arXiv subjects

Mingkuan Xu

Publications and source records attributed to Mingkuan Xu.

9 recordsLinked to original sources

arXiv2026

QALM: Escaping Local Minima via Interleaved Exploration and Exploitation in Quantum Circuit Optimization

Quantum circuit optimizers face a fundamental limitation in how they tolerate temporary cost increases. At one extreme, greedy rule-based optimizers immediately apply any cost-reducing transformation, achieving high efficiency but quickly becoming trapped in local minima. At the other extreme, search-based optimizers accept cost-increasing moves to explore the circuit space and escape such minima. However, because search-based optimizers cannot determine within a reasonable time budget whether a given point is promising, that is, whether its neighborhood contains a deeper local minimum, they must blindly explore higher-cost regions. As a result, escaping the current basin to reach a promising point takes exponentially many steps. In this work, we show that this limitation can be overcome with a hybrid framework that interleaves the exhaustive exploration capabilities of search algorithms with the efficiency of rule-based optimization. We implement this framework as QALM, a novel optimizer designed to escape local minima without incurring the runtime penalties of pure search. Crucially, our results demonstrate that QALM does not merely strike a balance; it outperforms existing rule-based and search-based optimizers in circuit reduction rates while operating with the computational efficiency of rule-based systems. In a comprehensive evaluation across 248 circuits, QALM matches or exceeds the fidelity of the strongest baseline on 83.9% of these circuits, given the same time budget.

quant-ph↗

arXiv2025

ConiQ: Enabling Concatenated Quantum Error Correction on Neutral Atom Arrays

Recent progress on concatenated codes, especially many-hypercube codes, achieves unprecedented space efficiency. Yet two critical challenges persist in practice. First, these codes lack efficient implementations of addressable logical gates. Second, the required high degree of parallelism and long-range interactions pose significant challenges for current hardware platforms. In this paper, we propose an efficient compilation approach for concatenated codes, specifically many-hypercube codes, targeted at neutral atom arrays, which provide the necessary parallelism and long-range interactions. Our approach builds on two key innovations. First, we introduce Automorphism-assisted Hierarchical Addressing (AHA) logical CNOT gates that significantly reduce spacetime overhead compared to conventional distillation-based methods. Second, we develop Virtual Atom Intermediate Representation (VAIR) that enables level-wise optimization and legalization. We implement these innovations in ConiQ, a hardware-aware quantum compiler designed to compile fault-tolerant quantum circuits for neutral atom arrays using many-hypercube codes. Our evaluation demonstrates that ConiQ achieves up to 2000x reduction in spacetime overhead and up to 10^6x reduction in compilation time compared to state-of-the-art compilers, with our AHA gates providing an additional overhead reduction of up to 20x. These results establish concatenated codes as a promising approach for fault-tolerant quantum computing in the near future.

cs.AR↗

arXiv2025

Leveraging Phase Polynomials for Quantum Circuit Optimization

Quantum circuits on resource-limited hardware require optimizing regions dominated by $\{\mathrm{CNOT}, R_z\}$, which account for a large fraction of operations and often dominate execution cost. This optimization can be challenging because phase-polynomial blocks are fragmented by basis-changing gates such as $H$, and optimizing phase parities alone may increase the cost of downstream basis transformations. Existing phase-polynomial approaches are limited to single-block or phase-only optimization, while subcircuit rewriting approaches are local and scale poorly beyond small rewrite windows. We introduce \emph{PhasePoly}, a compiler optimization pass that jointly optimizes phase-parity and output-parity networks and employs a cross-block intermediate representation to reuse parities across phase-polynomial block barriers. This approach is effective because its unified parity-matrix representation exposes long-range $\{\mathrm{CNOT}, R_z\}$ structure that local rewriting and single-block methods cannot capture. \emph{PhasePoly} reduces total gate count by up to 50.00\% (34.70\% on average) and CNOT count by up to 48.57\% (26.83\% on average), while scaling to large circuits and improving both fault-tolerant compilation and near-term hardware execution. \emph{PhasePoly} is available at https://github.com/ruadapt/PhasePoly.

cs.PL↗

arXiv2025

POPQC: Parallel Optimization for Quantum Circuits (Extended Version)

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 proposed a new approach that pursues a weaker form of optimality called local optimality. Parameterized by a natural number $\Omega$, local optimality insists that each and every $\Omega$-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. In this paper, we present a parallel algorithm for local optimization of quantum circuits. To ensure efficiency, the algorithm operates by keeping a set of fingers into the circuit and maintains the invariant that a $\Omega$-deep circuit needs to be optimized only if it contains a finger. Operating in rounds, the algorithm selects a set of fingers, optimizes in parallel the segments containing the fingers, and updates the finger set to ensure the invariant. For constant $\Omega$, we prove that the algorithm requires $O(n\lg{n})$ work and $O(r\lg{n})$ span, where $n$ is the circuit size and $r$ is the number of rounds. We prove that the optimized circuit returned by the algorithm is locally optimal in the sense that any $\Omega$-segment of the circuit is optimal with respect to the oracle.

