KANQAS: Kolmogorov-Arnold Network for Quantum Architecture Search

KANQAS: Kolmogorov-Arnold Network for Quantum Architecture Search

11 Dec 2024 | Akash Kundu, Aritra Sarkar, Abhishek Sadhu
KANQAS: Kolmogorov-Arnold Network for Quantum Architecture Search This paper introduces KANQAS, a quantum architecture search (QAS) algorithm that replaces the Multi-Layer Perceptron (MLP) structure in the Double Deep Q-Network (DDQN) with the Kolmogorov-Arnold Network (KAN). KAN is based on the Kolmogorov-Arnold representation theorem, which allows it to approximate complex functions using univariate spline functions. This makes KAN more efficient and interpretable than MLPs, which are based on the universal approximation theorem. In quantum state preparation, KAN outperforms MLPs in both noiseless and noisy scenarios. In noiseless scenarios, KAN achieves a higher success probability and more optimal circuit configurations. In noisy scenarios, KAN achieves higher fidelity in approximating quantum states. In quantum chemistry, KAN is used to find the ground state of molecules like H2 and LiH. KAN produces more compact parameterized quantum circuits with fewer 2-qubit gates and reduced circuit depth, while also requiring significantly fewer learnable parameters than MLPs. The KANQAS algorithm uses reinforcement learning (RL) to search for optimal quantum circuits. The RL agent interacts with a quantum simulator, generating output actions that are candidates for quantum gates on the circuit. The fidelity of the state from the constructed circuit is compared to the quantum state fidelity of the circuit, and the reward is sent back to the RL agent. This process is repeated iteratively to train the RL agent. The results show that KANQAS outperforms MLP-based QAS in both quantum state preparation and quantum chemistry tasks. In quantum state preparation, KAN achieves higher success probabilities and more optimal circuit configurations. In quantum chemistry, KAN produces more compact parameterized quantum circuits with fewer 2-qubit gates and reduced circuit depth, while also requiring significantly fewer learnable parameters than MLPs. The KANQAS algorithm is more efficient than MLP-based QAS in terms of the number of learnable parameters and the time required to execute each episode. However, KAN requires more execution time per episode than MLPs. Despite this, KAN is more effective and efficient in finding solutions in both noiseless and noisy quantum devices, making it a reasonable alternative to traditional MLPs in solving quantum architecture search problems.KANQAS: Kolmogorov-Arnold Network for Quantum Architecture Search This paper introduces KANQAS, a quantum architecture search (QAS) algorithm that replaces the Multi-Layer Perceptron (MLP) structure in the Double Deep Q-Network (DDQN) with the Kolmogorov-Arnold Network (KAN). KAN is based on the Kolmogorov-Arnold representation theorem, which allows it to approximate complex functions using univariate spline functions. This makes KAN more efficient and interpretable than MLPs, which are based on the universal approximation theorem. In quantum state preparation, KAN outperforms MLPs in both noiseless and noisy scenarios. In noiseless scenarios, KAN achieves a higher success probability and more optimal circuit configurations. In noisy scenarios, KAN achieves higher fidelity in approximating quantum states. In quantum chemistry, KAN is used to find the ground state of molecules like H2 and LiH. KAN produces more compact parameterized quantum circuits with fewer 2-qubit gates and reduced circuit depth, while also requiring significantly fewer learnable parameters than MLPs. The KANQAS algorithm uses reinforcement learning (RL) to search for optimal quantum circuits. The RL agent interacts with a quantum simulator, generating output actions that are candidates for quantum gates on the circuit. The fidelity of the state from the constructed circuit is compared to the quantum state fidelity of the circuit, and the reward is sent back to the RL agent. This process is repeated iteratively to train the RL agent. The results show that KANQAS outperforms MLP-based QAS in both quantum state preparation and quantum chemistry tasks. In quantum state preparation, KAN achieves higher success probabilities and more optimal circuit configurations. In quantum chemistry, KAN produces more compact parameterized quantum circuits with fewer 2-qubit gates and reduced circuit depth, while also requiring significantly fewer learnable parameters than MLPs. The KANQAS algorithm is more efficient than MLP-based QAS in terms of the number of learnable parameters and the time required to execute each episode. However, KAN requires more execution time per episode than MLPs. Despite this, KAN is more effective and efficient in finding solutions in both noiseless and noisy quantum devices, making it a reasonable alternative to traditional MLPs in solving quantum architecture search problems.
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