Variational quantum circuits (VQCs) are flexible models for optimization and learning based on parameterized quantum circuits trained via cost minimization. A key challenge in their optimization is the presence of barren plateaus, where gradients vanish exponentially with the number of qubits, severely limiting trainability. Local cost functions mitigate this issue by restricting evaluation to qubit subsets, improving gradient scaling. In this work, we propose an evolutionary strategy-inspired method to automatically identify informative qubit subsets for constructing local cost functions. Operating at the level of qubit selection rather than parameter optimization, the approach enables adaptive, circuit-aware objective design. Numerical experiments using the PennyLane framework show that the method alleviates barren plateaus and improves optimization performance in the identity-gate learning problem.
Variational quantum circuits (VQCs) are flexible models for optimization and learning based on parameterized quantum circuits trained via cost minimization. A key challenge in their optimization is the presence of barren plateaus, where gradients vanish exponentially with the number of qubits, severely limiting trainability. Local cost functions mitigate this issue by restricting evaluation to qubit subsets, improving gradient scaling. In this work, we propose an evolutionary strategy-inspired method to automatically identify informative qubit subsets for constructing local cost functions. Operating at the level of qubit selection rather than parameter optimization, the approach enables adaptive, circuit-aware objective design. Numerical experiments using the PennyLane framework show that the method alleviates barren plateaus and improves optimization performance in the identity-gate learning problem.
Variational quantum algorithms are viewed as promising candidates for demonstrating quantum advantage on near-term devices. These approaches typically involve the training of parameterized quantum circuits through a classical optimization loop. However, they often encounter challenges attributed to the exponentially diminishing gradient components, known as the barren plateau (BP) problem. This work introduces a novel optimization approach designed to alleviate the adverse effects of BPs during circuit training. In contrast to conventional gradient descent methods with a small learning parameter, our approach relies on making a finite hops along the search direction determined on a randomly chosen subsets of the free parameters. The optimization search direction, together with the range of the search, is determined by the distant features of the cost-function landscape. This enables the optimization path to navigate around barren plateaus without the need for external control mechanisms. We have successfully applied our optimization strategy to quantum circuits comprising 21 qubits and 15000 entangling gates, demonstrating robust resistance against BPs. Additionally, we have extended our optimization strategy by incorporating an evolutionary selection framework, enhancing its ability to avoid local minima in the landscape. The modified algorithm has been successfully utilized in quantum gate synthesis applications, showcasing a significantly improved efficiency in generating highly compressed quantum circuits compared to traditional gradient-based optimization approaches.
Abstract Parameterized quantum circuits (PQCs) are crucial for quantum machine learning and circuit synthesis, enabling the practical implementation of complex quantum tasks. However, PQC learning has been largely confined to classical optimization methods, which suffer from issues like gradient vanishing.In this work, we introduce a nested optimization model, a hybrid approach that leverages quantum gradients to improve PQC learning for arbitrary polynomial-type cost functions. The proposed approach decomposes the learning problem into multiple subproblems, each aimed at learning the state identified by the quantum gradient using current circuit synthesis methods.By leveraging quantum gradients, the optimization procedure is free of a specific type of gradient vanishing, such as unfavorable local stationary points and barren plateaus.Specifically, with the guidance of quantum gradient, unfavorable local stationary points can be overcome by increasing the depth of the ansatz, while barren plateaus can be mitigated by constraining the optimization region.Numerically, we demonstrate the feasibility of the approach on two tasks: the Max-Cut problem and polynomial optimization. Additionally, we analyze the overheads introduced by this approach, which are primarily polynomial in the number of qubits in the system and can be controlled by adjusting the learning rate.The method can generate circuits while avoiding gradient vanishing, thus effectively optimizing the cost function.From the perspective of quantum algorithms, our model improves quantum optimization for polynomial-type cost functions, addressing the challenge of exponential sample complexity growth.
