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

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.

Figures (12)

• Figure 1: Average norm of the gradient ($\norm{\nabla C}/C_0$) versus circuit runtime ($t_{cir}\xspace$). Here, $t_{cir}\xspace$ only accounts for the time of the gate implementation and measurement, but we removed the reset time between shots. Lines with markers show the data obtained from actual quantum hardware. Each color indicates the qubit size of the experiment. Lines without markers depict the 8-qubit density matrix simulations, where 'dep.' refers to depolarizing noise with strength $p$ of Eq. \ref{['eq:depolarizing']} and "A+D" denotes the noise model of Eq. \ref{['eq:T1T2noise']}. While depolarizing noise simulations show clear signal of NIPB, the gradient signal flattens at a constant value for large circuit runtimes for all hardware experiments and amplitude damping simulations.
• Figure 2: $T_{1}\xspace$ cumulative distribution function versus % of qubits contained in the $T_{1}\xspace$-range. Qubit numbers are marked with colored lines. For every circuit size, the vertical and horizontal lines indicate the mean (solid), and effective (dashed) $T_{1}\xspace$. The mean $\langle T_{1} \rangle \xspace$ region is denoted with the shaded gray area. The effective $T^{{\rm eff}}_{1}\xspace$ region is denoted with the green shaded area. This result suggests that the effective $T^{{\rm eff}}_{1}\xspace$ is determined by the $~\sim20\%$ of the qubits with the shortest coherence times.
• Figure 3: Gradient, $\norm{\nabla C}/C_0$, as a function of circuit times $t_{cir}\xspace$ for various setups. The data labeled 'short' refers to the different compilation of the same logical circuit (see \ref{['app:circuits_hardware']}), while 'heavy hex' indicates that a different Hamiltonian with same coupling topology as the hardware was used. These results show that the flattening phenomenon is consistent across different hardware and setups.
• Figure 4: $T^{{\rm eff}}_{1}\xspace$ relative to $\langle T_{1} \rangle \xspace$ as a function of the number of qubits and for various different experimental setups. Each color represents a different ibm device. 'short' (purple) and 'heavy hex' (brown) represent different compilation and a different topology for the Hamiltonian, respectively. The effective coherence times $T^{{\rm eff}}_{1}\xspace$ are significantly smaller than mean coherence times $\langle T_{1} \rangle \xspace$ of all qubits in the circuits.
• Figure 5: Examples of the same logical $L=1$ single layer circuit with $N=20$ qubits transpiled in the two different ways. Ladder structure (left) which is the default structure we used and parallel execution (right) which we termed 'short'.