Variational quantum algorithms (VQAs) are constrained by a trade-off: deeper circuits can cover a larger reachable quantum states but suffer from barren plateaus, while shallow circuits remain trainable yet can have insufficient reachability to the target state. Here, we propose a general framework to address this challenge by enhancing the VQA performance with a designed input state constructed using a linear combination technique. This approach modifies the set of states reachable by the original circuit, enhancing accuracy while preserving efficiency. We provide a rigorous proof that such framework increases the performance of any given VQA ansatz, and demonstrate its broad applicability across different ansatz families. In ground state preparation for representative quantum many-body models, it achieves consistently higher accuracy than standard methods at the same gate budget. These results highlight input-state design as a powerful complement to circuit design for improving reachability of the target state within a fixed ansatz. Variational quantum algorithms face a practical trade-off between circuit depth and trainability, which limits the reachability of target quantum states. Here, the authors show that input-state design based on linear combinations systematically modifies the reachable-state set of a fixed ansatz, thereby enhancing target-state reachability and improving ground-state preparation accuracy across representative quantum many-body models without increasing gate cost.
Variational quantum algorithms (VQAs) are constrained by a trade-off: deeper circuits can cover a larger reachable quantum states but suffer from barren plateaus, while shallow circuits remain trainable yet can have insufficient reachability to the target state. Here, we propose a general framework to address this challenge by enhancing the VQA performance with a designed input state constructed using a linear combination technique. This approach modifies the set of states reachable by the original circuit, enhancing accuracy while preserving efficiency. We provide a rigorous proof that such framework increases the performance of any given VQA ansatz, and demonstrate its broad applicability across different ansatz families. In ground state preparation for representative quantum many-body models, it achieves consistently higher accuracy than standard methods at the same gate budget. These results highlight input-state design as a powerful complement to circuit design for improving reachability of the target state within a fixed ansatz. Variational quantum algorithms face a practical trade-off between circuit depth and trainability, which limits the reachability of target quantum states. Here, the authors show that input-state design based on linear combinations systematically modifies the reachable-state set of a fixed ansatz, thereby enhancing target-state reachability and improving ground-state preparation accuracy across representative quantum many-body models without increasing gate cost.
Variational quantum algorithms (VQAs) are a leading framework for realizing quantum advantages in the Noisy Intermediate-Scale Quantum (NISQ) era, with applications spanning discrete combinatorial problems and continuous optimization. While the topologies of parameterized quantum circuits (ansatzes) fundamentally govern both expressibility and trainability in continuous landscapes, existing reviews predominantly focus on static algorithmic classifications or discrete settings, leaving the structural evolution and practical limitations of ansatz architectures insufficiently explored. To address this gap, this review presents a systematic analysis of variational ansatz architectures, tracing their progression from static, pre-defined topologies to adaptive growth mechanisms. Beyond traditional gradient-driven and architecture-search paradigms, we evaluate supplementary strategies such as layerwise training and noise-adaptive construction, revealing inherent vulnerabilities such as local minima entrapment and the compilation overhead induced by calibration drift. The mathematical foundations of VQAs are outlined, and representative fixed ansatz architectures, including hardware-efficient, physics-inspired, and problem-specific designs, are characterized within continuous-domain mappings. Intrinsic limitations arising from barren plateaus (BPs) and noise-induced barren plateaus (NIBPs) are analyzed, revealing the fundamental coupling between circuit depth, parameter scaling, and trainability degradation. Furthermore, adaptive construction strategies and recent advances in automated variational quantum architecture search (VQAS) are examined. Through the synthesis of intrinsic limitations (BPs, NIBPs, and hardware-algorithm coupling) and the evaluation of standardized benchmarking protocols, this review rigorously assesses the resource trade-offs of current VQA frameworks. Ultimately, next-generation ansatz design will adopt hardware–software co-design principles grounded in physical constraints, enabling scalable and noise-resilient quantum optimization.
