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Register a new userOptimizing Variational Quantum Circuits using Evolution Strategies
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Johannes S. Otterbach
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Quantum Machine Learning (QML) is considered to be one of the most promising applications of near term quantum devices. However, the optimization of quantum machine learning models presents numerous challenges arising from the imperfections of hardware and the fundamental obstacles in navigating an exponentially scaling Hilbert space. In this work, we evaluate the potential of contemporary methods in deep reinforcement learning to augment gradient based optimization routines in quantum variational circuits. We find that reinforcement learning augmented optimizers consistently outperform gradient descent in noisy environments. All code and pretrained weights are available to replicate the results or deploy the models at https://github.com/lockwo/rl_qvc_opt.
A notion of quantum natural evolution strategies is introduced, which provides a geometric synthesis of a number of known quantum/classical algorithms for performing classical black-box optimization. Recent work of Gomes et al. [2019] on heuristic combinatorial optimization using neural quantum states is pedagogically reviewed in this context, emphasizing the connection with natural evolution strategies. The algorithmic framework is illustrated for approximate combinatorial optimization problems, and a systematic strategy is found for improving the approximation ratios. In particular it is found that natural evolution strategies can achieve approximation ratios competitive with widely used heuristic algorithms for Max-Cut, at the expense of increased computation time.
Quantum state tomography is a key process in most quantum experiments. In this work, we employ quantum machine learning for state tomography. Given an unknown quantum state, it can be learned by maximizing the fidelity between the output of a variational quantum circuit and this state. The number of parameters of the variational quantum circuit grows linearly with the number of qubits and the circuit depth, so that only polynomial measurements are required, even for highly-entangled states. After that, a subsequent classical circuit simulator is used to transform the information of the target quantum state from the variational quantum circuit into a familiar format. We demonstrate our method by performing numerical simulations for the tomography of the ground state of a one-dimensional quantum spin chain, using a variational quantum circuit simulator. Our method is suitable for near-term quantum computing platforms, and could be used for relatively large-scale quantum state tomography for experimentally relevant quantum states.
The development of quantum computational techniques has advanced greatly in recent years, parallel to the advancements in techniques for deep reinforcement learning. This work explores the potential for quantum computing to facilitate reinforcement learning problems. Quantum computing approaches offer important potential improvements in time and space complexity over traditional algorithms because of its ability to exploit the quantum phenomena of superposition and entanglement. Specifically, we investigate the use of quantum variational circuits, a form of quantum machine learning. We present our techniques for encoding classical data for a quantum variational circuit, we further explore pure and hybrid quantum algorithms for DQN and Double DQN. Our results indicate both hybrid and pure quantum variational circuit have the ability to solve reinforcement learning tasks with a smaller parameter space. These comparison are conducted with two OpenAI Gym environments: CartPole and Blackjack, The success of this work is indicative of a strong future relationship between quantum machine learning and deep reinforcement learning.
Parameterized quantum circuits (PQCs), which are essential for variational quantum algorithms, have conventionally been optimized by parameterized rotational angles of single-qubit gates around predetermined set of axes. We propose a new method to optimize a PQC by continuous parameterization of both the angles and the axes of its single-qubit rotations. The method is based on the observation that when rotational angles are fixed, optimal axes of rotations can be computed by solving a system of linear equations whose coefficients can be determined from the PQC with small computational overhead. The method can be further simplified to select axes freely from continuous parameters with rotational angles fixed to $pi$. We show the simplified free-axis selection method has better expressibility against other structural optimization methods when measured with Kullback-Leibler (KL) divergence. We also demonstrate PQCs with free-axis selection are more effective to search the ground states of Heisenberg models and molecular Hamiltonians. Because free-axis selection allows designing PQCs without specifying their single-qubit rotational axes, it may significantly improve the handiness of PQCs.
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