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arXiv:2204.06904 · Quantum Science and Technology

Efficient and practical quantum compiler towards multi-qubit systems with deep reinforcement learning ∗

Qiuhao Chen, Yuxuan Du, Yuliang Jiao, Xiliang Lu, Xingyao Wu, Qi Zhao

Published Apr 23, 2024• 12 citations
arXivHTMLPDF

Abstract

Abstract Efficient quantum compiling is essential for complex quantum algorithms realization. The Solovay–Kitaev (S–K) theorem offers a theoretical lower bound on the required operations for approaching any unitary operator. However, it is still an open question that this lower bound can be actually reached in practice. Here, we present an efficient quantum compiler which, for the first time, approaches the S–K lower bound in practical implementations, both for single-qubit and two-qubit scenarios, marking a significant milestone. Our compiler leverages deep reinforcement learning (RL) techniques to address current limitations in terms of optimality and inference time. Furthermore, we show that our compiler is versatile by demonstrating comparable performance between inverse-free basis sets, which is always the case in real quantum devices, and inverse-closed sets. Our findings also emphasize the often-neglected constant term in scaling laws, bridging the gap between theory and practice in quantum compiling. These results highlight the potential of RL-based quantum compilers, offering efficiency and practicality while contributing novel insights to quantum compiling theory.

