Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2607.02616

MLIR for Quantum Beyond Gate Cancellation: Quantum Circuit Mapping Reimagined

Matthias Reumann, Yannick Stade, Robert Wille, Lukas Burgholzer

quant-phcs.ETSubmitted Jul 1, 2026• Announced Jul 3, 2026• 0 citations
arXivHTMLPDF

Abstract

The Multi-Level Intermediate Representation (MLIR) framework has become a cornerstone for building extensible, domain-specific compilers, with the quantum computing community already leveraging it to model quantum programs and implement basic optimizations. However, computationally intensive tasks in the quantum compilation pipeline, such as quantum circuit mapping, remain underexplored within the MLIR ecosystem. This paper proposes an MLIR-native blueprint for these non-local, quantum-specific optimization routines by reimplementing a well-established, state-of-the-art mapping A* search algorithm for qubit routing and SWAP insertion. Our evaluation demonstrates that this approach not only integrates seamlessly into an MLIR-based quantum compiler collection but also surpasses previous non-MLIR solutions in both solution quality and runtime. The implementation is open-source and publicly available at https://github.com/munich-quantum-toolkit/core.

Comments
11 pages, 14 figures

Related papers

The MQT Compiler Collection: A Blueprint for a Future-Proof Quantum-Classical Compilation Framework

Lukas Burgholzer, Daniel Haag, Yannick Stade +3 more

As the capabilities of quantum computing hardware continue to rise, algorithms that exploit them are becoming increasingly complex. These developments increase the need for sophisticated compilation frameworks that translate high-level algorithms into executable code. In the past, most solutions were built with a quantum-first approach and handled mostly pure quantum programs without classical elements such as structured control flow. However, developments in quantum algorithms, error correction, and optimization, as well as the integration into high-performance computing (HPC) environments, depend on such classical elements. As quantum-first approaches increasingly struggle to handle these concepts, classical-first approaches are becoming a promising alternative. In this work, we present the MQT Compiler Collection, a blueprint for a future-proof quantum-classical compilation framework built on the Multi-Level Intermediate Representation (MLIR). After years of experience with the quantum-first approach and its shortcomings, we propose a framework that embraces core MLIR concepts to support the full compilation pipeline from high-level algorithms to hardware-specific instructions. The proposed architecture is designed from the ground up to support complex optimizations beyond, e.g., simple gate cancellation. It is publicly available at https://github.com/munich-quantum-toolkit/core.

quant-pharXiv:2604.08674•Design, Automation, and Test in Europe•Apr 13, 2026•2 citations

Integrating Quantum Software Tools with(in) MLIR

Patrick Hopf, Erick Ochoa Lopez, Yannick Stade +6 more

Compilers transform code into action. They convert high-level programs into executable hardware instructions - a crucial step in enabling reliable and scalable quantum computation. However, quantum compilation is still in its infancy, and many existing solutions are ad hoc, often developed independently and from scratch. The resulting lack of interoperability leads to significant missed potential, as quantum software tools remain isolated and cannot be seamlessly integrated into cohesive toolchains. The Multi-Level Intermediate Representation (MLIR) has addressed analogous challenges in the classical domain. It was developed within the LLVM project, which has long powered robust software stacks and enabled compilation across diverse software and hardware components, with particular importance in high-performance computing environments. However, MLIR's steep learning curve poses a significant barrier to entry, particularly in quantum computing, where much of the software stack is still predominantly built by experimentalists out of necessity rather than by experienced software engineers. This paper provides a practical and hands-on guide for quantum software engineers to overcome this steep learning curve. Through a concrete case study linking Xanadu's PennyLane framework with the Munich Quantum Toolkit (MQT), we outline actionable integration steps, highlight best practices, and share hard-earned insights from real-world development. This work aims to support quantum tool developers in navigating MLIR's complexities and to foster its adoption as a unifying bridge across a rapidly growing ecosystem of quantum software tools, ultimately guiding the development of more modular, interoperable, and integrated quantum software stacks.

quant-pharXiv:2601.02062•International Conference on High Performance Computing in Asia-Pacific Region (HPC Asia)•Jan 6, 2026•4 citations

Towards a Unified Multi-Target Mlir-Based Compiler: A Heterogeneous Compilation Framework for High-Performance and Quantum Computing Integration

Martín Letras, Jorge Echavarria, Muhammad Nufail Farooqi +5 more

The Munich Quantum Software Stack (MQSS) is a compilation and runtime infrastructure designed to bridge the gap between high-performance computing (HPC) and quantum computing (QC). A unified, extensible, and efficient compilation framework becomes important as quantum devices and applications scale. This paper proposes the integration of Multi-Level Intermediate Representation (MLIR) as intermediate representation into the MQSS to address the challenges of optimizing and compiling hybrid classical-quantum applications across diverse quantum devices. Accordingly, the MQSS can separate abstraction layers, enabling high-level optimizations, seamless integration of existing quantum dialects, and targetspecific optimizations for diverse quantum devices.

