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.
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.
Variational quantum algorithms (VQAs) promise near-term quantum advantage, yet parametrized quantum states commonly built from the digital gate-based approach often suffer from scalability issues such as barren plateaus, where the loss landscape becomes flat. We study an analog VQA ansätze composed of M quenches of a disordered Ising chain, whose dynamics is native to several quantum simulation platforms. By tuning the disorder strength we place each quench in either a thermalized phase or a many-body-localized (MBL) phase and analyse (i) the ansätze’s expressivity and (ii) the scaling of loss variance. Numerics shows that both phases reach maximal expressivity at large M, but barren plateaus emerge at far smaller M in the thermalized phase than in the MBL phase. Here we propose an MBL initialization strategy by exploiting this gap: initialize the ansätze in the MBL regime at intermediate quench M, enabling initial trainability while retaining sufficient expressivity for subsequent optimization. The results link quantum phases of matter and VQA trainability, and provide practical guidelines for scaling analog-hardware VQAs. Variational quantum algorithms (VQAs) face scalability challenges, notably barren plateaus, where the loss landscape flattens with increasing system size. Here, the authors explore an analog VQA ansatz using quenches of a disordered Ising chain, demonstrating that initializing in a many-body-localized phase enhances initial trainability while retaining sufficient expressivity to solve optimization problems, offering practical insights for scaling analog VQAs.
Variational quantum algorithms have been widely demonstrated in both experimental and theoretical contexts to have extensive applications in quantum simulation, optimization, and machine learning. However, the exponential growth in the dimension of the Hilbert space results in the phenomenon of vanishing parameter gradients in the circuit as the number of qubits and circuit depth increase, known as the barren plateau phenomena. In recent years, research in non-equilibrium statistical physics has led to the discovery of the realization of many-body localization. As a type of floquet system, many-body localized floquet system has phase avoiding thermalization with an extensive parameter space coverage and has been experimentally demonstrated can produce time crystals. We applied this circuit to the variational quantum algorithms for the calculation of many-body ground states and studied the variance of gradient for parameter updates under this circuit. We found that this circuit structure can effectively avoid barren plateaus. We also analyzed the entropy growth, information scrambling, and optimizer dynamics of this circuit. Leveraging this characteristic, we designed a new type of variational ansatz, called the “many-body localization ansatz”. We applied it to solve quantum many-body ground states and examined its circuit properties. Our numerical results show that our ansatz significantly improved the variational quantum algorithm.
Variational quantum algorithms (VQAs) offer a promising route toward simulating many-body quantum systems on noisy intermediate-scale quantum (NISQ) hardware. However, their scalability is severely limited by noise-induced barren plateaus (NIBPs), where hardware noise causes the gradients of the cost function to vanish exponentially with circuit depth, rendering optimization impossible. In this work, we demonstrate that introducing nonunitary elements into the variational ansatz can mitigate NIBPs in open-quantum systems. Using an analytically tractable infinite-range dissipative Ising model, we show that a nonunitary ansatz restores finite gradients in the presence of depolarizing noise, enabling convergence to the correct symmetry-broken steady state. We also develop a Floquet-type variational ansatz in which each layer repeats the same parameters, reducing the deep variational circuit to an effective quantum channel whose fixed points can be analyzed directly. We then extend these ideas to a realistic quantum-chemistry system by simulating electron transport through Oligophenylethynylene-sulfurmethyl (OPE-SMe) using Hamiltonians and jump operators of the model derived from first-principles polarizable QM/MM calculations. Our results show that nonunitary variational ansätze provide a scalable and physically grounded route for simulating open-system steady states on NISQ hardware, offering a pathway to overcoming one of the limitations of current quantum hardware.
Abstract Variational quantum algorithms are among the most prominent methods in quantum computing, with applications in quantum machine learning, quantum simulation, and related fields. However, as the number of qubits grows, these algorithms often encounter the barren-plateau phenomenon, which severely limits their scalability. In this work, we introduce a novel parameter-initialization strategy based on Gaussian mixture models. We rigorously prove that for a hardware-efficient ansatz initialized in the | 0 ⟩ ⊗ N state, our scheme avoids barren plateaus regardless of circuit depth, qubit count, or choice of cost function. Specifically, the lower bound on the initial gradient norm provided by our method remains independent of the number of qubits Building on this foundation, we validate our theoretical results through numerical experiments, including variational ground-state searches for Hamiltonians, to demonstrate the practical effectiveness of our approach. Our findings highlight the critical role of Gaussian mixture model-based initialization in enhancing the trainability of quantum circuits and offer valuable guidance for future theoretical and experimental advances in quantum machine learning.
Variational quantum algorithms (VQAs), which classically optimize a parametrized quantum circuit to solve a computational task, promise to advance our understanding of quantum many-body systems and improve machine learning algorithms using near-term quantum computers. Prominent challenges associated with this family of quantum-classical hybrid algorithms are the control of quantum entanglement and quantum gradients linked to their classical optimization. Known as the barren plateau phenomenon, these quantum gradients may rapidly vanish in the presence of volume-law entanglement growth, which poses a serious obstacle to the practical utility of VQAs. Inspired by recent studies of measurement-induced entanglement transition in random circuits, we investigate the entanglement transition in variational quantum circuits endowed with intermediate projective measurements. Considering the Hamiltonian Variational Ansatz (HVA) for the XXZ model and the Hardware Efficient Ansatz (HEA), we observe a measurement-induced entanglement transition from volume-law to area-law with increasing measurement rate. Moreover, we provide evidence that the transition belongs to the same universality class of random unitary circuits. Importantly, the transition coincides with a “landscape transition” from severe to mild/no barren plateaus in the classical optimization. Our work may provide an avenue for improving the trainability of quantum circuits by incorporating intermediate measurement protocols in currently available quantum hardware.
Variational quantum circuits have recently gained much interest due to their relevance in real-world applications, such as combinatorial optimizations, quantum simulations, and modeling a probability distribution. Despite their huge potential, the practical usefulness of those circuits beyond tens of qubits is largely questioned. One of the major problems is the so-called barren plateaus phenomenon. Quantum circuits with a random structure often have a flat cost-function landscape and thus cannot be trained efficiently. In this paper, we propose two novel parameter conditions in which the hardware-efficient ansatz (HEA) is free from barren plateaus for arbitrary circuit depths. In the first condition, the HEA approximates to a time-evolution operator generated by a local Hamiltonian. Utilizing a recent result by [Park and Killoran, Quantum 8, 1239 (2024)], we prove a constant lower bound of gradient magnitudes in any depth both for local and global observables. On the other hand, the HEA is within the many-body localized (MBL) phase in the second parameter condition. We argue that the HEA in this phase has a large gradient component for a local observable using a phenomenological model for the MBL system. By initializing the parameters of the HEA using these conditions, we show that our findings offer better overall performance in solving many-body Hamiltonians. Our results indicate that barren plateaus are not an issue when initial parameters are smartly chosen, and other factors, such as local minima or the expressivity of the circuit, are more crucial.