We propose an algorithm for variational quantum algorithms (VQAs) to optimize the structure of parameterized quantum circuits (PQCs) efficiently. The algorithm optimizes the PQC structure on-the-fly in VQA by sequentially replacing a single-qubit gate with the optimal one to minimize the objective function. To directly find the optimal gate, our method uses the factorization of matrices whose elements are evaluated on a set of the slightly-modified circuits. The matrix factorization enables us to not only unify the existing sequential methods for further extension but also provide rigorous proofs of their limitation and potential in comparison with conventional gradient-based optimizers. Firstly, when the circuits are sufficiently deep, the sequential methods encounter a barren plateau that the spectrum of the matrix concentrates on a single value exponentially fast with respect to the number of qubits. Secondly, if the objective functions are local observables, they can avoid barren plateaus as long as the depth of the n-qubit PQCs is O(logn). Although the family of these optimizers does not directly employ gradients of the objective function, our results establish their connection with conventional optimizations providing a consistent picture of the barren plateau. We also perform numerical experiments showing the advantages over conventional VQAs and confirm the successful optimization getting over the barren plateau in the ground state problem of the mixed field Ising model up to 12 qubits.
Parameterized quantum circuits (PQCs) are crucial for quantum machine learning and circuit synthesis, enabling the practical implementation of complex quantum tasks. However, PQC learning has been largely confined to classical optimization methods, which suffer from issues like gradient vanishing. In this work, we introduce a nested optimization model that leverages quantum gradient to enhance PQC learning for polynomial-type cost functions. Our approach utilizes quantum algorithms to identify and overcome a type of gradient vanishing-a persistent challenge in PQC learning-by effectively navigating the optimization landscape. We also mitigate potential barren plateaus of our model and manage the learning cost via restricting the optimization region. Numerically, we demonstrate the feasibility of the approach on two tasks: the Max-Cut problem and polynomial optimization. The method excels in generating circuits without gradient vanishing and effectively optimizes the cost function. From the perspective of quantum algorithms, our model improves quantum optimization for polynomial-type cost functions, addressing the challenge of exponential sample complexity growth.
Variational Quantum Algorithms (VQAs) have gained prominence as a viable framework for exploiting near-term quantum devices in applications ranging from optimization and chemistry simulation to machine learning. However, the effectiveness of VQAs is often constrained by the so-called barren plateau problem, wherein gradients diminish exponentially as system size or circuit depth increases, thereby hindering training. In this work, we propose a reinforcement learning (RL)-based initialization strategy to alleviate the barren plateau issue by reshaping the initial parameter landscape to avoid regions prone to vanishing gradients. In particular, we explore several RL algorithms (Deterministic Policy Gradient, Soft ActorCritic, and Proximal Policy Optimization, etc.) to generate the circuit parameters (treated as “actions”) that minimize the VQAs cost function before standard gradient-based optimization. By pre-training with RL in this manner, subsequent optimization using methods such as gradient descent or Adam proceeds from a more favorable initial state. Extensive numerical experiments under various noise conditions and tasks consistently demonstrate that the RL-based initialization method significantly enhances both convergence speed and final solution quality. Moreover, comparisons among different RL algorithms highlight that multiple approaches can achieve comparable performance gains, underscoring the flexibility and robustness of our method. These findings shed light on a promising avenue for integrating machine learning techniques into quantum algorithm design, offering insights into how RL-driven parameter initialization can accelerate the scalability and practical deployment of VQAs. Opening up a promising path for the research community in machine learning for quantum, especially barren plateau problems in VQAs.
Parameterized quantum circuits used as variational ansatzes are emerging as promising tools to tackle complex problems ranging from quantum chemistry to combinatorial optimization.These variational quantum circuits can suffer from the well-known curse of barren plateaus, which is characterized by an exponential vanishing of the cost-function gradient with the system size, making training unfeasible for practical applications.Since a generic quantum circuit cannot be simulated efficiently, the determination of its trainability is an important problem.Here we find an efficient method to compute the gradient of the cost function and its variance for a wide class of variational quantum circuits.Our scheme relies on our proof of an exact mapping from randomly initialized circuits to a set of Clifford circuits that can be efficiently simulated on a classical computer by virtue of the celebrated Gottesman-Knill theorem.This method is scalable and can be used to certify trainability for variational quantum circuits and explore design strategies that can overcome the barren-plateau problem.As illustrative examples, we show results with up to 100 qubits.