Quantum computing is a promising tool for solving computational problems in several areas, including the simulation of physical and chemical systems. The design of practical quantum computing systems for these applications is a daunting task, requiring collaborative work by interdisciplinary teams considering different abstractions of the same systems. This dissertation presents work on the development of those abstractions, and on components that bridge multiple layers of abstraction. I first provide an introduction to quantum circuit model computation, error correction with stabilizer codes, and physics simulation algorithms. In joint work with the QSCOUT software team, I then describe the development of the Jaqal programming language and its supporting software packages. Next, I investigate the performance of the variational quantum eigensolver on an early fault tolerant architecture. Finally, in joint work with Andrew Landahl, I develop the logical fermion data type and demonstrate its benefits in optimizing physics simulations.
Quantum computing is a promising tool for solving computational problems in several areas, including the simulation of physical and chemical systems. The design of practical quantum computing systems for these applications is a daunting task, requiring collaborative work by interdisciplinary teams considering different abstractions of the same systems. This dissertation presents work on the development of those abstractions, and on components that bridge multiple layers of abstraction. I first provide an introduction to quantum circuit model computation, error correction with stabilizer codes, and physics simulation algorithms. In joint work with the QSCOUT software team, I then describe the development of the Jaqal programming language and its supporting software packages. Next, I investigate the performance of the variational quantum eigensolver on an early fault tolerant architecture. Finally, in joint work with Andrew Landahl, I develop the logical fermion data type and demonstrate its benefits in optimizing physics simulations.
Quantum algorithms have the potential to provide exponential speedups over some of the best known classical algorithms. These speedups may enable quantum devices to solve currently intractable problems such as those in the fields of optimization, material science, chemistry, and biology. Thus, the realization of large-scale, reliable quantum-computers will likely have a significant impact on the world. For this reason, the focus of this dissertation is on the development of quantum-computing applications and robust, scalable quantum-architectures. I begin by presenting an overview of the language of quantum computation. I then, in joint work with Ojas Parekh, analyze the performance of the quantum approximate optimization algorithm (QAOA) on a graph problem called Max Cut. Next, I present a new stabilizer simulation algorithm that gives improved runtime performance for topological stabilizer codes. After that, in joint work with Andrew Landahl, I present a new set of procedures for performing logical operations called "color-code lattice-surgery." Finally, I describe a software package I developed for studying, developing, and evaluating quantum error-correcting codes under realistic noise.
Quantum computing is positioned to be a transformative technology to key areas of scientific interest such as quantum chemistry, material science, and cryptography. At a hardware level, recent years have seen broad progress in a variety of qubit modalities, however, error rates are still orders of magnitude higher than what is necessary for large-scale quantum programs. This gap in error rates motivates the use of quantum error correction (QEC) and the realization of fault-tolerant quantum computing (FTQC), yet today, although the theory of FTQC is promising, effectively connecting it to real devices poses significant challenges. In this dissertation we study opportunities for more efficient and scalable FTQC architectures through the co-design of quantum hardware and software. We first look at how unique hardware capabilities in quantum computers made from 2D arrays of optically trapped atoms can improve QEC performance. For computation, we study how longer-range interactions between atoms can enable a novel embedding of QEC blocks on physical qubits that improves logical-level connectivity. For memory, we study how mid-circuit movement of atoms can effectively implement higher encoding rate QEC codes, creating a qubit-efficient memory system. We next consider the performance impact of real-time classical systems in FTQC architectures, and explore the use of speculation to improve large-scale decoding systems. Finally, we study how software systems can be used to improve QEC designs. We consider the problem of QEC circuit optimization, and study an automated approach based on iterative optimization of performance-reducing subcircuits.
