Contiguous Depth, Not Nominal Depth, Controls Gradient Visibility in Fragmented Hardware-Efficient Variational Circuits
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2026
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| _version_ | 1866901652940783616 |
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| author | Ahaneku, Oguike |
| author_facet | Ahaneku, Oguike |
| contents | <p>The barren plateau (BP) phenomenon—exponential decay of gradient variance in parameterized quantum circuits (PQCs) with system size—is a primary obstacle to scaling<br>variational quantum algorithms (VQAs). This paper reports a set of empirical benchmarks on hardware-efficient ansatz (HEA) circuits up to n = 20 qubits, showing that identity fragmentation—partitioning a circuit of nominal depth D into pairs of forward and inverse blocks of size k—substantially increases the variance of cost-function gradients, relative to unfragmented HEA at the same nominal depth. The fragmented design exhibits a suppression exponent αfrag = 0.225 ± 0.008 in Var(∂θ C) ∼ e−αn, versus αunfrag = 0.711 ± 0.025 for the unfragmented baseline (R2 ≥ 0.996 in both cases), giving a measured ratio of approximately 4 × 104 at n = 20, D = 24. In the tested fragmented HEA settings, the advantage is monotone in the maximum contiguous depth Lcontig, persists under finite-shot estimation (8000 shots), and is partially robust to depolarizing noise at gate-error rates relevant to current superconducting hardware. A direct training-drift test over ten gradient-descent steps on an X-basis cost at n = 8 shows the fragmentation gradient-variance advantage persists (50× at t = 0, 40× at t = 10) while the fragmented circuit reduces the cost ∼ 50× more than the unfragmented baseline over the same window. The design rule is derived from the Universal Suppression Law in companion theoretical work; the present paper’s role is to establish benchmark-level empirical support across the circuit families and noise settings studied here.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19793675 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
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| spellingShingle | Contiguous Depth, Not Nominal Depth, Controls Gradient Visibility in Fragmented Hardware-Efficient Variational Circuits Ahaneku, Oguike Barren Plateaus Hardware-Efficient Ansatz (HEA) Identity Fragmentation Contiguous Depth Gradient Variance QuEST <p>The barren plateau (BP) phenomenon—exponential decay of gradient variance in parameterized quantum circuits (PQCs) with system size—is a primary obstacle to scaling<br>variational quantum algorithms (VQAs). This paper reports a set of empirical benchmarks on hardware-efficient ansatz (HEA) circuits up to n = 20 qubits, showing that identity fragmentation—partitioning a circuit of nominal depth D into pairs of forward and inverse blocks of size k—substantially increases the variance of cost-function gradients, relative to unfragmented HEA at the same nominal depth. The fragmented design exhibits a suppression exponent αfrag = 0.225 ± 0.008 in Var(∂θ C) ∼ e−αn, versus αunfrag = 0.711 ± 0.025 for the unfragmented baseline (R2 ≥ 0.996 in both cases), giving a measured ratio of approximately 4 × 104 at n = 20, D = 24. In the tested fragmented HEA settings, the advantage is monotone in the maximum contiguous depth Lcontig, persists under finite-shot estimation (8000 shots), and is partially robust to depolarizing noise at gate-error rates relevant to current superconducting hardware. A direct training-drift test over ten gradient-descent steps on an X-basis cost at n = 8 shows the fragmentation gradient-variance advantage persists (50× at t = 0, 40× at t = 10) while the fragmented circuit reduces the cost ∼ 50× more than the unfragmented baseline over the same window. The design rule is derived from the Universal Suppression Law in companion theoretical work; the present paper’s role is to establish benchmark-level empirical support across the circuit families and noise settings studied here.</p> |
| title | Contiguous Depth, Not Nominal Depth, Controls Gradient Visibility in Fragmented Hardware-Efficient Variational Circuits |
| topic | Barren Plateaus Hardware-Efficient Ansatz (HEA) Identity Fragmentation Contiguous Depth Gradient Variance QuEST |
| url | https://doi.org/10.5281/zenodo.19793675 |