Recent advances in quantum architectures and computing have motivated the development of new optimizing compilers for quantum programs or circuits. Even though steady progress has been made, existing quantum optimization techniques remain asymptotically and practically inefficient and are unable to offer guarantees on the quality of the optimization. Because many global quantum circuit optimization problems belong to the complexity class QMA (the quantum analog of NP), it is not clear whether quality and efficiency guarantees can both be achieved. In this paper, we present optimization techniques for quantum programs that can offer both efficiency and quality guarantees. Rather than requiring global optimality, our approach relies on a form of local optimality that requires each and every segment of the circuit to be optimal. We show that the local optimality notion can be attained by a cut-and-meld circuit optimization algorithm. The idea behind the algorithm is to cut a circuit into subcircuits, optimize each subcircuit independently by using a specified "oracle" optimizer, and meld the subcircuits by optimizing across the cuts lazily as needed. We specify the algorithm and prove that it ensures local optimality. To prove efficiency, we show that, under some assumptions, the main optimization phase of the algorithm requires a linear number of calls to the oracle optimizer. We implement and evaluate the local-optimality approach to circuit optimization and compare with the state-of-the-art optimizers. The empirical results show that our cut-and-meld algorithm can outperform existing optimizers significantly, by more than an order of magnitude on average, while also slightly improving optimization quality. These results show that local optimality can be a relatively strong optimization criterion and can be attained efficiently.
Recent advances in quantum architectures and computing have motivated the development of new optimizing compilers for quantum programs or circuits. Even though steady progress has been made, existing quantum optimization techniques remain asymptotically and practically inefficient and are unable to offer guarantees on the quality of the optimization. Because many global quantum circuit optimization problems belong to the complexity class QMA (the quantum analog of NP), it is not clear whether quality and efficiency guarantees can both be achieved. In this paper, we present optimization techniques for quantum programs that can offer both efficiency and quality guarantees. Rather than requiring global optimality, our approach relies on a form of local optimality that requires each and every segment of the circuit to be optimal. We show that the local optimality notion can be attained by a cut-and-meld circuit optimization algorithm. The idea behind the algorithm is to cut a circuit into subcircuits, optimize each subcircuit independently by using a specified "oracle" optimizer, and meld the subcircuits by optimizing across the cuts lazily as needed. We specify the algorithm and prove that it ensures local optimality. To prove efficiency, we show that, under some assumptions, the main optimization phase of the algorithm requires a linear number of calls to the oracle optimizer. We implement and evaluate the local-optimality approach to circuit optimization and compare with the state-of-the-art optimizers. The empirical results show that our cut-and-meld algorithm can outperform existing optimizers significantly, by more than an order of magnitude on average, while also slightly improving optimization quality. These results show that local optimality can be a relatively strong optimization criterion and can be attained efficiently.
Recent advances in quantum architectures and computing have motivated the development of new optimizing compilers for quantum programs or circuits. Even though steady progress has been made, existing quantum optimization techniques remain asymptotically and practically inefficient. Because many global quantum circuit optimization problems belong to the complexity class QMA (the quantum analog of NP) [51], it is not clear whether efficiency guarantees can be achieved. In this paper, we present an algorithm that achieves efficiency by aiming at a form of local optimality rather than global optimality. Our local-optimization algorithm cuts a circuit into subcircuits, optimizes each subcircuit with the specified oracle optimizer, and melds the subcircuits by optimizing across the cuts lazily as needed. To prove efficiency, we show that, under some assumptions, the main optimization phase of the algorithm requires a linear number of calls to the oracle optimizer. Our empirical results show that our local-optimization algorithm can outperform existing optimizers significantly, by more than an order of magnitude on average. Perhaps surprisingly, the algorithm achieves these improvements without noticeable degradation in optimization quality. These results show that local optimization can be effective for optimizing quantum circuits.
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.
