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arXiv:2602.22851

Experimental demonstration of the absence of noise-induced barren plateaus using information content landscape analysis

Sebastian Schmitt, Linus Ekstrøm, Alberto Bottarelli, Xavier Bonet-Monroig

quant-phSubmitted Feb 26, 2026• Announced Feb 27, 2026• 0 citations
v1 · Feb 26, 2026v2 · Mar 9, 2026
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Abstract

Variational quantum algorithms are a very promising tool for near-term quantum computing. However, despite their flexibility and wide applicability, their performance is fundamentally limited by Barren Plateaus (BP), where gradients vanish and optimization becomes intractable. Noise-Induced Barren Plateaus (NIBP) are particularly interesting, as they are predicted to arise due to noise accumulation independent of circuit structure. We experimentally study NIBP on IBM quantum hardware and demonstrate their absence under non-unital amplitude damping characterized by the qubit's $T_1$ coherence times. We use Information Content Landscape Analysis (ICLA) to efficiently estimate gradient norms for circuits ranging from 8 to 102 qubits, with hundreds of parameters and circuit runtimes of hundreds of microseconds. Classical simulations of the 8-qubit case under noiseless, depolarizing, amplitude damping, and dephasing noise models serve as a baseline comparison. We thoroughly analyze the experimental results considering calibration data, shot-noise, and circuit structure. We robustly observe that the gradient magnitude saturates beyond a characteristic circuit runtime, in contrast with the exponential decay expected from NIBP. Using recent theoretical results, we corroborate that under $T_1$-dominated noise NIBP do not occur and extract an effective $T_1^\text{eff}$ that is significantly shorter than suggested by standard calibration data. Our results experimentally confirm recent predictions on the absence of NIBP under non-unital noise. These findings also indicate that conventional benchmarking metrics based on average values for device characteristics may be insufficient to predict variational algorithm performance, but full distributions need to be considered.

