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arXiv:1812.11619

Using Reinforcement Learning to find Efficient Qubit Routing Policies for Deployment in Near-term Quantum Computers

Steven Herbert, Akash Sengupta

Published Dec 30, 2018• 22 citations
arXivHTMLPDF

Abstract

This paper addresses the problem of qubit routing in first-generation and other near-term quantum computers. In particular, it is asserted that the qubit routing problem can be formulated as a reinforcement learning (RL) problem, and that this is sufficient, in principle, to discover the optimal qubit routing policy for any given quantum computer architecture. In order to achieve this, it is necessary to alter the conventional RL framework to allow combinatorial action space, and this represents a second contribution of this paper, which is expected to find additional application, beyond the qubit routing problem addressed herein. Numerical results are included demonstrating the advantage of the RL-trained qubit routing policy over using a sorting network.

DOI
10.48550/arxiv.1812.11619

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This paper addresses the problem of qubit routing in first-generation and other near-term quantum computers. In particular, it is asserted that the qubit routing problem can be formulated as a reinforcement learning (RL) problem, and that this is sufficient, in principle, to discover the optimal qubit routing policy for any given quantum computer architecture. In order to achieve this, it is necessary to alter the conventional RL framework to allow combinatorial action space, and this represents a second contribution of this paper, which is expected to find additional application, beyond the qubit routing problem addressed herein. Numerical results are included demonstrating the advantage of the RL-trained qubit routing policy over using a sorting network.
Qubit routing is the process of transforming quantum circuits to ensure that all two-qubit operations obey the connectivity constraints of a target architecture. The severe limitations of NISQ computers make qubit routing a vital compilation step. We propose a method to route quantum circuits based on deep reinforcement learning (RL). Moreover, we augment our approach with device calibration data to enable routing decisions based on the reliability of individual gates and we improve upon a previous technique for encoding circuits as a numerical matrix. We also implement enhancements such as BRIDGE operations, qubit embeddings, and commutation analysis. Using proximal policy optimization (PPO), we trained agents for five IBM topologies with between 5 and 27 qubits. For random circuits, the proposed strategy reduced the number of additional two-qubit gates by up to 37.3% and improved estimated success probability by up to 26.8% compared to the best algorithm from the Qiskit framework. For a dataset of realistic circuits, we achieved up to 27.5% and 15.2% improvements in gate count and circuit fidelity, respectively. We found no significant advantage from using calibration-aware models for IBM architectures, which deserves further exploration. Our work helps cement RL as a valuable qubit routing strategy, serving as another stepping stone toward practical applications for quantum computing.
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.
This paper investigates the application of quantum-inspired algorithms to the field of reinforcement learning (RL). Traditional RL methods often struggle with exploration challenges and can be computationally expensive, particularly in complex environments. We propose a novel RL algorithm that leverages concepts from quantum mechanics, specifically superposition and entanglement, to address these limitations. The core idea is to represent states, actions, and rewards using quantum-inspired representations, allowing the agent to explore the environment more efficiently and potentially converge to optimal policies faster. This work presents a detailed formulation of the algorithm, including the mathematical framework and key considerations for implementation. The potential benefits of this approach, including improved exploration and reduced computational complexity, are discussed. The algorithm is designed to iteratively refine its policy based on simulated quantum measurements, aiming to minimize the expected return. The exploration strategy is guided by the inherent probabilistic nature of quantum states, leading to a more diverse and potentially faster learning process. Further research is warranted to fully explore the capabilities and limitations of this approach across various RL benchmark problems.
As it becomes increasingly difficult to monolithically scale a quantum processor, distributed quantum computing (DQC) offers an alternative by distributing qubits across multiple smaller interconnected quantum processor modules. In such an architecture, the challenge of quantum circuit compilation shifts from placing and routing qubits within one module to placing, routing and using the qubits efficiently across modules. In order to optimize circuit execution time, the right state-dependent networking decisions must be found, such as when and where to generate shared remote quantum states to support remote operations. Reinforcement learning (RL) provides a natural framework for this problem, generating a compilation policy that can generalize across different circuits. Building on the framework of Promponas et al. (2024), we introduce an agent that combines a novel action-space formulation with effective action-masking strategies. A comprehensive numerical comparison of the two approaches under different coupling constraints shows that our agent achieves improved training and inference performance with a relative reduction in the modeled execution time of up to 35\%.
Quantum computing is gaining more and more attention due to its huge potential and the constant progress in quantum computer development. IBM and Google have released quantum architectures with more than 50 qubits. However, in these machines, the physical qubits are not fully connected so that two-qubit interaction can only be performed between specific pairs of the physical qubits. To execute a quantum circuit, it is necessary to transform it into a functionally equivalent one that respects the constraints imposed by the target architecture. Quantum circuit transformation inevitably introduces additional gates which reduces the fidelity of the circuit. Therefore, it is important that the transformation method completes the transformation with minimal overheads. It consists of two steps, initial mapping and qubit routing. Here we propose a reinforcement learning-based model to solve the initial mapping problem. Initial mapping is formulated as sequence-to-sequence learning and self-attention network is used to extract features from a circuit. For qubit routing, a DEAR (Dynamically-Extract-and-Route) framework is proposed. The framework iteratively extracts a subcircuit and uses A* search to determine when and where to insert additional gates. It helps to preserve the lookahead ability dynamically and to provide more accurate cost estimation efficiently during A* search. The experimental results show that our RL-model generates better initial mappings than the best known algorithms with 12% fewer additional gates in the qubit routing stage. Furthermore, our DEAR-framework outperforms the state-of-the-art qubit routing approach with 8.4% and 36.3% average reduction in the number of additional gates and execution time starting from the same initial mapping.
The progress in machine learning during the last decade has had a considerable impact on many areas of science and technology, including quantum technology. This work explores the application of reinforcement learning (RL) methods to the quantum control problem of state transfer in a single qubit. The goal is to create an RL agent that learns an optimal policy and thus discovers optimal pulses to control the qubit. The most crucial step is to mathematically formulate the problem of interest as a Markov decision process (MDP). This enables the use of RL algorithms to solve the quantum control problem. Deep learning and the use of deep neural networks provide the freedom to employ continuous action and state spaces, offering the expressivity and generalization of the process. This flexibility helps to formulate the quantum state transfer problem as an MDP in several different ways. All the developed methodologies are applied to the fundamental problem of population inversion in a qubit. In most cases, the derived optimal pulses achieve fidelity equal to or higher than 0.9999, as required by quantum computing applications. The present methods can be easily extended to quantum systems with more energy levels and may be used for the efficient control of collections of qubits and to counteract the effect of noise, which are important topics for quantum sensing applications.