Quantum error mitigation techniques are at the heart of quantum hardware implementation, and are the key to performance improvement of the variational quantum learning scheme (VQLS). Although VQLS is partially robust to noise, both empirical and theoretical results exhibit that noise would rapidly deteriorate the performance of most variational quantum algorithms in large-scale problems. Furthermore, VQLS suffers from the barren plateau phenomenon---the gradient generated by the classical optimizer vanishes exponentially with respect to the qubit number. Here we devise a resource and runtime efficient scheme, the quantum architecture search scheme (QAS), to maximally improve the robustness and trainability of VQLS. In particular, given a learning task, QAS actively seeks an optimal circuit architecture to balance benefits and side-effects brought by adding more quantum gates. Specifically, while more quantum gates enable a stronger expressive power of the quantum model, they introduce a larger amount of noise and a more serious barren plateau scenario. Consequently, QAS can effectively suppress the influence of quantum noise and barren plateaus. We implement QAS on both the numerical simulator and real quantum hardware, via the IBM cloud, to accomplish data classification and quantum chemistry tasks. Numerical and experimental results show that QAS significantly outperforms conventional variational quantum algorithms with heuristic circuit architectures. Our work provides practical guidance for developing advanced learning-based quantum error mitigation techniques on near-term quantum devices.
Quantum error mitigation techniques are at the heart of quantum hardware implementation, and are the key to performance improvement of the variational quantum learning scheme (VQLS). Although VQLS is partially robust to noise, both empirical and theoretical results exhibit that noise would rapidly deteriorate the performance of most variational quantum algorithms in large-scale problems. Furthermore, VQLS suffers from the barren plateau phenomenon---the gradient generated by the classical optimizer vanishes exponentially with respect to the qubit number. Here we devise a resource and runtime efficient scheme, the quantum architecture search scheme (QAS), to maximally improve the robustness and trainability of VQLS. In particular, given a learning task, QAS actively seeks an optimal circuit architecture to balance benefits and side-effects brought by adding more quantum gates. Specifically, while more quantum gates enable a stronger expressive power of the quantum model, they introduce a larger amount of noise and a more serious barren plateau scenario. Consequently, QAS can effectively suppress the influence of quantum noise and barren plateaus. We implement QAS on both the numerical simulator and real quantum hardware, via the IBM cloud, to accomplish data classification and quantum chemistry tasks. Numerical and experimental results show that QAS significantly outperforms conventional variational quantum algorithms with heuristic circuit architectures. Our work provides practical guidance for developing advanced learning-based quantum error mitigation techniques on near-term quantum devices.
Abstract Variational quantum algorithms (VQAs) are expected to be a path to quantum advantages on noisy intermediate-scale quantum devices. However, both empirical and theoretical results exhibit that the deployed ansatz heavily affects the performance of VQAs such that an ansatz with a larger number of quantum gates enables a stronger expressivity, while the accumulated noise may render a poor trainability. To maximally improve the robustness and trainability of VQAs, here we devise a resource and runtime efficient scheme termed quantum architecture search (QAS). In particular, given a learning task, QAS automatically seeks a near-optimal ansatz (i.e., circuit architecture) to balance benefits and side-effects brought by adding more noisy quantum gates to achieve a good performance. We implement QAS on both the numerical simulator and real quantum hardware, via the IBM cloud, to accomplish data classification and quantum chemistry tasks. In the problems studied, numerical and experimental results show that QAS cannot only alleviate the influence of quantum noise and barren plateaus but also outperforms VQAs with pre-selected ansatze.
Variational quantum algorithms (VQAs) have shown strong evidence to gain provable computational advantages in diverse fields such as finance, machine learning, and chemistry. However, the heuristic ansatz exploited in modern VQAs is incapable of balancing the trade-off between expressivity and trainability, which may lead to degraded performance when executed on noisy intermediate-scale quantum (NISQ) machines. To address this issue, here, we demonstrate the first proof-of-principle experiment of applying an efficient automatic ansatz design technique, i.e., quantum architecture search (QAS), to enhance VQAs on an 8-qubit superconducting quantum processor. In particular, we apply QAS to tailor the hardware-efficient ansatz toward classification tasks. Compared with heuristic ansätze, the ansatz designed by QAS improves the test accuracy from 31% to 98%. We further explain this superior performance by visualizing the loss landscape and analyzing effective parameters of all ansätze. Our work provides concrete guidance for developing variable ansätze to tackle various large-scale quantum learning problems with advantages.
