Compiler Optimization for Quantum Computing Using Reinforcement Learning

I. INTRODUCTION

• Quantum compilers are still early in development, with no consolidated best pass combinations, limited interoperability, slow uptake of research, and little flexibility in optimization goals.The authors note that techniques from classical compilers cannot be transferred straightforwardly because quantum and classical computation differ.Source: §I · p. 1
• The framework models compilation as a Markov Decision Process and uses reinforcement learning to learn an ordering of compilation passes and optimizations.The approach adapts classical compiler-optimization research to quantum compilation.Source: §I · p. 1
• Distinct state constraints and a unified interface make the framework platform agnostic and extendable with methods from different SDKs and tools.The paper presents this as a way to build optimized flows that can incorporate new methods as the field develops.Source: §I · p. 2
• 73% of cases showed better expected fidelity than the individual Qiskit and TKET flows when the framework combined passes from both tools.The evaluation also reports improvements in critical depth and its combination with expected fidelity.Source: §I · p. 2

II. BACKGROUND: QUANTUM CIRCUIT COMPILATION

• Quantum programs are sequences of operations on qubits, and executing them on a QPU requires compilation.Device-independent optimizations can simplify circuits, for example by cancelling consecutive X gates.Source: §II · p. 2
• Synthesis expresses non-native gates using a device’s native gate set, which can create further optimization opportunities.The example decomposes a Hadamard gate into native gates and then cancels an Rz gate pair.Source: §II · p. 2
• Mapping assigns logical qubits to physical qubits and routes interactions to satisfy device connectivity.When connectivity prevents direct execution, routing may insert SWAP gates; some resulting overhead can be reduced by cancelling CNOT gates.Source: §II · p. 2
• The paper proposes a framework to address the growing complexity of available synthesis, mapping, and optimization passes.The cited figure is identified as compilation of a quantum circuit to a targeted device.Source: Figure 1 · p. 2, §II · p. 3

III. PROPOSED FRAMEWORK

• The approach builds on decades of classical compiler optimization research to address quantum compilation.The paper frames quantum compilation as a setting where the available passes and their order must be selected.Source: §III · p. 3
• The framework programmatically models quantum circuit compilation before applying reinforcement learning.Source: §III · p. 3
• Reinforcement learning is used to learn a sequence of compilation passes based on characteristics of the initial circuit.The goal is an optimized compiler for quantum circuits.Source: §III · p. 3

A. Modeling as a Markov Decision Process

• Compilation is modeled as an MDP whose states represent circuit progress and whose actions apply transformations toward an executable circuit.The process begins with the initial circuit and proceeds through compilation steps.Source: A. Modeling as a Markov Decision Process · p. 3
• Device-independent optimizations can be applied before selecting a quantum platform, which fixes the target native gate set.Examples include gate fusion, cancellation, commutation, and high-level synthesis.Source: A. Modeling as a Markov Decision Process · p. 3
• Selecting a device fixes its qubit count and topology, after which compilation must meet native-gate and connectivity constraints.Synthesis addresses native gates, while mapping addresses device topology.Source: A. Modeling as a Markov Decision Process · p. 3
• Each state has efficiently checkable constraints, and actions share a circuit input/output interface across SDKs and tools.Source: A. Modeling as a Markov Decision Process · p. 3
• The shared interface allows compiler passes from different SDKs and tools to be combined in one optimized compiler.The authors also say this can help mitigate vendor lock-in and ease integration of new methods.Source: A. Modeling as a Markov Decision Process · p. 4

• Reinforcement learning improves a policy that selects compilation passes from observations of the current circuit state to maximize expected cumulative reward.The environment specifies the MDP's states and actions, observations, and reward function; training data is not required.Source: B. Compiler Optimization Using… · p. 4
• Circuit features provide observations, while a sparse reward scores final circuits by a chosen metric such as gate count, depth, or expected fidelity.The target metric can be selected for a dedicated use case.Source: B. Compiler Optimization Using… · p. 4
• After training, the learned action policy can be used as an optimized compiler for quantum circuits.Source: B. Compiler Optimization Using… · p. 4

• Prior quantum-compilation machine-learning work includes layout and routing, fidelity prediction, compilation-flow selection, and learning gate-transformation strategies.The cited approaches vary from individual action optimization to predicting combinations of devices and compilation flows.Source: C. Related Work · p. 4
• Earlier approaches either optimize a specific action type or predict options at a high abstraction level within one quantum SDK.Source: C. Related Work · p. 4
• The proposed framework uses fine-grained steps to combine methods from multiple SDKs into a compilation flow with a customizable optimization objective.Source: C. Related Work · p. 4

• The study evaluates the resulting optimized compiler against state-of-the-art compilation flows in IBM’s Qiskit and Quantinuum’s TKET.Source: §IV · p. 4
• The feasibility study first describes a particular framework instantiation and then evaluates its performance against the two compilers.Source: §IV · p. 4
• The developments and results are publicly available on GitHub as part of the Munich Quantum Toolkit.Source: §IV · p. 4

• The action space covers platform and device selection, synthesis, mapping, and optimization, with methods integrated from Qiskit and TKET.The implementation uses Qiskit 0.39.2 and TKET 1.8.1; selected mapping and optimization methods include passes from both toolkits.Source: A. Instantiation · p. 4
• The selected device set includes superconducting and trapped-ion platforms, including IBM, Rigetti, IonQ, and OQC devices.The listed devices range from 8 to 127 qubits.Source: A. Instantiation · p. 4
• The learning agent observes seven circuit features: qubit count, circuit depth, and five composite features.The composite features are program communication, critical-depth, entanglement-ratio, parallelism, and liveness.Source: A. Instantiation · p. 5
• The framework uses expected fidelity and 1 − critical depth as reward functions, averages them for a combination reward in [0,1], and uses Proximal Policy Optimization (PPO) for reinforcement learning.Source: A. Instantiation · p. 5

B. Results

• 73%/80%, 84%/86%, and 75%/78.5% of cases outperform Qiskit/TKET for expected fidelity, critical depth, and their combination, respectively.Fig. 3a–c show the distributions of reward differences; positive values indicate improvement.Source: B. Results · p. 5
• Fig. 3d and 3e compare average reward differences per benchmark algorithm, subsuming instances with varying qubit counts.Source: B. Results · p. 5
• For all three quality metrics, the model trained for that purpose produces the compiled circuits with the highest rewards.Table I compares average rewards for each metric across all three trained models.Source: B. Results · p. 5, Table I · p. 5

V. CONCLUSIONS

• In 73%, 84%, and 75% of cases, trained models outperform Qiskit/TKET regarding expected fidelity, critical depth, and their combination, respectively.Average absolute improvements are 4.9%/10.7%, 22.6%/22.8%, and 5.5%/8.5% for those objectives, respectively.Source: §V · p. 5
• The framework models compilation as a Markov Decision Process with distinct state constraints and a unified interface for actions from multiple SDKs and toolkits.Source: §V · p. 5
• The authors make the framework publicly available as open-source and hope it will support further exploration of quantum compiler optimization.Source: §V · p. 5