Quantum computing (QC) aims to solve certain computational problems beyond the capabilities of even the largest classical high-performance computers. By leveraging the quantum mechanical principles of superposition and entanglement, QC algorithms have the potential to revolutionize areas such as machine learning, quantum chemistry, and cryptography. To perform quantum advantages, a scalable quantum computing system is essential. This thesis demonstrates techniques that address problems of the development of scalable quantum computers. The first part of the thesis describes our technique to perform scalable quantum circuit optimization by using synthesis. Traditional quantum synthesis can only be used for circuits on a handful of qubits. The proposed technique partitions the circuit into multiple small pieces of circuits and performs quantum synthesis individually. This technique enables quantum circuit synthesis for large circuits. The second section is the design and evaluation of the trapped-ion linear-tape architecture. This study provides an alternative idea towards scalable quantum computing systems. The last section of the thesis is our technique to increase the capability of quantum circuit simulation on classical supercomputing systems. Our hybrid data compression technique is introduced into the simulation of quantum computing. This work allows us to further push the limit of classical simulation, and hence verify a larger size of quantum computing systems.
Quantum computing (QC) aims to solve certain computational problems beyond the capabilities of even the largest classical high-performance computers. By leveraging the quantum mechanical principles of superposition and entanglement, QC algorithms have the potential to revolutionize areas such as machine learning, quantum chemistry, and cryptography. To perform quantum advantages, a scalable quantum computing system is essential. This thesis demonstrates techniques that address problems of the development of scalable quantum computers. The first part of the thesis describes our technique to perform scalable quantum circuit optimization by using synthesis. Traditional quantum synthesis can only be used for circuits on a handful of qubits. The proposed technique partitions the circuit into multiple small pieces of circuits and performs quantum synthesis individually. This technique enables quantum circuit synthesis for large circuits. The second section is the design and evaluation of the trapped-ion linear-tape architecture. This study provides an alternative idea towards scalable quantum computing systems. The last section of the thesis is our technique to increase the capability of quantum circuit simulation on classical supercomputing systems. Our hybrid data compression technique is introduced into the simulation of quantum computing. This work allows us to further push the limit of classical simulation, and hence verify a larger size of quantum computing systems.
Quantum computing is a revolutionary approach to computation that leverages the principles of quantum mechanics, enabling computers to process information in fundamentally different ways than classical computers. Unlike traditional bits, which represent data as either 0s or 1s, quantum bits, or qubits, can exist in multiple states simultaneously due to superposition. Additionally, qubits can be entangled, allowing them to be interconnected in ways that enhance computational power and efficiency. This unique behavior has the potential to run certain types of computation tasks much faster than classical computers can, marking a significant leap forward in technology. When building actual quantum computers to run practical quantum algorithms, one needs efficient ways to map the algorithms to the hardware components, similar to compiling classical algorithms onto CPU/GPU hardware. This thesis aims to tackle some of the important problems in the mapping process. First, can we address hardware errors and algorithm errors at the same time? Second, can we build a better circuit complexity metric to inspire better quantum architecture design, and can we design better quantum algorithms and compilation techniques using this improved metric? Lastly, can we use physics-level simulation results to inspire better circuit-level optimization techniques? We hope to provide positive answers to all three questions above through three separate architectural innovations.
Quantum computing may solve selected classes of problems more efficiently than classical computers, with applications in areas such as cryptography, chemistry, and optimization. However, current quantum systems remain limited in scale and reliability and depend on substantial classical-computing support. This thesis investigates this challenge in two complementary contexts: classical simulation, where efficient computation enables the exploration of larger quantum systems; and quantum error correction, where efficient real-time decoding enables more reliable quantum operation.The first part examines the classical simulation of quantum computers, focusing on the computational and memory challenges that limit its scalability. It organizes the field across device, gate, and algorithmic levels, with particular attention to state-vector, path-based, hybrid, and tensor-based methods. The survey relates their computation, memory, data-movement, and communication bottlenecks to acceleration approaches for CPUs, GPUs, FPGAs, and distributed systems. It further highlights recurring optimization strategies, including reduced precision, data compression, parallel execution, improved memory locality, specialized matrix units, and reconfigurable hardware, providing a common framework for current techniques and future acceleration opportunities.The second part addresses the real-time classical processing required for quantum error correction. Starting from a high-accuracy Graph Neural Network surface-code decoder, it applies algorithm-hardware co-design through hardware-guided pruning and retraining, input-graph filtering, quantization, and a custom FPGA architecture. For code distances up to d=7, the resulting designs satisfy both max-latency and average-latency decoding requirements while reducing the logical error rate by 13% and 40%, respectively, compared with the evaluated Minimum Weight Perfect Matching baseline.Together, these works show how classical computer-architecture techniques can support quantum computing from scalable exploration through simulation to reliable operation through real-time error correction.
