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arXiv:2311.12498 · IEEE International Conference on Rebooting Computing (ICRC)

Cost Explosion for Efficient Reinforcement Learning Optimisation of Quantum Circuits

Ioana Moflic, Alexandru Paler

Published Dec 5, 2023• 3 citations
arXivHTMLPDF

Abstract

Large scale optimisation of quantum circuits is a computationally challenging problem. Reinforcement Learning (RL) is a recent approach for learning strategies to optimise quantum circuits by increasing the reward of an optimisation agent. The reward is a function of the quantum circuit costs, such as gate and qubit counts, or circuit depth. Our goal is to improve the agent’s optimization strategy, by including hints about how quantum circuits are optimized manually: there are situations when the cost of a circuit should be allowed to temporary explode, before applying optimisations which significantly reduce the circuit’s cost. We bring numerical evidence, using Bernstein-Vazirani circuits, to support the advantage of this strategy. Our results are preliminary, and show that allowing cost explosions offers significant advantages for RL training, such as reaching optimum circuits. Cost explosion strategies have the potential to be an essential tool for RL of large-scale quantum circuit optimisation.

DOI
10.1109/icrc60800.2023.10386864

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Large scale optimisation of quantum circuits is a computationally challenging problem. Reinforcement Learning (RL) is a recent approach for learning strategies to optimise quantum circuits by increasing the reward of an optimisation agent. The reward is a function of the quantum circuit costs, such as gate and qubit counts, or circuit depth. Our goal is to improve the agent’s optimization strategy, by including hints about how quantum circuits are optimized manually: there are situations when the cost of a circuit should be allowed to temporary explode, before applying optimisations which significantly reduce the circuit’s cost. We bring numerical evidence, using Bernstein-Vazirani circuits, to support the advantage of this strategy. Our results are preliminary, and show that allowing cost explosions offers significant advantages for RL training, such as reaching optimum circuits. Cost explosion strategies have the potential to be an essential tool for RL of large-scale quantum circuit optimisation.
Reinforcement learning for the optimization of quantum circuits uses an agent whose goal is to maximize the value of a reward function that decides what is correct and what is wrong during the exploration of the search space. It is an open problem how to formulate reward functions that lead to fast and efficient learning. We propose an exponential reward function which is sensitive to structural properties of the circuit. We benchmark our function on circuits with known optimal depths, and conclude that our function is reducing the learning time and improves the optimization. Our results are a next step towards fast, large scale optimization of quantum circuits.
Quantum circuit optimization remains a significant challenge in the development of practical quantum computing. Traditional methods often rely on heuristics or exhaustive searches, which are computationally expensive and may not effectively adapt to the specific characteristics of the quantum data being processed. This paper proposes a novel approach leveraging reinforcement learning (RL) to achieve contextualized quantum circuit optimization. The core idea is to train an RL agent to dynamically modify quantum circuits in real-time, guided by a reward function that balances circuit fidelity and execution time. Crucially, the agent incorporates a learned contextual representation of the input data, allowing it to tailor the circuit design to the specific context. We demonstrate the potential of this approach by outlining the key components, the reward function design, and the overall architecture. The potential benefits include improved circuit fidelity, reduced execution time, and the ability to adapt to diverse quantum datasets. This represents a shift from static circuit design to adaptive, context-aware optimization, potentially unlocking the full potential of quantum computation.
This paper presents a novel approach to quantum circuit compilation leveraging reinforcement learning (RL). The core idea is to train an RL agent to dynamically optimize quantum circuit structures, aiming to minimize gate count and enhance overall circuit performance. Traditional quantum circuit compilation methods often rely on static heuristics and pre-defined optimization strategies, which may not be optimal for all quantum algorithms or hardware platforms. Our approach addresses this limitation by allowing the RL agent to learn a policy that adapts to the specific characteristics of the algorithm and the target quantum hardware. The agent learns by interacting with a simulated quantum circuit environment, receiving rewards based on circuit fidelity, depth, and gate count. The results demonstrate the potential of RL to significantly improve the efficiency and robustness of quantum computations. The key components of the system are: a high-level quantum algorithm representation, an RL agent, a quantum circuit simulator, and a reward function. The agent's policy is represented as a neural network, enabling it to generalize across different algorithms and hardware. We demonstrate the effectiveness of this approach through simulations, showcasing its ability to outperform conventional compilation methods in terms of reducing circuit depth and gate count while maintaining high fidelity.
