Quantum Circuit Compilation

High Performance Computing (HPC) and Quantum Computing (QC) systems are increasingly converging towards unified High Performance Computing-Quantum Computing (HPCQC) infrastructures, driven by a growing need to bridge classical and quantum workflows, which affects all levels of the system stack, from the hardware to compilers and runtimes, all the way to applications. However, today's QC devices are still in the Noisy Intermediate-Scale Quantum (NISQ) era, are error-prone and resource-limited, and therefore require specialized optimizations and topology mappings to achieve sufficient fidelity. This places special emphasis on proper compilation and optimization within the overall quantum software stack. Many existing stacks remain fragmented, with separate components responsible for device selection, compiler-pass optimization, and job queue scheduling. This paper proposes a unified, learning-based selector that integrates these disparate stages into a cohesive framework. Our proposed selector scheme leverages reinforcement learning and deep learning models that can be extended to simultaneously optimize multiple objectives -- such as fidelity, compilation time, and scheduling latency -- while dynamically adapting to circuit characteristics and device conditions.

Quantum circuit optimization replaces a circuit with an equivalent one of fewer gates and lower depth, reducing execution cost and error rate. We ask whether a generative model can learn this transformation directly from examples, rather than selecting from a fixed rewrite library or rigid algebraic routines. We present Bridge of $Ψ$'s (BOPS), a generative model based on Schrödinger bridges, using a custom denoiser architecture, that learns a transformation from a source circuit into an equivalent optimized circuit. We train it on data constructed to be hard for existing optimizers, by applying rewrite rules backwards so that each input has a known lower-cost target. On held-out 8 qubits $\times$ 64 depth Clifford+$T$ circuits, BOPS reduces gate count by $2.46\times$ and depth by $2.45\times$ in geometric mean, outperforming all nine baseline optimizers. This constitutes the first generative model bridging quantum circuits and frontier machine learning methods, opening up the quantum compilation stack to learned optimization along multiple axes.

Quantum software engineering is an emerging research field focusing on efficiently embedding the quantum programming paradigm into existing software ecosystems. A key aspect of this field is the realization of quantum algorithms using gate-based programming and the subsequent low-level optimization of the resulting quantum circuits, a process that is commonly performed by so-called transpilation pipelines. One significant challenge in these pipelines is determining which optimizations to apply to a given circuit. This decision is usually based on fixed default configurations that are uniformly applied to all circuits, frequently resulting in missed opportunities for more aggressive circuit optimization. In this work, we tackle this challenge by applying autotuning with supervised machine learning to develop an automated method for selection of transpiler passes. To train our machine-learning models, we employ feature-model based sampling to generate a representative dataset that examines how different combinations of Qiskit transpiler passes perform across thousands of circuits drawn from the state-of-the-art benchmarking suite MQT Bench. Using these data, we build a predictive model extension for the Qiskit transpilation pipeline that uses a machine learning model to automatically select combinations of transpiler passes aiming to achieve a maximum reduction in two-qubit gates. Our empirical evaluation shows that the combinations selected by our model are never outperformed by Qiskit's optimization levels, achieve on average an additional 19.1$\%$ - 32.4$\%$ reduction in two-qubit gates, and for some circuits finds reductions of up to $95.8\%$ in cases where Qiskit achieves no reduction at all.

Trapped-ion quantum computers rely on shuttling compilers, which cast an input algorithm into a sequence of ion-qubit movements within a given architecture. We present the first study in which a single frontier large language model (LLM), Claude Opus 4.7, generates and iteratively refines the full Python code of shuttling compilers from written specifications. We start with a compiler for (i) a linear segmented trap, extend it to (ii) a trap with junctions, and finally achieve efficient compilation for (iii) a broad class of connected trap graphs. The compilers for the more general cases are seeded with code from the previous ones. We benchmark the LLM-generated compilers against state-of-the-art hand-crafted ones using a common suite of quantum circuits. The number of shuttling timesteps is reduced by up to 76% for (i) and up to 39% for (ii). For the broad case (iii) of freely connected architectures, we find large variations in the required number of shuttling timesteps, depending on the connectivity. A densely connected, junction-rich architecture yields an order-of-magnitude reduction in shuttling timesteps compared to a corridor-like one. Repeating the complete generation and evaluation with a second frontier LLM, Claude Fable 5, reproduces these findings, with the Fable 5 compilers surpassing the hand-crafted ones more often on the largest circuits. Our results show that an unmodified frontier LLM can produce working, correct, and competitive shuttling compilers without additional manual algorithmic engineering, thus reducing the development time for new architectures from several months to a few days.