Quantum computing not only holds the potential to solve long-standing problems in quantum physics, but also to offer speed-ups across a broad spectrum of other fields. Access to a computational space that incorporates quantum effects, such as superposition and entanglement, enables the derivation of promising quantum algorithms for important tasks, including preparing the ground state of a quantum system or predicting its evolution over time. Successfully tackling these tasks promises insights into significant theoretical and technological questions, such as superconductivity and the design of new materials. The aim of quantum algorithms is to use a series of quantum operations in a quantum circuit to solve a problem beyond the reach of classical computers. However, the noise and limited scale of current quantum computers restricts these circuits to moderate sizes and depths. As a result, many prominent algorithms are currently infeasible to run for problem sizes of practical interest. In response, recent research focused on variational quantum algorithms, which allow the selection of circuits that act within a quantum device's capabilities. Yet, these algorithms can require the execution of a large number of circuits, leading to prohibitively long computation times. This doctoral thesis develops two main techniques to reduce these quantum computational resource requirements, with the goal of scaling up application sizes on current quantum processors. The first approach is based on stochastic approximations of computationally costly quantities, such as quantum circuit gradients or the quantum geometric tensor (QGT). The second method takes a different perspective on the QGT, leading to a potentially more efficient description of time evolution on current quantum computers. Both techniques rely on maintaining available information and only computing necessary corrections, instead of re-computing possibly redundant data. The main focus of application for our algorithms is the simulation of quantum systems, broadly defined as including the preparation of ground and thermal states, and the real- and imaginary-time propagation of a system. The developed subroutines, however, can further be utilized in the fields of optimization or machine learning. Our algorithms are benchmarked on a range of representative models, such as Ising or Heisenberg spin models, both in numerical simulations and experiments on the hardware. In combination with error mitigation techniques, the latter is scaled up to 27 qubits; into a regime that variational quantum algorithms are challenging to scale to on noisy quantum computers without our algorithms.
Quantum computing has emerged as a transformative paradigm capable of solving complex computational problems that are intractable for classical computers. Central to the advancement of this technology is the development of efficient quantum algorithms and high fidelity simulations that enable the design, testing, and optimization of quantum solutions before deployment on physical hardware. This study focuses on the design and implementation of quantum algorithms tailored for solving a variety of quantum problems, including quantum chemistry, optimization, and cryptography. Using state of the art simulation platforms such as Qiskit, Cirq, and Pennylane, algorithm performance was evaluated in terms of accuracy, execution time, scalability, and resilience to noise. Benchmarks demonstrate that algorithms such as the Variational Quantum Eigensolver (VQE) and Quantum Approximate Optimization Algorithm (QAOA) achieve significant speedups in problem specific domains, while hybrid quantum–classical methods provide robust pathways for near term quantum advantage. Simulation results reveal that algorithmic efficiency can be significantly improved through optimized circuit depth, qubit connectivity mapping, and advanced error mitigation techniques. The findings highlight the potential of simulation driven quantum algorithm development in accelerating the practical realization of quantum computing applications across disciplines such as materials discovery, molecular modeling, secure communications, and complex optimization tasks.
Quantum computing, with its potential to revolutionize computation, relies fundamentally on the development of efficient algorithms to leverage its unparalleled processing capabilities. This research delves into the creation, exploration, and refinement of quantum computing algorithms, focusing on their applications in optimization, cryptography, and machine learning. Quantum algorithms such as Shor's and Grover's have demonstrated remarkable advantages in factorization and search problems, while more recent innovations are tackling complex challenges in global optimization and data analysis. By integrating principles of quantum mechanics—such as superposition, entanglement, and interference—these algorithms promise exponential speed-ups over classical counterparts in specific domains. This study critically analyzes existing quantum algorithms, proposes advancements in hybrid quantum-classical frameworks, and explores their implications for practical problem-solving. Through simulations and theoretical evaluations, it aims to bridge the gap between quantum theory and real-world applications, contributing to the evolution of quantum computing as a transformative technology.
Optimizing and simulating quantum circuits at scale are critical bottlenecks in realizing the full potential of quantum computing. This thesis delivers a comprehensive suite of systems to overcome these limitations, spanning both physical compilation and classical simulation. For quantum circuit optimization, we first automate the discovery and verification of transformation rules by introducing Equivalence Circuit Class (ECC) sets and an efficient generation algorithm for arbitrary gate sets. We deploy these rules within the superoptimizer Quartz, which utilizes a cost-based backtracking search to escape local minima that trap traditional rule-based methods. To eliminate the exponential runtime penalties inherent to pure search, we introduce QALM, a hybrid optimization framework. By unifying search-based exploration with greedy rule-based exploitation in an interleaved control loop, QALM dynamically escapes local minima without exhaustive backtracking. Evaluated across a large benchmark suite of 248 diverse circuits, QALM outperforms existing search-based optimizers in final circuit quality while operating with the computational efficiency of rule-based systems. While the prior two approaches aim for global optimization, this problem is intrinsically QMA-hard, creating a bottleneck for large programs. To circumvent this issue and scale up, we introduce OAC, a cut-and-meld circuit optimization algorithm. OAC cuts a circuit into subcircuits, applies an existing oracle optimizer independently, and seamlessly melds the results. This algorithm operates with a linear number of oracle calls while attaining local optimality. Empirical evaluation shows that OAC significantly improves the efficiency of state-of-the-art optimizers while enhancing overall quality. Beyond physical execution, the scalable simulation of quantum circuits on classical hardware presents another major challenge. To address this, we present Atlas, a distributed GPU-based simulator that hierarchically partitions circuits to exploit data parallelism while minimizing communication overhead. By leveraging integer linear programming to allocate structurally related gates to nearby GPUs and dynamic programming for kernel scheduling, Atlas runs significantly faster than prior state-of-the-art GPU simulators. Together, these frameworks provide a robust toolchain, improving both the execution of quantum circuits on physical devices and their scalable classical simulation.