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 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 Eigensolver (VQE) algorithms suffer from barren plateaus, where gradients vanish with system size and circuit depth. Although many mitigation strategies exist, their connection to convergence performance under different iteration budgets remains unclear. Moreover, a systematic analysis identifying which state-of-the-art mitigation techniques perform best under specific scenarios is also lacking. We benchmark four approaches, Local-Global, Adiabatic, State Efficient Ansatz (SEA), and Pretrained VQE, against standard VQE on molecular systems from 4 to 14 qubits, analyzing gradient variance up to 50 layers and convergence over 1000 iterations. Our results show that the impact of gradient preservation is iteration-dependent. In the 14-qubit BeH2 system, Pretrained VQE outperforms SEA at 100 iterations despite lower gradient variance, but SEA becomes 2.2x more accurate at 1000 iterations. For smaller systems, SEA achieves near-exact energies (H2: 10^-5 Ha, LiH: 2x10^-4 Ha) with fidelities 0.999, while standard methods plateau early. The results demonstrate that robust barren plateau mitigation depends on aligning the chosen strategy with both system size and available computational budget, rather than treating gradient variance as the sole predictor of performance.
Variational Quantum Algorithms (VQAs) have received considerable attention due to their potential for achieving near-term quantum advantage. However, more work is needed to understand their scalability. One known scaling result for VQAs is barren plateaus, where certain circumstances lead to exponentially vanishing gradients. It is common folklore that problem-inspired ansatzes avoid barren plateaus, but in fact, very little is known about their gradient scaling. In this work we employ tools from quantum optimal control to develop a framework that can diagnose the presence or absence of barren plateaus for problem-inspired ansatzes. Such ansatzes include the Quantum Alternating Operator Ansatz (QAOA), the Hamiltonian Variational Ansatz (HVA), and others. With our framework, we prove that avoiding barren plateaus for these ansatzes is not always guaranteed. Specifically, we show that the gradient scaling of the VQA depends on the degree of controllability of the system, and hence can be diagnosed through the dynamical Lie algebra g obtained from the generators of the ansatz. We analyze the existence of barren plateaus in QAOA and HVA ansatzes, and we highlight the role of the input state, as different initial states can lead to the presence or absence of barren plateaus. Taken together, our results provide a framework for trainability-aware ansatz design strategies that do not come at the cost of extra quantum resources. Moreover, we prove no-go results for obtaining ground states with variational ansatzes for controllable system such as spin glasses. Our work establishes a link between the existence of barren plateaus and the scaling of the dimension of g .
Abstract Variational quantum algorithms (VQAs) are widely applied in the noisy intermediate-scale quantum era and are expected to demonstrate quantum advantage. However, training VQAs faces difficulties, one of which is the so-called barren plateaus (BPs) phenomenon, where gradients of cost functions vanish exponentially with the number of qubits. In this paper, inspired by transfer learning, where knowledge of pre-solved tasks could be further used in a different but related work with training efficiency improved, we report a parameter initialization method to mitigate BP. In the method, a small-sized task is solved with a VQA. Then the ansatz and its optimum parameters are transferred to tasks with larger sizes. Numerical simulations show that this method could mitigate BP and improve training efficiency. A brief discussion on how this method can work well is also provided. This work provides a reference for mitigating BP, and therefore, VQAs could be applied to more practical problems.
Variational Quantum Algorithms (VQAs) may be a path to quantum advantage on Noisy Intermediate-Scale Quantum (NISQ) computers. A natural question is whether noise on NISQ devices places fundamental limitations on VQA performance. We rigorously prove a serious limitation for noisy VQAs, in that the noise causes the training landscape to have a barren plateau (i.e., vanishing gradient). Specifically, for the local Pauli noise considered, we prove that the gradient vanishes exponentially in the number of qubits n if the depth of the ansatz grows linearly with n. These noise-induced barren plateaus (NIBPs) are conceptually different from noise-free barren plateaus, which are linked to random parameter initialization. Our result is formulated for a generic ansatz that includes as special cases the Quantum Alternating Operator Ansatz and the Unitary Coupled Cluster Ansatz, among others. For the former, our numerical heuristics demonstrate the NIBP phenomenon for a realistic hardware noise model.
Recent advances in the variational quantum eigensolver (VQE) have strengthened its promise for molecular electronic-structure calculations on near-term noisy intermediate-scale quantum (NISQ) devices. However, barren plateaus (BPs) remain a major obstacle to scaling VQE, as vanishing gradients can severely obstruct optimization at large scale. While most BP studies focus on randomly initialized circuits and global gradient behavior, practical quantum chemistry VQE typically uses chemically motivated initializations and local optimization around HF- or MP2-derived states. Although chemically informed initializations are widely expected to improve VQE trainability, how they mitigate local barren plateaus remains unclear. We therefore study the occurrence of local barren plateaus in molecular UCCSD-VQE, considering both chemically motivated initialization points and iterates along the corresponding optimization trajectories. In the benchmarks considered here, chemically initialized starting points and variational trajectories show polynomial decay of local gradient variance with system size instead of the exponential BP-like decay observed for random controls, indicating that chemical initialization mitigates barren plateaus in the local optimization regions and highlights the trainability advantage of chemically motivated VQE strategies.
Variational quantum algorithms (VQAs) represent a promising pathway toward achieving practical quantum advantage on near-term hardware. Despite this promise, for generic, expressive ansätze, their scalability is critically hindered by barren plateaus—regimes of exponentially vanishing gradients. We demonstrate that initializing a hardware-efficient, Floquet-structured ansatz within the many-body localized (MBL) phase mitigates barren plateaus and enhances algorithmic trainability. Through analysis of the inverse participation ratio, entanglement entropy, and a novel low-weight stabilizer Rényi entropy, we characterize a distinct MBL--thermalization transition. Below a critical kick strength, the circuit avoids forming a unitary 2-design, exhibits robust area-law entanglement, and maintains non-vanishing gradients. Leveraging this MBL regime facilitates the efficient variational preparation of ground states for several model Hamiltonians with significantly reduced computational resources. Crucially, experiments on a 127-qubit superconducting processor provide evidence for the preservation of trainable gradients in the MBL phase for a kicked Heisenberg chain, validating our approach on contemporary noisy hardware. Our findings position MBL-based initialization as a viable strategy for developing scalable VQAs and motivate broader integration of localization into quantum algorithm design.