dissertation, we present novel solutions to both of these questions. To address the first question, we identify an important class of problems in condensed-matter physics, namely the identification and characterization of quantum phases of matter, as one promising application of current and near-term quantum information processors. We develop new algorithms for using such quantum devices to solve these problems, and we demonstrate how our methods substantially outperform existing approaches. In addition, we respond to the second question by developing hardware-efficient quantum error correction protocols. By leveraging the distinctive properties and advantages of a given experimental setup to overcome its particular limitations, our proposals significantly reduce the number of quantum bits and operations required for performing quantum error correction and fault-tolerant quantum computation. Together, the works in this dissertation thus pave the way for the near-term realization of quantum computational advantages.
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.