Recent years have seen quantum computers move from theory to practice, with the first prototypes of \emph{fault-tolerant} quantum computers capable of correcting their own errors. This marks the beginning of an exciting era of \emph{early fault tolerance}, with the first practical applications on the horizon. Among the most promising is quantum simulation, where a quantum computer is used to study another quantum system, such as molecules or materials. However, a central challenge is how to reliably extract accurate information from these early imperfect devices under realistic constraints, including noise, limited qubit numbers, circuit depth, and control. This thesis addresses this challenge by developing and analyzing algorithms for quantum phase estimation in these regimes, a key primitive for determining the energy spectra. It also considers the problem of learning the underlying dynamics of a quantum system, demonstrating the advantage of active control over passive observation. Together, these results contribute to ongoing efforts to overcome the limitations of early quantum hardware through improved algorithms and classical post-processing.
Recent years have seen quantum computers move from theory to practice, with the first prototypes of \emph{fault-tolerant} quantum computers capable of correcting their own errors. This marks the beginning of an exciting era of \emph{early fault tolerance}, with the first practical applications on the horizon. Among the most promising is quantum simulation, where a quantum computer is used to study another quantum system, such as molecules or materials. However, a central challenge is how to reliably extract accurate information from these early imperfect devices under realistic constraints, including noise, limited qubit numbers, circuit depth, and control. This thesis addresses this challenge by developing and analyzing algorithms for quantum phase estimation in these regimes, a key primitive for determining the energy spectra. It also considers the problem of learning the underlying dynamics of a quantum system, demonstrating the advantage of active control over passive observation. Together, these results contribute to ongoing efforts to overcome the limitations of early quantum hardware through improved algorithms and classical post-processing.
Progress in fault-tolerant quantum computation (FTQC) has driven the pursuit of practical applications with (EFTQC). These devices, limited in their qubit counts and fault-tolerance capabilities, require algorithms that can accommodate some degrees of error, which are known as EFTQC algorithms. To predict the onset of early quantum advantage, a comprehensive methodology is needed to develop and analyze EFTQC algorithms, drawing insights from both the methodologies of noisy intermediate-scale quantum and traditional FTQC. To address this need, we propose such a methodology for modeling algorithm performance on EFTQC devices under varying degrees of error. As a case study, we apply our methodology to analyze the performance of randomized Fourier estimation (RFE) [Kshirsagar, Katabarwa, and Johnson, ], an EFTQC algorithm for phase estimation. We investigate the runtime performance and the fault-tolerant overhead of RFE in comparison to the traditional quantum phase estimation algorithm. Our analysis reveals that RFE achieves significant savings in physical qubit counts while having a much higher runtime upper bound. We anticipate even greater physical qubit savings when considering more realistic assumptions about the performance of EFTQC devices. By providing insights into the performance trade-offs and resource requirements of EFTQC algorithms, our work contributes to the development of practical and efficient quantum computing solutions on the path to quantum advantage. Published by the American Physical Society 2024
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 computing offers a new, orthogonal direction for investigating fundamental physics, extending beyond classical numerical methods and conventional observables. Realizing this potential requires directly confronting the noise limiting currently available quantum computers. Progress rests on advancing algorithms, interpreting their results, and managing their errors together. This thesis presents several advancements in the use of quantum simulation and quantum information to probe fundamental physics.
The first is in the use of quantum computers to simulate collisions in quantum field theories. Central to these simulations are new wavepacket preparation, time evolution, and error mitigation techniques, which allow for simulations with some of the largest effective circuit volumes to date. These methods enable the first quantum simulation providing numerical evidence for inelastic particle production, a key process in fundamental physics.
The second advancement centers on the role quantum-information-theoretic quantities play in physical processes. Beyond mere correlations with the physics of the process, entanglement and magic are shown to probe the interactions present in scattering and hadronization dynamics.
A precision study requires a complete quantification of algorithmic and hardware uncertainties, an outstanding goal as quantum simulations mature. The third advancement in this thesis addresses error management. A framework minimizing the effect of algorithmic errors in analog quantum simulations is presented. In a step toward fault tolerance, error detection in encoded quantum simulations is shown to improve estimation of local observables relative to unencoded runs.
Together, the developments in this thesis mark practical progress toward fault-tolerant quantum simulations of fundamental physics capable of scientific discovery.
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 computing is entering a period in which progress will be shaped as much by advances in computer science as by improvements in hardware. The central thesis of this report is that early fault-tolerant quantum computing shifts many of the primary bottlenecks from device physics alone to computer-science-driven system design, integration, and evaluation. While large-scale, fully fault-tolerant quantum computers remain a long-term objective, near- and medium-term systems will support early fault-tolerant computation with small numbers of logical qubits and tight constraints on error rates, connectivity, latency, and classical control. How effectively such systems can be used will depend on advances across algorithms, error correction, software, and architecture. This report identifies key research challenges for computer scientists and organizes them around these four areas, each centered on a fundamental question.
Abstract The hope of the quantum computing field is that quantum architectures are able to scale up and realize fault-tolerant quantum computing. Due to engineering challenges, such “cheap” error cor- rection may be decades away. In the meantime, we anticipate an era of “costly” error correction, or early fault-tolerant quantum computing. Costly error correction might warrant settling for error-prone quantum computations. This motivates the development of quantum algorithms which are robust to some degree of error as well as methods to analyze their performance in the presence of error. We introduce a randomized algorithm for the task of phase estimation and give an analysis of its performance under two simple noise models. In both cases the analysis leads to a noise threshold, below which arbitrarily high accuracy can be achieved by increasing the number of samples used in the algorithm. As an application of this general analysis, we compute the maximum ratio of the largest circuit depth and the dephasing scale such that performance guarantees hold. We calculate that the randomized algorithm can succeed with arbitrarily high probability as long as the required circuit depth is less than 0.916 times the dephasing scale.