IEEE International Conference on Quantum Computing and Engineering (QCE)•Aug 30, 2025•1 citation

A MLIR Dialect for Quantum Assembly Languages

Alexander McCaskey, Thien Nguyen

We demonstrate the utility of the Multi-Level Intermediate Representation (MLIR) for quantum computing. Specifically, we extend MLIR with a new quantum dialect that enables the expression and compilation of common quantum assembly languages. The true utility of this dialect is in its ability to be lowered to the LLVM intermediate representation (IR) in a manner that is adherent to the quantum intermediate representation (QIR) specification recently proposed by Microsoft. We leverage a qcor-enabled implementation of the QIR quantum runtime API to enable a retargetable (quantum hardware agnostic) compiler workflow mapping quantum languages to hybrid quantum-classical binary executables and object code. We evaluate and demonstrate this novel compiler workflow with quantum programs written in OpenQASM 2.0. We provide concrete examples detailing the generation of MLIR from OpenQASM source files, the lowering process from MLIR to LLVM IR, and ultimately the generation of executable binaries targeting available quantum processors.

arXiv:2101.11365•IEEE International Conference on Quantum Computing and Engineering (QCE)•Oct 1, 2021•43 citations

Quantum Circuit Transformations with a Multi-Level Intermediate Representation Compiler

Thien Nguyen, Dmitry I. Lyakh, Raphael C. Pooser +3 more

Quantum computing promises remarkable approaches for processing information, but new tools are needed to compile program representations into the physical instructions required by a quantum computer. Here we present a novel adaptation of the multi-level intermediate representation (MLIR) integrated into a quantum compiler that may be used for checking program execution. We first present how MLIR enables quantum circuit transformations for efficient execution on quantum computing devices and then give an example of compiler transformations based on so-called mirror circuits. We demonstrate that mirror circuits inserted during compilation may test hardware performance by assessing quantum circuit accuracy on several superconducting and ion trap hardware platforms. Our results validate MLIR as an efficient and effective method for collecting hardware-dependent diagnostics through automated transformations of quantum circuits.

arXiv:2112.10677•Dec 20, 2021•0 citations

Reducing the Compilation Time of Quantum Circuits Using Pre-Compilation on the Gate Level

Nils Quetschlich, Lukas Burgholzer, Robert Wille

In order to implement a quantum computing application, problem instances must be encoded into a quantum circuit and then compiled for a specific platform. The lengthy compilation process is a key bottleneck in this workflow, especially for problems that arise repeatedly with a similar yet distinct structure (each of which requires a new compilation run thus far). In this paper, we aim to overcome this bottleneck by proposing a comprehensive pre-compilation technique that tries to minimize the time spent for compiling recurring problems while preserving the solution quality as much as possible. The following concepts underpin the proposed approach: Beginning with a problem class and a corresponding quantum algorithm, a predictive encoding scheme is applied to encode a representative problem instance into a general-purpose quantum circuit for that problem class. Once the real problem instance is known, the previously constructed circuit only needs to be adjusted-with (nearly) no compilation necessary. Experimental evaluations on QAOA for the MaxCut problem as well as a case study involving a satellite mission planning problem show that the proposed approach significantly reduces the compilation time by several orders of magnitude compared to Qiskit's compilation schemes while maintaining comparable compiled circuit quality. All implementations are available on GitHub (https://github.com!cda-tum!mqt-problemsolver) as part of the Munich Quantum Toolkit (MQT).