Ansatz selection is a key factor in the performance of variational quantum algorithms (VQAs). While much of the state-of-the-art still relies on heuristic choices, an inadequate circuit structure can compromise both the expressive power and the trainability of the resulting model. Recent results have also established theoretical connections between expressibility and the onset of barren plateaus, highlighting the need for systematic criteria for ansatz selection. In this work, the ansatz is treated as a design feature to be optimized rather than a fixed block, and a design space exploration (DSE) is performed over a diverse set of parametrized quantum circuits (PQCs). Three complementary metrics -- expressibility, trainability, and resource cost -- are evaluated and used to analyze the trade-offs that emerge across different PQCs. Beyond identifying Pareto-optimal candidates, this multi-objective perspective helps clarify the interplay between these metrics and contributes quantitative evidence toward understanding the expressibility--trainability tension in variational circuits.
Variational quantum algorithms have emerged as a leading paradigm that extracts practical computation from near-term intermediate-scale quantum devices, enabling advances in quantum chemistry simulations, combinatorial optimization, and quantum machine learning. However, the performance of variational quantum algorithms is highly sensitive to the design of the ansatze. To be effective, ansatze must be expressive enough to capture target states but shallow enough to be trainable. We propose a genetic algorithm-inspired framework for designing ansatze that achieve high expressibility while maintaining shallow depth and low parameter count. Our approach evolves ansatze through mutation and selection based on an expressibility metric. The circuit generated by our framework consistently demonstrates high expressibility at any target depth and performs comparably to traditional ansatz design approaches. This work presents a problem-agnostic, scalable solution for ansatz design, producing expressive, low-depth circuits that need to be designed only once and can serve a wide range of applications.
While variational quantum algorithms (VQAs) have demonstrated considerable success in unconstrained optimization, their application to constrained combinatorial problems face a trade-off. Penalty-based methods, despite their circuit simplicity, suffer from a fundamental limitation: inefficient sampling in vast infeasible regions. This often results in suboptimal solutions that violate constraints and impede convergence to high-quality results. In contrast, ansatz-based approaches enforce solution feasibility by design but require complex, problem-specific circuits that are challenging to implement on current noisy intermediate-scale quantum devices. To overcome these limitations, we introduce an alternative VQA whose core innovation lies in a strategically designed loss function. This function offers a dual advantage. First, it is provably guaranteed that its global minimum corresponds uniquely to the optimal feasible solution, as this is achieved by ensuring universally higher loss values for all infeasible solutions. Second, it furnishes distinct computational pathways for feasible versus infeasible regions, thus creating clear and non competing guidance for the optimizer. As a result of these combined features, the algorithm's overall performance is significantly enhanced. Regarding hardware overhead, our design requires adding only an efficient validation oracle module to the penalty-based circuit, resulting in a circuit complexity significantly lower than that of ansatz-based approaches with their custom mixers. To validate the practical efficiency of our method, we empirically demonstrate its effectiveness by solving minimum vertex cover and maximum independent set problems on random graphs of varying small-scale sizes.
Variational quantum algorithms (VQAs) are expected to establish valuable applications on near-term quantum computers. However, recent works have pointed out that the performance of VQAs greatly relies on the expressibility of the ansatzes and is seriously limited by optimization issues such as barren plateaus (i.e., vanishing gradients). This work proposes the state efficient ansatz (SEA) for accurate ground state preparation with improved trainability. We show that the SEA can generate an arbitrary pure state with much fewer parameters than a universal ansatz, making it efficient for tasks like ground state estimation. Then, we prove that barren plateaus can be efficiently mitigated by the SEA and the trainability can be further improved most quadratically by flexibly adjusting the entangling capability of the SEA. Finally, we investigate a plethora of examples in ground state estimation where we obtain significant improvements in the magnitude of the cost gradient and the convergence speed.
Variational quantum algorithms (VQAs) are the quantum analog of classical neural networks (NNs). A VQA consists of a parameterized quantum circuit (PQC) which is composed of multiple layers of ansatzes (simpler PQCs, which are an analogy of NN layers) that differ only in selections of parameters. Previous work has identified the alternating layered ansatz as potentially a new standard ansatz in near-term quantum computing. Indeed, shallow alternating layered VQAs are easy to implement and have been shown to be both trainable and expressive. In this work, we introduce a training algorithm with an exponential reduction in training cost of such VQAs. Moreover, our algorithm uses classical shadows of quantum input data, and can hence be run on a classical computer with rigorous performance guarantees. We demonstrate 2-3 orders of magnitude improvement in the training cost using our algorithm for the example problems of finding state preparation circuits and the quantum autoencoder.