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arXiv:2511.13408

Taming Barren Plateaus in Arbitrary Parameterized Quantum Circuits without Sacrificing Expressibility

Zhenyu Chen, Yuguo Shao, Zhengwei Liu, Zhaohui Wei

quant-phcs.CCcs.ITcs.LGSubmitted Nov 17, 2025• Announced Nov 18, 2025• 0 citations• Revised Nov 18, 2025 (v2)

v1 · Nov 17, 2025 v2 · Nov 18, 2025 v3 · Jan 8, 2026

Abstract

Quantum algorithms based on parameterized quantum circuits (PQCs) have enabled a wide range of applications on near-term quantum devices. However, existing PQC architectures face several challenges, among which the ``barren plateaus" phenomenon is particularly prominent. In such cases, the loss function concentrates exponentially with increasing system size, thereby hindering effective parameter optimization. To address this challenge, we propose a general and hardware-efficient method for eliminating barren plateaus in an arbitrary PQC. Specifically, our approach achieves this by inserting a layer of easily implementable quantum channels into the original PQC, each channel requiring only one ancilla qubit and four additional gates, yielding a modified PQC (MPQC) that is provably at least as expressive as the original PQC and, under mild assumptions, is guaranteed to be free from barren plateaus. Furthermore, by appropriately adjusting the structure of MPQCs, we rigorously prove that any parameter in the original PQC can be made trainable. Importantly, the absence of barren plateaus in MPQCs is robust against realistic noise, making our approach directly applicable to current noisy intermediate-scale quantum (NISQ) hardware. Numerically, we demonstrate the practicality of our method by modifying a commonly used PQC for thermal-state preparation. The results show that {barren plateaus are effectively eliminated} in this class of circuits with up to 100 qubits and 2400 layers, whereas the original ansatz suffers from severe gradient vanishing.

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Quantum algorithms based on parameterized quantum circuits (PQCs) have enabled a wide range of applications on near-term quantum devices. However, existing PQC architectures face several challenges, among which the ``barren plateaus" phenomenon is particularly prominent. In such cases, the loss function concentrates exponentially with increasing system size, thereby hindering effective parameter optimization. To address this challenge, we propose a general and hardware-efficient method for eliminating barren plateaus in an arbitrary PQC. Specifically, our approach achieves this by inserting a layer of easily implementable quantum channels into the original PQC, each channel requiring only one ancilla qubit and four additional gates, yielding a modified PQC (MPQC) that is provably at least as expressive as the original PQC and, under mild assumptions, is guaranteed to be free from barren plateaus. Furthermore, by appropriately adjusting the structure of MPQCs, we rigorously prove that any parameter in the original PQC can be made trainable. Importantly, the absence of barren plateaus in MPQCs is robust against realistic noise, making our approach directly applicable to current noisy intermediate-scale quantum (NISQ) hardware. Numerically, we demonstrate the practicality of our method by modifying a commonly used PQC for thermal-state preparation. The results show that {barren plateaus are effectively eliminated} in this class of circuits with up to 100 qubits and 2400 layers, whereas the original ansatz suffers from severe gradient vanishing.

Variational quantum algorithms, which combine highly expressive parameterized quantum circuits (PQCs) and optimization techniques in machine learning, are one of the most promising applications of a near-term quantum computer. Despite their huge potential, the utility of variational quantum algorithms beyond tens of qubits is still questioned. One of the central problems is the trainability of PQCs. The cost function landscape of a randomly initialized PQC is often too flat, asking for an exponential amount of quantum resources to find a solution. This problem, dubbed barren plateaus , has gained lots of attention recently, but a general solution is still not available. In this paper, we solve this problem for the Hamiltonian variational ansatz (HVA), which is widely studied for solving quantum many-body problems. After showing that a circuit described by a time-evolution operator generated by a local Hamiltonian does not have exponentially small gradients, we derive parameter conditions for which the HVA is well approximated by such an operator. Based on this result, we propose an initialization scheme for the variational quantum algorithms and a parameter-constrained ansatz free from barren plateaus.

Classical optimization of parameterized quantum circuits is a widely studied methodology for the preparation of complex quantum states, as well as the solution of machine learning and optimization problems. However, it is well known that many proposed parameterized quantum circuit architectures suffer from drawbacks which limit their utility, such as their classical simulability or the hardness of optimization due to a problem known as "barren plateaus". We propose and study a class of dynamic parameterized quantum circuit architectures. These are parameterized circuits containing intermediate measurements and feedforward operations. In particular, we show that these architectures: 1. Provably do not suffer from barren plateaus. 2. Are expressive enough to describe arbitrarily deep unitary quantum circuits. 3. Are competitive with state of the art methods for preparing ground states and facilitating the representation of nontrivial thermal states. These features make the proposed architectures promising candidates for a variety of applications.

Whether parameterized quantum circuits (PQCs) can be systematically constructed to be both trainable and expressive remains an open question. Highly expressive PQCs often exhibit barren plateaus, while several trainable alternatives admit efficient classical simulation. We address this question by deriving a finite-sample, dimension-independent concentration bound for estimating the variance of a PQC cost function, yielding explicit trainability guarantees. Across commonly used ansätze, we observe an anticorrelation between trainability and expressibility, consistent with theoretical insights. Building on this observation, we propose a property-based ansatz-search framework for identifying circuits that combine trainability and expressibility. We demonstrate its practical viability on a real quantum computer and apply it to variational quantum algorithms. We identify quantum neural network ansätze with improved effective dimension using over

6 \times

fewer parameters, and for VQE on

\mathrm{H}_2

we achieve UCCSD-like accuracy at substantially reduced circuit complexity.

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(\log{n})

. 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.

Variational quantum algorithms (VQAs) are a promising paradigm for quantum advantage, yet their trainability is severely hampered by barren plateaus (BPs). Several recent works have proposed dynamic parameterized quantum circuits (DPQCs), which interleave unitary layers with parameterized CPTP maps, such as engineered dissipation, feedforward gadgets, and periodic resets, as a possible strategy for mitigating BPs. We unify this class of circuits into a formalization for DPQCs.We identify constraints on the nature and the structure of DPQCs if they are to prevent a significant number of parameters from becoming untrainable. Using purification and Pauli-path analysis, we further identify a mechanism by which the cost function can remain anti-concentrated even when many parameters remain untrainable. Our analysis reveals ways to design DPQCs that do not have an exponentially concentrated cost function, and our results suggest that BP mitigation via DPQCs is at least as hard as designing BP-free unitaries.

Parameterized quantum circuits (PQCs) are central to quantum machine learning and near-term quantum simulation, but their scalability is often hindered by barren plateaus (BPs), where gradients decay exponentially with system size. Prior explanations, including expressivity, entanglement, locality, and noise, are often presented in ways that conflate two distinct issues: concentration of the measured observable and loss of parameter sensitivity caused by circuit dynamics.We develop a unified statistical framework that separates these mechanisms. We show that several standard BP explanations, including locality- and entanglement-related effects, can be understood through a single phenomenon that we term observable concentration (OC). Importantly, we prove that avoiding OC is necessary but not sufficient for trainability. Beyond OC, we identify two distinct mid-circuit sources of gradient suppression. First, in circuits with effectively independent forward and backward blocks, parameter perturbations can propagate outside the measurement light cone and become inaccessible to the final observable, yielding information-loss-induced BPs. Second, BPs can also arise in circuits with highly correlated forward and backward blocks, as we demonstrate through an echo-type circuit model that is reminiscent of information scrambling.