The transition from noisy intermediate-scale quantum (NISQ) processors to large-scale fault-tolerant machines requires more than incremental improvements in physical qubit fidelity. While advances in quantum error correction (QEC) theory continue to lower the theoretical overhead of quantum computing, much of this research remains abstracted from the physical realities of qubit implementations. This disconnect often results in hardware-agnostic designs that are inefficient or impractical to build. In this dissertation, I identify three primary gaps between theoretical QEC research and practical hardware: (1) the high levels of noise and temporal instability in experimental devices that impede scalable QEC; (2) the prohibitively large qubit and time costs of useful algorithms, driven largely by the limitations of the standard surface code; and (3) the failure of current resource estimates to account for hardware-level constraints, such as limited connectivity and the complexity of implementing non-local operations. To bridge these gaps, I propose a holistic, cross-stack approach where the error correction protocols and the physical hardware are designed in concert. By developing realistic device models and hardware-aware solutions at the lowest levels of the software stack, we can accelerate the path toward functional fault-tolerance. I present my work across three research thrusts: first, leveraging codesign to mitigate hardware-specific noise and reduce physical error rates; second, developing software tools for fault-tolerant quantum computers to reduce the space-time overhead of the QEC layer; and third, proposing two novel hardware-aware QEC architectures that provide practical, high-performance routes to scalable quantum computation.
Quantum computing has recently transitioned from a theoretical prediction to a nascent technology. Nevertheless, there is still a gap between the computational ability and reliability of current QIP technologies and the requirements of the first useful quantum computing applications. It will require tremendous efforts and investment to solve the engineering and research challenges to close the gap. Because of the uncertainties and difficulties in relying on hardware breakthroughs, it will also be crucial to close the gap using higher-level quantum optimizations and software-hardware co-design, which could maximally utilize noisy devices and potentially provide an accelerated pathway to real-world quantum computing applications. This thesis develops methods to explore the vast design space for highly optimized and reliable quantum computing architectures and software and focuses on the compilation, verification, and error correction aspects of the quantum computing stack. Specifically, the three main chapters in this thesis discuss, respectively, a direct-to-pulse compiler, a protocol to fault-tolerantly prepare approximate GKP (Gottesman-Kitave-Preskill) qubit states, and a verification framework that helps quantum programmers write provably correct compiler components through formal verification. Though touching many aspects of the stack and based on different technologies in physics and computer science, the majority of this thesis can be connected by a main theme --- improving the efficiency of existing quantum computing stacks by breaking the abstraction between layers in the quantum computing stack.
This study examines the current technological components of quantum computing through a multi layered approach. It begins by comparing quantum and classical computers across fundamental aspects such as information representation, computational power, fault tolerance, and computational complexity, with the key differences summarized in a technical comparison table. Subsequently, the study analyzes the primary architectural approaches in quantum hardware, including superconducting qubits, trapped ion systems, and photonic platforms. On the software side, quantum programming languages such as Qiskit, Cirq, and PennyLane are evaluated in terms of their features, supported infrastructures, and learning curves. The significance of variational quantum algorithms tailored for the noisy intermediate-scale quantum (NISQ) era namely, the Variational Quantum Eigensolver (VQE) and the Quantum Approximate Optimization Algorithm (QAOA) along with hybrid computing systems, is also emphasized. Overall, this work aims to provide a comprehensive overview of the current state of modern quantum computing from both hardware and software perspectives, highlighting key developments and ongoing progress in the field.
Bringing the promise of quantum computation into reality requires not only building a quantum computer but also correctly programming it to run a quantum algorithm. To obtain asymptotic advantage over classical algorithms for applications including simulation, search, and optimization, quantum algorithms rely on the ability of data in quantum superposition to exhibit phenomena such as interference and entanglement. In turn, an implementation of the algorithm as a program must correctly orchestrate these phenomena in the states of qubits. Otherwise, it would yield incorrect outputs or lose quantum computational advantage. Given a quantum algorithm, what are the challenges and costs of realizing it as a program that can run on a physical quantum computer? In this thesis, I answer this question by showing how the basic abstractions of programming upon which many quantum algorithms rely – such as data structures and control flow – can fail to work correctly or efficiently on a quantum computer. I then demonstrate how we can leverage insights from research in programming languages to re-invent the software stack – including abstractions, libraries, and compilers – to meet the demands of quantum algorithms. This approach holds out a promise of expressive and efficient tools to program a quantum computer and thereby practically realize its computational advantage.