arXiv:2305.04941•IEEE International Conference on Quantum Computing and Engineering (QCE)•Sep 17, 2023•5 citations
The Multi-Level Intermediate Representation (MLIR) framework has become a cornerstone for building extensible, domain-specific compilers, with the quantum computing community already leveraging it to model quantum programs and implement basic optimizations. However, computationally intensive tasks in the quantum compilation pipeline, such as quantum circuit mapping, remain underexplored within the MLIR ecosystem. This paper proposes an MLIR-native blueprint for these non-local, quantum-specific optimization routines by reimplementing a well-established, state-of-the-art mapping A* search algorithm for qubit routing and SWAP insertion. Our evaluation demonstrates that this approach not only integrates seamlessly into an MLIR-based quantum compiler collection but also surpasses previous non-MLIR solutions in both solution quality and runtime. The implementation is open-source and publicly available at https://github.com/munich-quantum-toolkit/core.
As the capabilities of quantum computing hardware continue to rise, algorithms that exploit them are becoming increasingly complex. These developments increase the need for sophisticated compilation frameworks that translate high-level algorithms into executable code. In the past, most solutions were built with a quantum-first approach and handled mostly pure quantum programs without classical elements such as structured control flow. However, developments in quantum algorithms, error correction, and optimization, as well as the integration into high-performance computing (HPC) environments, depend on such classical elements. As quantum-first approaches increasingly struggle to handle these concepts, classical-first approaches are becoming a promising alternative. In this work, we present the MQT Compiler Collection, a blueprint for a future-proof quantum-classical compilation framework built on the Multi-Level Intermediate Representation (MLIR). After years of experience with the quantum-first approach and its shortcomings, we propose a framework that embraces core MLIR concepts to support the full compilation pipeline from high-level algorithms to hardware-specific instructions. The proposed architecture is designed from the ground up to support complex optimizations beyond, e.g., simple gate cancellation. It is publicly available at https://github.com/munich-quantum-toolkit/core.
Compilers transform code into action. They convert high-level programs into executable hardware instructions - a crucial step in enabling reliable and scalable quantum computation. However, quantum compilation is still in its infancy, and many existing solutions are ad hoc, often developed independently and from scratch. The resulting lack of interoperability leads to significant missed potential, as quantum software tools remain isolated and cannot be seamlessly integrated into cohesive toolchains. The Multi-Level Intermediate Representation (MLIR) has addressed analogous challenges in the classical domain. It was developed within the LLVM project, which has long powered robust software stacks and enabled compilation across diverse software and hardware components, with particular importance in high-performance computing environments. However, MLIR's steep learning curve poses a significant barrier to entry, particularly in quantum computing, where much of the software stack is still predominantly built by experimentalists out of necessity rather than by experienced software engineers. This paper provides a practical and hands-on guide for quantum software engineers to overcome this steep learning curve. Through a concrete case study linking Xanadu's PennyLane framework with the Munich Quantum Toolkit (MQT), we outline actionable integration steps, highlight best practices, and share hard-earned insights from real-world development. This work aims to support quantum tool developers in navigating MLIR's complexities and to foster its adoption as a unifying bridge across a rapidly growing ecosystem of quantum software tools, ultimately guiding the development of more modular, interoperable, and integrated quantum software stacks.
The Munich Quantum Software Stack (MQSS) is a compilation and runtime infrastructure designed to bridge the gap between high-performance computing (HPC) and quantum computing (QC). A unified, extensible, and efficient compilation framework becomes important as quantum devices and applications scale. This paper proposes the integration of Multi-Level Intermediate Representation (MLIR) as intermediate representation into the MQSS to address the challenges of optimizing and compiling hybrid classical-quantum applications across diverse quantum devices. Accordingly, the MQSS can separate abstraction layers, enabling high-level optimizations, seamless integration of existing quantum dialects, and targetspecific optimizations for diverse quantum devices.
We demonstrate the utility of the Multi-Level Intermediate Representation (MLIR) for quantum computing. Specifically, we extend MLIR with a new quantum dialect that enables the expression and compilation of common quantum assembly languages. The true utility of this dialect is in its ability to be lowered to the LLVM intermediate representation (IR) in a manner that is adherent to the quantum intermediate representation (QIR) specification recently proposed by Microsoft. We leverage a qcor-enabled implementation of the QIR quantum runtime API to enable a retargetable (quantum hardware agnostic) compiler workflow mapping quantum languages to hybrid quantum-classical binary executables and object code. We evaluate and demonstrate this novel compiler workflow with quantum programs written in OpenQASM 2.0. We provide concrete examples detailing the generation of MLIR from OpenQASM source files, the lowering process from MLIR to LLVM IR, and ultimately the generation of executable binaries targeting available quantum processors.
Quantum computing promises remarkable approaches for processing information, but new tools are needed to compile program representations into the physical instructions required by a quantum computer. Here we present a novel adaptation of the multi-level intermediate representation (MLIR) integrated into a quantum compiler that may be used for checking program execution. We first present how MLIR enables quantum circuit transformations for efficient execution on quantum computing devices and then give an example of compiler transformations based on so-called mirror circuits. We demonstrate that mirror circuits inserted during compilation may test hardware performance by assessing quantum circuit accuracy on several superconducting and ion trap hardware platforms. Our results validate MLIR as an efficient and effective method for collecting hardware-dependent diagnostics through automated transformations of quantum circuits.
In order to implement a quantum computing application, problem instances must be encoded into a quantum circuit and then compiled for a specific platform. The lengthy compilation process is a key bottleneck in this workflow, especially for problems that arise repeatedly with a similar yet distinct structure (each of which requires a new compilation run thus far). In this paper, we aim to overcome this bottleneck by proposing a comprehensive pre-compilation technique that tries to minimize the time spent for compiling recurring problems while preserving the solution quality as much as possible. The following concepts underpin the proposed approach: Beginning with a problem class and a corresponding quantum algorithm, a predictive encoding scheme is applied to encode a representative problem instance into a general-purpose quantum circuit for that problem class. Once the real problem instance is known, the previously constructed circuit only needs to be adjusted-with (nearly) no compilation necessary. Experimental evaluations on QAOA for the MaxCut problem as well as a case study involving a satellite mission planning problem show that the proposed approach significantly reduces the compilation time by several orders of magnitude compared to Qiskit's compilation schemes while maintaining comparable compiled circuit quality. All implementations are available on GitHub (https://github.com!cda-tum!mqt-problemsolver) as part of the Munich Quantum Toolkit (MQT).