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Variational quantum algorithms are a very promising tool for near-term quantum computing. However, despite their flexibility and wide applicability, their performance is fundamentally limited by Barren Plateaus (BP), where gradients vanish and optimization becomes intractable. Noise-Induced Barren Plateaus (NIBP) are particularly interesting, as they are predicted to arise due to noise accumulation independent of circuit structure. We experimentally study NIBP on IBM quantum hardware and demonstrate their absence under non-unital amplitude damping characterized by the qubit's T1T_1T1​ coherence times. We use Information Content Landscape Analysis (ICLA) to efficiently estimate gradient norms for circuits ranging from 8 to 102 qubits, with hundreds of parameters and circuit runtimes of hundreds of microseconds. Classical simulations of the 8-qubit case under noiseless, depolarizing, amplitude damping, and dephasing noise models serve as a baseline comparison. We thoroughly analyze the experimental results considering calibration data, shot-noise, and circuit structure. We robustly observe that the gradient magnitude saturates beyond a characteristic circuit runtime, in contrast with the exponential decay expected from NIBP. Using recent theoretical results, we corroborate that under T1T_1T1​-dominated noise NIBP do not occur and extract an effective T1effT_1^\text{eff}T1eff​ that is significantly shorter than suggested by standard calibration data. Our results experimentally confirm recent predictions on the absence of NIBP under non-unital noise. These findings also indicate that conventional benchmarking metrics based on average values for device characteristics may be insufficient to predict variational algorithm performance, but full distributions need to be considered.
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.
Variational quantum algorithms (VQAs) hold much promise but face the challenge of exponentially small gradients. Unmitigated, this barren plateau (BP) phenomenon leads to an exponential training overhead for VQAs. Perhaps the most pernicious are noise-induced barren plateaus (NIBPs), a type of unavoidable BP arising from open system effects, which have so far been shown to exist for unital noise maps. Here, we generalize the study of NIBPs to more general completely positive, trace-preserving maps, investigating the existence of NIBPs in the unital case and a class of non-unital maps we call Hilbert-Schmidt (HS)-contractive. The latter includes amplitude damping. We identify the associated phenomenon of noise-induced limit sets (NILS) of the VQA cost function and prove its existence for both unital and HS-contractive non-unital noise maps. Along the way, we extend the parameter shift rule of VQAs to the noisy setting. We provide rigorous bounds in terms of the relevant variables that give rise to NIBPs and NILSs, along with numerical simulations of the depolarizing and amplitude-damping maps that illustrate our analytical results.
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.
Realizing successful quantum algorithms on current generation of quantum hardware depends on developing appropriate parametrized quantum circuits, which are the quantum computing counterpart to classical neural networks. A key consideration in this context is the algorithm’s trainability that can be hindered by the existence of so-called barren plateaus. In this case, the algorithm suffers from exponentially vanishing gradients as the number of qubits increases, resulting in a flat optimization landscape and making an efficient training intractable. Due to its serious impact on the success of such algorithms, this problem has gained substantial attention in recent years of quantum computing research. Theoretical and heuristic approaches have been proposed to investigate, avoid and mitigate this issue. In this work, we explore this phenomenon in detail and study the underlying mathematical concepts in depth, investigating the factors that influence the structure of the optimization landscape. Using corresponding mathematical tools, we diagnose whether a given variational circuit will exhibit barren plateaus when going beyond tens of qubits. Additionally, a review of mitigation strategies will be provided. The theory will then be applied to a use case that involves image classification to evaluate whether the model is affected by this phenomenon and which hyperparameters improve or degrade the overall performance.
Barren plateaus-regions of exponentially small gradients-are a major obstacle for training variational quantum algorithms on non-trivial problem sizes. Existing results analyze specific causes in isolation, such as random deep circuits or global cost functions, but lack a unified picture that integrates circuit design, data encoding, cost structure, and noise. In this work, we develop a comprehensive theory of barren plateaus for parametrized quantum circuits. We prove that three mechanisms jointly control gradient scaling: (1) ansatz-induced concentration, where highly expressive or sufficiently deep circuits approximate unitary 2-designs causing gradient variance to scale as O(2 −n); (2) data-encoding-induced concentration, where certain feature maps wash out class-conditional structure; and (3) probleminduced concentration, where cost functions effectively average over exponentially many degrees of freedom. For each mechanism, we derive explicit scaling laws for the gradient variance as a function of qubit count n, depth L, and encoding complexity. We show that appropriately constrained expressibility, locality, and symmetry breaking can prevent gradients from vanishing exponentially and obtain conditions under which gradients remain at worst polynomially small. This yields architectural and initialization design principles for plateau-resistant circuits, including shallow, problem-informed ansätze, layer-wise training, and structured data encodings. Numerical experiments on up to 100 qubits for VQE, QAOA, and quantum classifiers confirm our theoretical predictions and demonstrate 10-100× improvements in effective gradient magnitudes over standard architectures. Our framework subsumes existing barren plateau results and provides a practical toolkit for diagnosing and mitigating trainability issues in variational quantum algorithms.
Abstract In variational quantum algorithms the parameters of a parameterized quantum circuit are optimized in order to minimize a cost function that encodes the solution of the problem. The barren plateau phenomenon manifests as an exponentially vanishing dependence of the cost function with respect to the variational parameters, and thus hampers the optimization process. We discuss how, and in which sense, the phenomenon of noise-induced barren plateaus emerges in parameterized quantum circuits with a layered noise model. Previous results have shown the existence of noise-induced barren plateaus in the presence of local Pauli noise (Wang et al 2021 Nat. Commun. 12 6961). We extend these results analytically to arbitrary completely-positive trace preserving maps in two cases: (1) when a parameter-shift rule holds, (2) when the parameterized quantum circuit at each layer forms a unitary 2-design. The second example shows how highly expressive unitaries give rise not only to standard barren plateaus (McClean et al 2018 Nat. Commun. 9 4812), but also to noise-induced ones. In the second part of the paper, we study numerically the emergence of noise-induced barren plateaus in QAOA circuits focusing on the case of MaxCut problems on d -regular graphs and amplitude damping noise.