The key challenge in the noisy intermediate-scale quantum era is finding useful circuits compatible with current device limitations. Variational quantum algorithms (VQAs) offer a potential solution by fixing the circuit architecture and optimizing individual gate parameters in an external loop. However, parameter optimization can become intractable, and the overall performance of the algorithm depends heavily on the initially chosen circuit architecture. Several quantum architecture search (QAS) algorithms have been developed to design useful circuit architectures automatically. In the case of parameter optimization alone, noise effects have been observed to dramatically influence the performance of the optimizer and final outcomes, which is a key line of study. However, the effects of noise on the architecture search, which could be just as critical, are poorly understood. This work addresses this gap by introducing a curriculum-based reinforcement learning QAS (CRLQAS) algorithm designed to tackle challenges in realistic VQA deployment. The algorithm incorporates (i) a 3D architecture encoding and restrictions on environment dynamics to explore the search space of possible circuits efficiently, (ii) an episode halting scheme to steer the agent to find shorter circuits, and (iii) a novel variant of simultaneous perturbation stochastic approximation as an optimizer for faster convergence. To facilitate studies, we developed an optimized simulator for our algorithm, significantly improving computational efficiency in simulating noisy quantum circuits by employing the Pauli-transfer matrix formalism in the Pauli-Liouville basis. Numerical experiments focusing on quantum chemistry tasks demonstrate that CRLQAS outperforms existing QAS algorithms across several metrics in both noiseless and noisy environments.
Variational quantum algorithms (VQAs) represent the most promising approach for achieving quantum advantage in near-term supervised learning, yet they face two fundamental challenges that severely limit their practical deployment: device noise degrades classification performance, and barren plateaus render gradient-based training ineffective. We address both challenges simultaneously through a novel hybrid architecture that selectively applies stabilizer quantum error correction only to the most noise-sensitive circuit components while preserving the variational structure essential for NISQ-era feasibility. Our approach combines Steane [7, 1, 3] encoding around entangling layers with a learned variational recovery mechanism (VarQEC). We establish rigorous theoretical foundations through two main contributions: First, we prove an explicit error-suppression theorem showing that selective protection reduces logical error scaling from O(p) to O(p 2) in the physical depolarizing rate p, with the exact leading constant p L ≤ 147 9 p 2 + O(p 3) derived through deterministic combinatorial enumeration of harmful Pauli patterns. Second, we demonstrate enhanced trainability by proving that selective encoding mitigates barren plateaus (reducing exponential suppression from physical to logical qubit scaling) while simultaneously improving noise-induced gradient attenuation from O(p) to O(p 2) through rigorous Weingarten calculus analysis. The manuscript provides complete implementation details including gate-level circuits, unambiguous training algorithms, and reproducible numerical experiments, positioning this work as both a theoretical advance and a practical framework for noise-resilient quantum machine learning.
Quantum architecture search (QAS) has shown significant promise in automating quantum circuit design for Variational Quantum Algorithms (VQAs). However, a central challenge remains in the high computational cost of evaluating the ground-truth performance of numerous circuit architectures during the search process. This challenge is further complicated by factors such as inefficient gradient computation, the barren plateau phenomenon, and frequent data exchange between classical and quantum systems within VQAs, all of which restrict the scalability of QAS for increasingly complex VQAs. In this study, we investigate whether quantum architectures discovered on small-scale systems can be directly extended to large-scale quantum circuits. Our results demonstrate that the performance advantage of an optimal quantum architecture, identified on a small-scale system via a layerwise construction method, can be largely preserved and effectively transferred to large-scale systems. This work establishes a viable and efficient paradigm for designing effective large-scale quantum circuits, offering a practical shortcut that bypasses the primary bottlenecks of conventional QAS.
A significant hurdle in the noisy intermediate-scale quantum (NISQ) era is identifying functional quantum circuits. These circuits must also adhere to the constraints imposed by current quantum hardware limitations. Variational quantum algorithms (VQAs), a class of quantum-classical optimization algorithms, were developed to address these challenges in the currently available quantum devices. However, the overall performance of VQAs depends on the initialization strategy of the variational circuit, the structure of the circuit (also known as ansatz), and the configuration of the cost function. Focusing on the structure of the circuit, in this thesis, we improve the performance of VQAs by automating the search for an optimal structure for the variational circuits using reinforcement learning (RL). Within the thesis, the optimality of a circuit is determined by evaluating its depth, the overall count of gates and parameters, and its accuracy in solving the given problem. The task of automating the search for optimal quantum circuits is known as quantum architecture search (QAS). The majority of research in QAS is primarily focused on a noiseless scenario. Yet, the impact of noise on the QAS remains inadequately explored. In this thesis, we tackle the issue by introducing a tensor-based quantum circuit encoding, restrictions on environment dynamics to explore the search space of possible circuits efficiently, an episode halting scheme to steer the agent to find shorter circuits, a double deep Q-network (DDQN) with an ε-greedy policy for better stability. The numerical experiments on noiseless and noisy quantum hardware show that in dealing with various VQAs, our RL-based QAS outperforms existing QAS. Meanwhile, the methods we propose in the thesis can be readily adapted to address a wide range of other VQAs.