DOI
10.1088/2058-9565/ad420a

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Abstract Efficient quantum compiling is essential for complex quantum algorithms realization. The Solovay–Kitaev (S–K) theorem offers a theoretical lower bound on the required operations for approaching any unitary operator. However, it is still an open question that this lower bound can be actually reached in practice. Here, we present an efficient quantum compiler which, for the first time, approaches the S–K lower bound in practical implementations, both for single-qubit and two-qubit scenarios, marking a significant milestone. Our compiler leverages deep reinforcement learning (RL) techniques to address current limitations in terms of optimality and inference time. Furthermore, we show that our compiler is versatile by demonstrating comparable performance between inverse-free basis sets, which is always the case in real quantum devices, and inverse-closed sets. Our findings also emphasize the often-neglected constant term in scaling laws, bridging the gap between theory and practice in quantum compiling. These results highlight the potential of RL-based quantum compilers, offering efficiency and practicality while contributing novel insights to quantum compiling theory.
Abstract Effectively implementing quantum algorithms on noisy intermediate-scale quantum (NISQ) processors is a central task in modern quantum technology. NISQ processors feature tens to a few hundreds of noisy qubits with limited coherence times and gate operations with errors, so NISQ algorithms naturally require employing circuits of short lengths via quantum compilation. Here, we evaluate a reinforcement learning (RL)-based quantum compiler on a superconducting processor. Our experiments reveal that for two-qubit circuits, the RL-based compiler surpasses conventional methods, demonstrating its ability to discover hardware-amenable circuits with near-optimal lengths. However, for three-qubit circuits, the RL-based compiler does not achieve unity theoretical fidelity. To address this limitation, we integrate a variational strategy with the RL-based compiler, highlighting their complementary strengths. Systematic experiments show that this variational RL-based compiler consistently identifies near-optimal circuits, even under stringent hardware constraints, outperforming conventional techniques. Furthermore, we analyze the impact of decoherence and gate errors, providing critical insights into the practical performance of RL-based compilers on quantum hardware. These findings exemplify the codesign of the software with hardware for efficient quantum compilation, offering valuable insights for the advancement of RL-based compilers.
Abstract The general problem of quantum compiling is to approximate any unitary transformation that describes the quantum computation as a sequence of elements selected from a finite base of universal quantum gates. The Solovay-Kitaev theorem guarantees the existence of such an approximating sequence. Though, the solutions to the quantum compiling problem suffer from a tradeoff between the length of the sequences, the precompilation time, and the execution time. Traditional approaches are time-consuming, unsuitable to be employed during computation. Here, we propose a deep reinforcement learning method as an alternative strategy, which requires a single precompilation procedure to learn a general strategy to approximate single-qubit unitaries. We show that this approach reduces the overall execution time, improving the tradeoff between the length of the sequence and execution time, potentially allowing real-time operations.
The Solovay-Kitaev algorithm is a fundamental result in quantum computation. It gives an algorithm for efficiently compiling arbitrary unitaries using universal gate sets: any unitary can be approximated by short gates sequences, whose length scales merely poly-logarithmically with accuracy. As a consequence, the choice of gate set is typically unimportant in quantum computing. However, the Solovay-Kitaev algorithm requires the gate set to be inverse-closed. It has been a longstanding open question if efficient algorithmic compilation is possible without this condition. In this work, we provide the first inverse-free Solovay-Kitaev algorithm, which makes no assumption on the structure within a gate set beyond universality, answering this problem in the affirmative, and providing an efficient compilation algorithm in the absence of inverses for both SU(d)\text{SU}(d)SU(d) and SL(d,C)\text{SL}(d, \mathbb{C})SL(d,C). The algorithm works by showing that approximate gate implementations of the generalized Pauli group can self-correct their errors.
Quantum computers promise significant computational advantages over classical computers for specific tasks. However, one of the challenges in the noisy intermediate-scale quantum (NISQ) era is the efficient compilation of quantum states and gates, which is crucial for the implementation of quantum algorithms. Given the high dimensionality of quantum systems, this compilation task is non-trivial. Reinforcement learning (RL) is a machine learning subfield focused on developing algorithms for decision-making in dynamic environments. An agent learns by interacting with its environment, how to act to optimize its performance on a certain task. Recently, the integration of deep learning has given rise to deep reinforcement learning (DRL), where deep neural networks approximate functions like value or policy, allowing agents to tackle high-dimensional and complex tasks with greater efficiency and success. Recently, deep reinforcement learning (DRL) has been proposed as a method to automate quantum compiling. In this thesis, we explore the application of RL for quantum state and unitary matrix synthesis, focusing on the use of two reinforcement learning algorithms Deep Q-Networks (DQN) and Proximal Policy Optimization (PPO). Our results indicate that DRL shows promise in generalizing the task of quantum unitary synthesis and quantum state preparation. However, the current state-of-the-art is still limited to working in the no-volume law entangled part of the Hilbert space.
The practical implementation of quantum algorithms on noisy intermediate-scale quantum devices encounters operational limitations due to decoherence and other sources of noise inherent in real hardware. To mitigate these errors while preserving the original functionality of the algorithm, shorter quantum circuits are therefore preferred. This motivates the development of effective quantum circuit optimization algorithms. Learning-based approaches have emerged as a leading candidate, yet existing autonomous agents remain inefficient, spending most of their training capacity rediscovering elementary reductions that deterministic rule-based methods already handle reliably. To address this challenge, we propose a reinforcement learning framework that embeds a deterministic Commutation-and-Reduction (CR) algorithm directly into the training environment. After every agent action, the CR algorithm automatically resolves elementary commutations and cancellations, enabling the agent to focus its learning capacity on the non-trivial optimizations where reinforcement learning adds real value. Empirical evaluation across two gate sets, the universal Clifford+T basis and the CNOT+Pauli basis, shows that RL+CR produces shorter circuits than a standard RL agent at all tested scales. We demonstrate that RL trained on smaller quantum circuits can be applied to larger quantum circuits. On 20-qubit Clifford+T circuits, five times larger than the training circuits, RL+CR removes twice as many gates as standard RL. This work provides a robust approach that could accelerate the compilation and optimization processes for future fault-tolerant and utility-scale quantum systems.
The general problem of quantum compiling is to approximate any unitary transformation that describes the quantum computation as a sequence of elements selected from a finite base of universal quantum gates.The Solovay-Kitaev theorem guarantees the existence of such an approximating sequence.Though, the solutions to the quantum compiling problem suffer from a tradeoff between the length of the sequences, the precompilation time, and the execution time.Traditional approaches are time-consuming, unsuitable to be employed during computation.Here, we propose a deep reinforcement learning method as an alternative strategy, which requires a single precompilation procedure to learn a general strategy to approximate single-qubit unitaries.We show that this approach reduces the overall execution time, improving the tradeoff between the length of the sequence and execution time, potentially allowing real-time operations.