cs.DC↗

arXiv2025

Local Optimization of Quantum Circuits (Extended Version)

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.

cs.PL↗

arXiv2024

Atlas: Hierarchical Partitioning for Quantum Circuit Simulation on GPUs (Extended Version)

This paper presents techniques for theoretically and practically efficient and scalable Schrödinger-style quantum circuit simulation. Our approach partitions a quantum circuit into a hierarchy of subcircuits and simulates the subcircuits on multi-node GPUs, exploiting available data parallelism while minimizing communication costs. To minimize communication costs, we formulate an Integer Linear Program that rewards simulation of "nearby" gates on "nearby" GPUs. To maximize throughput, we use a dynamic programming algorithm to compute the subcircuit simulated by each kernel at a GPU. We realize these techniques in Atlas, a distributed, multi-GPU quantum circuit simulator. Our evaluation on a variety of quantum circuits shows that Atlas outperforms state-of-the-art GPU-based simulators by more than 2$\times$ on average and is able to run larger circuits via offloading to DRAM, outperforming other large-circuit simulators by two orders of magnitude.

cs.DC↗

arXiv2022

Quartz: Superoptimization of Quantum Circuits (Extended Version)

Existing quantum compilers optimize quantum circuits by applying circuit transformations designed by experts. This approach requires significant manual effort to design and implement circuit transformations for different quantum devices, which use different gate sets, and can miss optimizations that are hard to find manually. We propose Quartz, a quantum circuit superoptimizer that automatically generates and verifies circuit transformations for arbitrary quantum gate sets. For a given gate set, Quartz generates candidate circuit transformations by systematically exploring small circuits and verifies the discovered transformations using an automated theorem prover. To optimize a quantum circuit, Quartz uses a cost-based backtracking search that applies the verified transformations to the circuit. Our evaluation on three popular gate sets shows that Quartz can effectively generate and verify transformations for different gate sets. The generated transformations cover manually designed transformations used by existing optimizers and also include new transformations. Quartz is therefore able to optimize a broad range of circuits for diverse gate sets, outperforming or matching the performance of hand-tuned circuit optimizers.

cs.PL↗

arXiv2021

AsyncTaichi: On-the-fly Inter-kernel Optimizations for Imperative and Spatially Sparse Programming

Leveraging spatial sparsity has become a popular approach to accelerate 3D computer graphics applications. Spatially sparse data structures and efficient sparse kernels (such as parallel stencil operations on active voxels), are key to achieve high performance. Existing work focuses on improving performance within a single sparse computational kernel. We show that a system that looks beyond a single kernel, plus additional domain-specific sparse data structure analysis, opens up exciting new space for optimizing sparse computations. Specifically, we propose a domain-specific data-flow graph model of imperative and sparse computation programs, which describes kernel relationships and enables easy analysis and optimization. Combined with an asynchronous execution engine that exposes a wide window of kernels, the inter-kernel optimizer can then perform effective sparse computation optimizations, such as eliminating unnecessary voxel list generations and removing voxel activation checks. These domain-specific optimizations further make way for classical general-purpose optimizations that are originally challenging to directly apply to computations with sparse data structures. Without any computational code modification, our new system leads to $4.02\times$ fewer kernel launches and $1.87\times$ speed up on our GPU benchmarks, including computations on Eulerian grids, Lagrangian particles, meshes, and automatic differentiation.

cs.PL↗

arXiv2019

Rule Designs for Optimal Online Game Matchmaking

Online games are the most popular form of entertainment among youngsters as well as elders. Recognized as e-Sports, they may become an official part of the Olympic Games by 2020. However, a long waiting time for matchmaking will largely affect players' experiences. We examine different matchmaking mechanisms for 2v2 games. By casting the mechanisms into a queueing theoretic framework, we decompose the rule design process into a sequence of decision making problems, and derive the optimal mechanism with minimum expected waiting time. We further the result by exploring additional static as well as dynamic rule designs' impacts. In the static setting, we consider the game allows players to choose sides before the battle. In the dynamic setting, we consider the game offers multiple zones for players of different skill levels. In both settings, we examine the value of choice-free players. Closed form expressions for the expected waiting time in different settings illuminate the guidelines for online game rule designs.

cs.PF↗