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

Variational quantum algorithms are promising candidates for near-term quantum computing but can be hindered by barren plateaus, where gradients vanish exponentially and optimization becomes intractable. Noise-Induced Barren Plateaus (NIBP) are particularly concerning because they are predicted to arise generically from noise accumulation, independent of system size, circuit structure, and observable locality. We experimentally investigate NIBP on IBM quantum hardware. Using Information Content Landscape Analysis (ICLA), we efficiently estimate gradient norms for variational circuits ranging from 8 to 102 qubits, up to hundreds of parameters and circuit runtimes of hundreds of microseconds. Contrary to NIBP expectations, we observe that gradient magnitudes saturate beyond a characteristic runtime rather than decaying exponentially. Classical simulations of the 8-qubit case under noiseless, depolarizing, amplitude-damping, and dephasing noise models support this behavior. Consistent with recent theory, our results show that $T_1$-dominated non-unital noise inhibits the emergence of NIBP. Our analysis suggest that average calibration metrics may be insufficient to predict variational algorithm performance.

💡 Research Summary

Variational quantum algorithms (VQAs) are among the most promising approaches for near‑term quantum computing, yet their scalability is threatened by barren plateaus (BPs), where the gradient of the cost function vanishes exponentially with system size, rendering classical optimization ineffective. A particularly worrisome subclass, noise‑induced barren plateaus (NIBPs), has been theoretically predicted to arise generically from the accumulation of noise, independent of the number of qubits, circuit depth, or observable locality. Recent theoretical work, however, suggests that non‑unital noise—especially amplitude‑damping (T₁) processes—can prevent the emergence of NIBPs, because the system relaxes toward a pure ground state rather than a maximally mixed state.

In this paper the authors provide the first experimental verification of the absence of NIBPs on real quantum hardware. They run a series of variational circuits on IBM superconducting quantum processors ranging from 8 to 102 qubits, with circuit depths corresponding to runtimes of up to several hundred microseconds and with up to hundreds of tunable parameters. The cost function is the energy of a nearest‑neighbour Ising Hamiltonian (a 2‑local observable), implemented via a QAOA‑style ansatz that alternates cost and mixing layers. Because the Hamiltonian is 2‑local, conventional (observable‑induced) BPs are not expected, allowing the study to focus solely on noise‑related effects.

To efficiently estimate the magnitude of the gradient on hardware, the authors employ Information Content Landscape Analysis (ICLA). ICLA samples O(m) random points in the m‑dimensional parameter space, computes finite differences of the cost between successive points, maps each difference to a symbolic alphabet {−, ⊙, +}, and evaluates the empirical information content H(ε) as a function of a threshold ε. The ε that maximizes H(ε) yields a scaling factor ε_M, from which the average gradient norm is approximated as ‖∇C‖/C₀ ≈ ε_M √m. This method requires only a linear number of circuit evaluations, making it practical for large‑scale variational experiments.

The experimental results show a clear deviation from the NIBP prediction. As the circuit depth (and thus total runtime) increases, the estimated gradient norm does not decay exponentially; instead, after a characteristic runtime it saturates at a finite value. This saturation persists across all device sizes tested, indicating that NIBPs do not manifest under the experimental conditions. To corroborate the findings, the authors perform classical simulations of the 8‑qubit case under four noise models: (i) noiseless, (ii) depolarizing, (iii) amplitude‑damping (non‑unital), and (iv) pure dephasing (unital). Only the non‑unital amplitude‑damping model reproduces the observed saturation, while the depolarizing model yields the exponential decay expected for NIBPs. These simulations align with the hardware data and reinforce the conclusion that T₁‑dominated non‑unital noise suppresses NIBP formation.

An additional insight concerns the relationship between the device’s calibrated coherence times and the effective coherence time experienced during a VQA. By comparing the runtime at which the gradient plateaus with the reported average T₁ values, the authors infer an effective T_eff that is significantly shorter than the mean T₁. This discrepancy suggests that average calibration metrics (mean T₁, T₂, gate error rates) are insufficient predictors of VQA performance; task‑specific, runtime‑dependent metrics are needed.

The paper’s contributions are threefold: (1) it provides the first experimental evidence that NIBPs are absent on superconducting hardware when non‑unital noise dominates, (2) it demonstrates that ICLA is a fast, scalable tool for probing gradient magnitudes and thus for diagnosing barren‑plateau phenomena, and (3) it highlights the inadequacy of standard calibration data for assessing the trainability of variational algorithms, proposing the use of ICLA‑derived effective coherence times as a more relevant benchmark.

Limitations are acknowledged. The cost function’s 2‑local nature precludes observable‑induced BPs, so the results may not directly extend to highly non‑local cost functions. ICLA yields only an average gradient norm and does not capture the full landscape structure (e.g., variance, presence of local minima). Future work should explore deeper circuits, more complex observables, and other hardware platforms (e.g., trapped ions) to generalize the findings. Nonetheless, this study substantially advances our understanding of noise effects in VQAs and provides practical diagnostics for the emerging field of quantum algorithm benchmarking.