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 github.com/munich-quantum-toolkit/core.

Abstract The top-down solver TD is a generic fixpoint algorithm that can be used to compute partial post-solutions of equation systems for abstract interpretation. We consider two extensions of the TD to deal with infinite strictly ascending chains. For the TD extended with warrowing , we formally prove that it always returns partial post-solutions, while for the TD extended with widening and narrowing in phases, we prove termination provided that the set of unknowns is finite. By proving the equivalence of the two extensions, we deduce the total correctness of both solvers. For the equivalence to hold, we in particular assume the equation system to have right-hand sides that are both monotonic and have monotonic dependencies . We demonstrate with counterexamples that the violation of any of the assumptions may compromise the equivalence. All proofs have been formalized using the interactive theorem prover Isabelle.

Quantum computing promises to solve problems previously deemed infeasible. However, high error rates necessitate quantum error correction for practical applications. Seminal experiments with zoned neutral atom architectures have shown remarkable potential for fault-tolerant quantum computing. To fully harness their potential, efficient software solutions are vital. A key aspect of quantum error correction is the initialization of physical qubits representing a logical qubit in a highly entangled state. This process, known as state preparation, is the foundation of most quantum error correction codes and, hence, a crucial step towards fault-tolerant quantum computing. Generating a schedule of target-specific instructions to perform the state preparation is highly complex. First software tools exist but are not suitable for the zoned neutral atom architectures. This work addresses this gap by leveraging the computational power of SMT solvers and generating minimal schedules for the state preparation of logical arrays. Experimental evaluations demonstrate that actively utilizing zones to shield idling qubits consistently results in higher fidelities than solutions disregarding these zones. The complete code is publicly available in open-source as part of the Munich Quantum Toolkit (MQT) at https://github.com/cdatum/mqt-qmap.

Quantum computing promises to solve previously intractable problems, with neutral atoms emerging as a promising technology. Zoned neutral atom architectures allow for immense parallelism and higher coherence times by shielding idling atoms from interference with laser beams. However, in addition to hardware, successful quantum computation requires sophisticated software support, particularly compilers that optimize quantum algorithms for hardware execution. In the compilation flow for zoned neutral atom architectures, the effective interplay of the placement and routing stages decides the overhead caused by rearranging the atoms during the quantum computation. Suboptimal placements can lead to unnecessary serialization of the rearrangements in the subsequent routing stage. Despite this, all existing compilers treat placement and routing independently thus far—focusing solely on minimizing travel distances. This work introduces the first routing-aware placement method to address this shortcoming. It groups compatible movements into parallel rearrangement steps to minimize both rearrangement steps and travel distances. The implementation utilizing the A* algorithm reduces the rearrangement time by 17% on average and by 49% in the best case compared to the state-of-the-art. The complete code is publicly available in open-source as part of the Munich Quantum Toolkit (MQT) at https://github.com/cda-tum/mqt-qmap.

Quantum computing (QC) introduces a novel mode of computation with the possibility of greater computational power that remains to be exploitedpresenting exciting opportunities for high-performance computing (HPC) applications. However, recent advancements in the field have made clear that QC does not supplant conventional HPC, but can rather be incorporated into current heterogeneous HPC infrastructures as an additional accelerator, thereby enabling the optimal utilization of both paradigms. The desire for such integration significantly affects the development of software for quantum computers, which in turn influences the necessary software infrastructure. To date, previous review articles have investigated various quantum programming tools (QPTs) (such as languages, libraries, frameworks) in their ability to program, compile, and execute quantum circuits. However, the integration effort with classical HPC frameworks or systems has not been addressed. This study aims to characterize existing QPTs from an HPC perspective, investigating if existing QPTs have the potential to be efficiently integrated with classical computing models and determining where work is still required. This work structures a set of criteria into an analysis blueprint that enables HPC scientists to assess whether a QPT is suitable for a high-performance computing quantum computing (HPCQC) environment.

Abstract The top-down solver (TD) is a local fixpoint algorithm for arbitrary equation systems. It considers the right-hand sides as black boxes and detects dependencies between unknowns on the fly—features that significantly increase both its usability and practical efficiency. At the same time, the recursive evaluation strategy of the TD, combined with the non-local destabilization mechanism, obfuscates the correctness of the computed solution. To strengthen the confidence in tools relying on the TD as their fixpoint engine, we provide a first machine-checked proof of the partial correctness of the TD. Our proof builds on the observation that the TD can be obtained from a considerably simpler recursive fixpoint algorithm, the plain TD, by applying an optimization that neither affects the termination behavior nor the computed result. Accordingly, we break down the proof into a partial correctness proof of the plain TD, which is only then extended to include the optimization. The backbone of our proof is a mutual induction following the solver’s computation trace. We establish sufficient invariants about the solver state to conclude the correctness of its optimization, i.e., the plain TD terminates if and only if the TD terminates, and they return the identical result. The proof is written using Isabelle/HOL and is available in the archive of formal proofs.

We study graph expansion grammars, a type of graph grammar that has recently been introduced with motivations in natural language processing. Graph expansion generalizes the well-known hyperedge replacement. In contrast to the latter, the former is able to generate graph languages of unbounded treewidth, like the set of all graphs. In an earlier paper, the complexity of the membership problem of the generated languages was studied, the main result being a polynomial parsing algorithm for local DAG expansion grammars (there called local DAG expansion grammars), a subclass of graph expansion grammars that generates directed acyclic graphs. Here, we study the generative power of local graph expansion grammars. While they, unrestricted, are able to simulate Turing machines, we identify natural restrictions that give rise to a pumping lemma and ensure that the generated languages have regular path languages as well as a semi-linear Parikh image.

Abstract A quantum circuit is often executed on the initial state where each qubit is in the zero state. Therefore, we propose to perform a symbolic execution of the circuit. Our approach simulates groups of entangled qubits exactly up to a given complexity. Here, the complexity corresponds to the number of basis states expressing the quantum state of one entanglement group. By doing that, the groups need neither be determined upfront nor be bound by the number of involved qubits. Still, we ensure that the simulation runs in polynomial time - opposed to exponential time as required for the simulation of the entire circuit. The information made available at gates is exploited to remove superfluous controls and gates. We implemented our approach in the tool quantum constant propagation (QCP) and evaluated it on the circuits in the benchmark suite MQTBench. By applying our tool, only the work that cannot be carried out efficiently on a classical computer is left for the quantum computer, hence exploiting the strengths of both worlds.