An important task in quantum computing is unitary circuit synthesis compatible with physical hardware constraints. This problem has a natural hybrid structure as local single-qubit gates are continuous variables on the Lie group $SU(2)$ while the entangling circuit structure is discrete and hardware-dependent. In this work, we use generative models to perform quantum circuit synthesis incorporating both the natural $SU(2)$ manifold geometry of quantum gates and hardware constraints that determine the overall circuit structure. Our model comprises two components: a circuit skeleton selector that chooses an entangling circuit and a diffusion model that generates quantum gates on the given circuit template by performing diffusion on the curved manifold $\mathrm{SU(2)} \simeq S^3$ itself. We demonstrate this approach with unitary compilation of physically motivated three-qubit Hamiltonian simulation targets such as the Transverse Field Ising Model and the Heisenberg-XXZ Model and show that Lie group diffusion outperforms comparable baselines. The synthesised circuits can also be customised subject to constraints, which we demonstrate by producing circuits with large and small gate rotation angles for the same target unitary evolution. We also investigate the fidelity-complexity frontier of the synthesised gates to demonstrate that the circuit selector learns to select circuits that balance fidelity with complexity rather than collapsing onto the most expansive entangling template. These results demonstrate that Lie group diffusion provides a natural generative framework for hardware-aware quantum circuit synthesis.

Quantum circuit routing is a key step in compiling programs for noisy intermediate-scale quantum processors. Routes that appear efficient by standard overhead metrics can still lose fidelity when they pass through poorly calibrated couplers. We study a calibration-aware graph reinforcement-learning router that uses same-day IBM Heron r2 calibration data to choose hardware-edge SWAPs. We train the policy with proximal policy optimization and evaluate it with exact simulated fidelity across nine Munich Quantum Toolkit (MQT) Bench circuits and three calibration snapshots. Across these evaluations, pooled mean exact fidelity is $0.727$, compared with $0.440$ for SABRE-best20 and $0.481$ for target-aware SABRE. We observed that fidelity gains came with higher routed two-qubit counts and were concentrated in 5 qubit and 8 qubit circuit families; under the fixed tree action graph, all 10 qubit families favored SABRE-best20. Overall, our results show that calibration-aware learned routing can improve fidelity beyond gate-count-driven compilation.

Noisy intermediate-scale quantum (NISQ) processors are entering an early fault-tolerance regime where full quantum error correction carries prohibitive resource costs, yet lightweight error detection can meaningfully improve algorithmic success rates. Existing compilation and error-detection toolchains treat these concerns in isolation, with no principled way to balance detection overhead against success probability under latency constraints. We present an integrated hardware-aware compilation and data-driven quantum error-detection (QED) framework that jointly optimises qubit mapping, SWAP insertion, and syndrome-schedule placement via a noise-weighted cost function and a learned multi-objective scheduler. Simulation experiments on an HPC cluster using GPU-accelerated density-matrix simulation (NVIDIA cuQuantum SDK) across VQE, phase-estimation, and Grover benchmarks, three noise profiles, and circuit sizes of 6-20 qubits (depths 10-160), show that joint co-design raises algorithmic success probability by up to 68 percent (95 percent CI: 60 percent to 76 percent) over SABRE on an 8-qubit VQE instance with post-selection.

A quantum compiler is a critical piece in the quantum computing pipeline since it allows an abstract quantum circuit to be run on a physical quantum computer. One extremely important subproblem in quantum compilation is the generation of a logical to physical qubit mapping. Typically in quantum compilers this step is either implemented as a random or a heuristic based assignment that aims to minimize additional (SWAP) gate overhead in the quantum circuit. In this paper, we present an alternative approach to solving the qubit mapping problem. Specifically, we formulate the qubit mapping problem with a combinatorial optimization (CO) objective. We then present a method to find a solution to the CO problem by training a reinforcement learning (RL) policy. We also propose a local search based post-processing algorithm to further reduce the overhead. Our results show a dramatic improvement over conventional techniques in reducing the number of SWAPs. On different real world datasets like MQTBench and Queko circuits, our trained policy achieves a \textbf{65-85%} reduction in SWAP overhead when compared to existing quantum compilers.

Trotter Suzuki product formulas are the standard route to Hamiltonian evolution on noisy intermediate-scale quantum (\NISQ{}) hardware, but their accuracy depends on three coupled choices: term grouping, product-formula order, and time-step allocation. Grouping and order are discrete, which makes direct gradient optimization infeasible and forces existing compilers to rely on static heuristics. We describe P-GONE, a method that combines a conditional diffusion model (D3PM + DDPM), a graph neural network (\GNN{}) encoder, and closed-loop REINFORCE fine-tuning to jointly learn grouping, order, and time-step optimization over a mixed discrete-continuous space. Under fidelity-matched conditions ($F \geq 0.95$), the method achieves circuit depth 86 versus 1673 for Qiskit fourth-order (ungrouped, Suzuki-4), about $19.4\times$ compression, and 141 for Paulihedral (first-order Trotter), about $1.6\times$ compression. At $T=0.90$ the method also beats the Qiskit group-commuting teacher (65 vs 103, $1.6\times$ compression), though at $T=0.95$ the teacher still leads -- a stratified pattern that points toward fidelity-aware fine-tuning. Under a standard depolarizing noise model, the method achieves noisy fidelity roughly $2\times$ the Qiskit fourth-order baseline (0.743 vs 0.380). Ablation shows a clear hierarchy: order learning $>$ time allocation $>$ grouping. Best-of-N sampling ($N=32$ is a practical sweet spot) and CFG guidance give flexible fidelity-depth trade-offs at inference. The method works well on structured Hamiltonians (TFIM, Heisenberg), but random Pauli Hamiltonians fail entirely at $T \geq 0.95$ -- a boundary that defines where the method applies.