Reinforcement learning (RL) is a promising method for quantum circuit optimisation. However, the state space that has to be explored by an RL agent is extremely large when considering all the possibilities in which a quantum circuit can be transformed through local rewrite operations. This state space explosion slows down the learning of RL-based optimisation strategies. We present for the first time how to use graph neural network (GNN) autoencoders for the optimisation of quantum circuits. We construct directed acyclic graphs from the quantum circuits, encode the graphs and use the encodings to represent RL states. We illustrate our proof of concept implementation on Bernstein-Vazirani circuits and, from preliminary results, we conclude that our autoencoder approach: a) maintains the optimality of the original RL method; b) reduces by 20 \% the size of the table that encodes the learned optimisation strategy. Our method is the first realistic first step towards very large scale RL quantum circuit optimisation.
We propose a novel Reinforcement Learning (RL) method for optimizing quantum circuits using graph-theoretic simplification rules of ZX-diagrams. The agent, trained using the Proximal Policy Optimization (PPO) algorithm, employs Graph Neural Networks to approximate the policy and value functions. We demonstrate the capacity of our approach by comparing it against the best performing ZX-Calculus-based algorithm for the problem in hand. After training on small Clifford+T circuits of 5-qubits and few tenths of gates, the agent consistently improves the state-of-the-art for this type of circuits, for at least up to 80-qubit and 2100 gates, whilst remaining competitive in terms of computational performance. Additionally, we illustrate the versatility of the agent by incorporating additional optimization routines on the workflow during training, improving the two-qubit gate count state-of-the-art on multiple structured quantum circuits for relevant applications of much larger dimension and different gate distributions than the circuits the agent trains on. This conveys the potential of tailoring the reward function to the specific characteristics of each application and hardware backend. Our approach is a valuable tool for the implementation of quantum algorithms in the near-term intermediate-scale range (NISQ).
Quantum computing promises significant computational advantages over classical methods in certain applications but is currently too unstable for executing complex tasks. High-fidelity quantum circuits are critical to overcoming this challenge, yet they are computationally challenging to design. On current noisy intermediate-scale quantum (NISQ) hardware, shallower circuits with fewer two-qubit gates generally run with higher fidelity. Increased fidelity can be sought by sequentially rewriting the circuit, which involves a vast search space. This costly search space exploration could be circumvented by using reinforcement learning (RL) to teach an agent to rewrite the circuit in a sequential decision-making process. This thesis aims to implement a Deep Q-Network (DQN) algorithm to optimize BernsteinVazirani (BVZ) circuits. The DQN algorithm interacts with a Cirq-based environment. The environment provides valid rewrite actions to the DQN algorithm, which gains a scalar reward emphasizing depth and gate reduction. In the thesis we compare two different state encodings as input for the neural network: a compact state summarizing vector representation with three features, and an image-like encoding that maps circuit state topology with tokens through a fixed embedding. Both input encodings use the same action rewrite set and reward design. The network is implemented in PyTorch and trained with Adam optimizer, and runs on GPU via CUDA. Empirically, the agent shows promising initial optimizing performance. On several BVZ circuits with varying qubit count and topology, the agent drives the depth toward the theoretical optimum of three. The simplistic vector encoding already reaches reasonable circuit depth plateaus, with the image-like encoding together with hyperparameter tuning improving reliability, showing avenues for continued improvement. We conclude that DQN is a viable foundation for automated circuit optimization on BVZ circuits. To achieve reliable circuit optimization at scale, future research should investigate even richer encoding methods and reward function shaping. Finally, the results support applying the DQN to be applied to circuit families beyond BVZ.