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.
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.
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.
A reinforcement learning (RL) framework is introduced for the efficient synthesis of quantum circuits that generate specified target quantum states from a fixed initial state, addressing a central challenge in both the Noisy Intermediate-Scale Quantum (NISQ) era and future fault-tolerant quantum computing. The approach utilizes tabular Q-learning, based on action sequences, within a discretized quantum state space, to effectively manage the exponential growth of the space dimension. The framework introduces a hybrid reward mechanism, combining a static, domain-informed reward that guides the agent toward the target state with customizable dynamic penalties that discourage inefficient circuit structures such as gate congestion and redundant state revisits. This is a circuit-aware reward, in contrast to the current trend of works on this topic, which are primarily fidelity-based. By leveraging sparse matrix representations and state-space discretization, the method enables practical navigation of high-dimensional environments while minimizing computational overhead. Benchmarking on graph-state preparation tasks for up to seven qubits, we demonstrate that the algorithm consistently discovers minimal-depth circuits with optimized gate counts. Moreover, extending the framework to a universal gate set still yields low depth circuits, highlighting the algorithm’s robustness and adaptability. The results confirm that this RL-driven approach, with our completely circuit-aware method, efficiently explores the complex quantum state space and synthesizes near-optimal quantum circuits, providing a resource-efficient foundation for quantum circuit optimization.
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.
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.
Reinforcement learning (RL) enables agents to learn optimal policies through environmental interaction. However, RL suffers from reduced learning efficiency due to the curse of dimensionality in high-dimensional spaces. Quantum reinforcement learning (QRL) addresses this issue by leveraging superposition and entanglement in quantum computing, allowing efficient handling of high-dimensional problems with fewer resources. QRL combines quantum neural networks (QNNs) with RL, where the parameterized quantum circuit (PQC) acts as the core computational module. The PQC performs linear and nonlinear transformations through gate operations, similar to hidden layers in classical neural networks. Previous QRL studies, however, have used fixed PQC structures based on empirical intuition without verifying their optimality. This paper proposes a QRLNAS algorithm that integrates quantum neural architecture search (QNAS) to optimize PQC structures within QRL. Experiments demonstrate that QRL-NAS achieves higher rewards than QRL with fixed circuits, validating its effectiveness and practical utility.