Qubit routing is a fundamental problem in quantum compilation, known to be NP-hard. Its dynamic nature makes local routing decisions propagate and compound over time, making global efficient solutions challenging. Existing heuristic methods rely on local rules with limited lookahead, while recent learning-based approaches often treat routing as a generic sequential decision problem without fully exploiting its underlying structure. In this paper, we introduce QAP-Router, framing qubit routing based on a dynamic Quadratic Assignment Problem (QAP) formulation. By modeling logical interactions, or quantum gates, as flow matrices and hardware topology as a distance matrix, our approach captures the interaction-distance coupling in a unified objective, which defines the reward in the reinforcement learning environment. To further exploit this structure, the policy network employs a solution-aware Transformer backbone that encodes the interaction between the flow matrix and the distance matrix into the attention mechanism. We also integrate a lookahead mechanism that blends naturally into the QAP framework, preventing myopic decisions. Extensive experiments on 1,831 real-world quantum circuits from the MQTBench, AgentQ and QUEKO datasets show that our method substantially reduces the CNOT gate count of routed circuits by 15.7%, 30.4% and 12.1%, respectively, relative to existing industry compilers.

We consider the problem of synthesizing Clifford quantum circuits for devices with all-to-all qubit connectivity. We approach this task as a reinforcement learning problem in which an agent learns to discover a sequence of elementary Clifford gates that reduces a given symplectic matrix representation of a Clifford circuit to the identity. This formulation permits a simple learning curriculum based on random walks from the identity. We introduce a novel neural network architecture that is equivariant to qubit relabelings of the symplectic matrix representation, and which is size-agnostic, allowing a single learned policy to be applied across different qubit counts without circuit splicing or network reparameterization. On six-qubit Clifford circuits, the largest regime for which optimal references are available, our agent finds circuits within one two-qubit gate of optimality in milliseconds per instance, and finds optimal circuits in 99.2% of instances within seconds per instance. After continued training on ten-qubit instances, the agent scales to unseen Clifford tableaus with up to thirty qubits, including targets generated from circuits with over a thousand Clifford gates, where it achieves lower average two-qubit gate counts than Qiskit's Aaronson-Gottesman and greedy Clifford synthesizers.

High-fidelity circuit execution on noisy intermediate-scale quantum devices is bottlenecked by compilation pipelines that disregard complex, correlated noise. To address this, this methodology article proposes a quantum machine learning control (QMLC) framework for generative quantum circuit synthesis from gate-set tomography (GST) data that bypasses the traditional two-step pipeline of characterizing native quantum gates via GST followed by unitary decomposition algorithms. Instead, a generative concept space is directly learnt from GST data, enabling conditional synthesis of quantum circuits on a desired output distribution. Our approach tokenizes GST germ circuits and embeds them into a structured latent space using a curriculum-learning-motivated strategy, starting with short circuits and progressively incorporating longer ones with diverse output statistics. The embedded sequences are processed by a set-vision transformer with permutation-invariant pooling, producing k-seed vectors that represent the learned concept space of the quantum device. Aggregating data across multiple circuits makes this latent representation inherently context-aware, capturing the shared physical noise environment (e.g., crosstalk, drift) that isolated gate metrics miss. We propose an unconditional diffusion model to sample from the concept space. During inference, a user provides a target measurement distribution, and the model generates a corresponding circuit. To ensure fidelity and robustness, the output is denoised using a diffusion model that operates on the target conditional covariance matrix. This end-to-end framework is a step towards context-aware, hardware-native circuit synthesis directly from raw GST data, which offers a new paradigm for integrating quantum control and compilation. The QMLC framework is particularly suited for near-term quantum devices with complex calibration procedures.

In trapped-ion quantum computers, qubits must be shuttled between segments to interact. The routing logic that schedules these movements is written by hand for every new trap architecture. We present shuttling compilers based on five large language models (LLMs). Each LLM is fine-tuned on shuttling schedules produced by hand-coded heuristics for linear and branched one-dimensional trap architectures. We investigate how the shuttling operation counts of their schedules compare with those of the heuristics and how far they generalize to unseen architectures. For circuits of up to 16 qubits, the fine-tuned LLMs generate valid schedules on both training architectures, more often the fewer qubits a circuit has. In 12% of the compilations yielding a schedule, the best of ten runs needs up to 21% fewer operations than the heuristic baselines, after a rule-based post-processing step. A single run of one fine-tuned LLM produces a valid shuttling schedule for a previously unseen four-way branched architecture. This is preliminary evidence of cross-architecture generalization. On two other unseen architectures no LLM produces a valid schedule. Thus, LLM-learned shuttling compilation is feasible, and we show how far it currently reaches.