Optimization of quantum programs or circuits is a fundamental problem in quantum computing and remains a major challenge. State-of-the-art quantum circuit optimizers rely on heuristics and typically require superlinear, and even exponential, time. Recent work [8] proposed a new approach that pursues a weaker form of optimality called local optimality. Parameterized by a natural number Ω, local optimality insists that each and every Ω-segment of the circuit is optimal with respect to an external optimizer, called the oracle. Local optimization can be performed using only a linear number of calls to the oracle but still incurs quadratic computational overheads in addition to oracle calls. Perhaps most importantly, the algorithm is sequential.
Noisy intermediate-scale quantum (NISQ) devices with limited qubit count and connectivity limit the scale of quantum circuits that can be executed. Circuit cutting methods simulate larger quantum computers by decomposing large circuits into small subcircuits that can be executed on NISQ hardware. Existing circuit cutting methods only consider the qubit count of the target hardware for finding the locations of cuts on the circuits. This can result in deeper subcircuits after mapping on the hardware. Fidelity decays exponentially with circuit depth and diminishes the quality of execution. We propose a circuit-cutting framework that reduces variance in the depth of subcircuits after mapping to the hardware. Our method formulates the initial circuit cutting as a multi-objective optimization problem based on an evolutionary search method with the number of cuts and the maximum depth of individual routed subcircuits as fitness objectives. This method is implemented as an extension to the existing Qiskit Circuit Cutting Addon, which allows for integration in existing flows. Our approach achieves reductions in routed subcircuit depth of up to 9.9% across benchmark circuits compared with baseline methods.
Quantum circuit optimization is essential for improving the performance of quantum algorithms, particularly on Noisy Intermediate-Scale Quantum (NISQ) devices with limited qubit connectivity and high error rates. Pattern matching has proven to be an effective technique for identifying and optimizing subcircuits by replacing them with functionally equivalent, efficient versions, including reducing circuit depth and facilitating platform portability. However, existing approaches face challenges in handling large-scale circuits and numerous transformation rules, often leading to redundant matches and increased compilation time. In this study, we propose a novel framework for quantum circuit optimization based on pattern matching to enhance its efficiency. Observing redundancy in applying existing transformation rules, our method employs a pattern tree structure to organize these rules, reducing redundant operations during the execution of the pattern-matching algorithm and improving matching efficiency. We design and implement a compilation framework to demonstrate the practicality of the pattern tree approach. Experimental results show that pattern-tree-based pattern matching can reduce execution time by an average of 20% on a well-accepted benchmark set. Furthermore, we analyze how to build a pattern tree to maximize the optimization of compilation time. The evaluation results demonstrate that our approach has the potential to optimize compilation time by 90%.
Linear Optical Quantum Computing (LOQC) is emerging as a promising technology in large-scale quantum computing. Corresponding devices, including linear optical circuits, are rapidly growing in size and fabrication precision. However, even with improved quality, the circuits still exhibit imperfections leading to photon loss or phase noise that vary across the circuit. Already small deficiencies can have a vast impact on both accuracy and efficiency. For computations that do not require the entire linear optical circuit, so-called subcircuits, one can choose where to perform the computation, opening optimization opportunities that are addressed by subcircuit compilation. Current compilers spread the subcircuit's computation across the entire circuit, connecting the same input and output ports, thereby failing to fully exploit the optimization opportunities. However, given the subcircuit's reduced size compared to the entire circuit, one can keep its implementation localized and intentionally route photons to connect good input and output ports. This, however, is a highly non-trivial task, as numerous options must be weighed against one another, and the quality of the solution is influenced by a wide range of hardware parameters. In particular, the reflectivities of imperfect beam splitters can lead to photon losses during routing, which must be traded off against losses at the input and output ports due to imperfect transmission rates. Since current compilers do not account for these effects, we propose the first efficient subcircuit compilation method that optimizes for the coincidence rate, the probability of successfully measuring all desired photons, by handling hardware imperfections. Our evaluations demonstrate significant improvement over existing methods in robustness against phase noise and significantly increased coincidence rates across all benchmarks of up to plus 33.2%.