Khairy, Sami, Shaydulin, Ruslan, Cincio, Lukasz, Alexeev, Yuri, Balaprakash, Prasanna

Quantum computing exploits basic quantum phenomena such as state superposition and entanglement to perform computations. The Quantum Approximate Optimization Algorithm (QAOA) is arguably one of the leading quantum algorithms that can outperform classical state-of-the-art methods in the near term. QAOA is a hybrid quantum-classical algorithm that combines a parameterized quantum state evolution with a classical optimization routine to approximately solve combinatorial problems. The quality of the solution obtained by QAOA within a fixed budget of calls to the quantum computer depends on the performance of the classical optimization routine used to optimize the variational parameters. In this work, we propose an approach based on reinforcement learning (RL) to train a policy network that can be used to quickly find high-quality variational parameters for unseen combinatorial problem instances. The RL agent is trained on small problem instances which can be simulated on a classical computer, yet the learned RL policy is generalizable and can be used to efficiently solve larger instances. Extensive simulations using the IBM Qiskit Aer quantum circuit simulator demonstrate that our trained RL policy can reduce the optimality gap by a factor up to 8.61 compared with other off-the-shelf optimizers tested.

Cerezo, M., Arrasmith, Andrew, Babbush, Ryan, Benjamin, Simon C., Endo, Suguru, Fujii, Keisuke, McClean, Jarrod R., Mitarai, Kosuke, Yuan, Xiao, Cincio, Lukasz, Coles, Patrick J.

Applications such as simulating large quantum systems or solving large-scale linear algebra problems are immensely challenging for classical computers due their extremely high computational cost. Quantum computers promise to unlock these applications, although fault-tolerant quantum computers will likely not be available for several years. Currently available quantum devices have serious constraints, including limited qubit numbers and noise processes that limit circuit depth. Variational Quantum Algorithms (VQAs), which employ a classical optimizer to train a parametrized quantum circuit, have emerged as a leading strategy to address these constraints. VQAs have now been proposed for essentially all applications that researchers have envisioned for quantum computers, and they appear to the best hope for obtaining quantum advantage. Nevertheless, challenges remain including the trainability, accuracy, and efficiency of VQAs. In this review article we present an overview of the field of VQAs. Furthermore, we discuss strategies to overcome their challenges as well as the exciting prospects for using them as a means to obtain quantum advantage.

Recent advancements in quantum computing have driven the scientific community's quest to solve a certain class of complex problems for which quantum computers would be better suited than traditional supercomputers. To improve the efficiency with which quantum computers can solve these problems, scientists are investigating the use of artificial intelligence approaches. In a new study, scientists at the U.S. Department of Energy's (DOE) Argonne National Laboratory have developed a new algorithm based on reinforcement learning to find the optimal parameters for the Quantum Approximate Optimization Algorithm (QAOA), which allows a quantum computer to solve certain combinatorial problems such as those that arise in materials design, chemistry and wireless communications. "It's a bit like having a self-driving car in traffic; the algorithm can detect when it needs to make adjustments in the'dials' it uses to do the computation." "Combinatorial optimization problems are those for which the solution space gets exponentially larger as you expand the number of decision variables," said Argonne computer scientist Prasanna Balaprakash.

Arrasmith, Andrew, Cerezo, M., Czarnik, Piotr, Cincio, Lukasz, Coles, Patrick J.

Barren plateau landscapes correspond to gradients that vanish exponentially in the number of qubits. Such landscapes have been demonstrated for variational quantum algorithms and quantum neural networks with either deep circuits or global cost functions. For obvious reasons, it is expected that gradient-based optimizers will be significantly affected by barren plateaus. However, whether or not gradient-free optimizers are impacted is a topic of debate, with some arguing that gradient-free approaches are unaffected by barren plateaus. Here we show that, indeed, gradient-free optimizers do not solve the barren plateau problem. Our main result proves that cost function differences, which are the basis for making decisions in a gradient-free optimization, are exponentially suppressed in a barren plateau. Hence, without exponential precision, gradient-free optimizers will not make progress in the optimization. We numerically confirm this by training in a barren plateau with several gradient-free optimizers (Nelder-Mead, Powell, and COBYLA algorithms), and show that the numbers of shots required in the optimization grows exponentially with the number of qubits.

Ostaszewski, Mateusz, Trenkwalder, Lea M., Masarczyk, Wojciech, Scerri, Eleanor, Dunjko, Vedran

The study of Variational Quantum Eigensolvers (VQEs) has been in the spotlight in recent times as they may lead to real-world applications of near-term quantum devices. However, their performance depends on the structure of the used variational ansatz, which requires balancing the depth and expressivity of the corresponding circuit. In recent years, various methods for VQE structure optimization have been introduced but the capacities of machine learning to aid with this problem has not yet been fully investigated. In this work, we propose a reinforcement learning algorithm that autonomously explores the space of possible ans{\"a}tze, identifying economic circuits which still yield accurate ground energy estimates. The algorithm is intrinsically motivated, and it incrementally improves the accuracy of the result while minimizing the circuit depth. We showcase the performance of our algorithm on the problem of estimating the ground-state energy of lithium hydride (LiH). In this well-known benchmark problem, we achieve chemical accuracy, as well as state-of-the-art results in terms of circuit depth.