Universal scaling framework for parameterized quantum evolutions at criticality

• URL: http://arxiv.org/abs/2607.22863v1
• Date: Fri, 24 Jul 2026 19:09:19 GMT
• Title: Universal scaling framework for parameterized quantum evolutions at criticality
• Abstract summary: Variational anstze are cornerstones of quantum many-body physics.<n>Recent quantum-technology advances have introduced a new class based on layered parameterized evolutions.<n>We show that correlations span all length scales, while finite circuit depth limits how far they extend.
• Score: 39.255502531644204
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Variational ansätze are a cornerstone of quantum many-body physics, providing compact approximations to complex ground states using finite resources. Recent quantum-technology advances have introduced a new class based on layered parameterized evolutions. Assessing whether they can represent critical ground states is challenging: correlations span all length scales, while finite circuit depth limits how far they extend. Building on finite-resource scaling from tensor networks, we assign each ansatz an emergent correlation length $ξ_D$, the longest range over which it faithfully captures critical correlations. Its growth with refinement parameter $D$, $ξ_D \propto D^κ$, defines an exponent $κ$ measuring how efficiently an architecture converts resources into long-distance correlations. Applying this framework to the critical transverse-field Ising model, with $D$ the circuit depth of parameterized evolutions, we compare ansätze with nearest-neighbor and long-range generators, and layers where generators act separately or combined. All ansätze are compatible with algebraic growth, but fitted exponents range from $κ\simeq1$ to $κ\simeq3$. Exponential interactions give the largest exponents, while power-law interactions stay close to nearest-neighbor behavior, showing long-range support alone gives no scaling advantage. Combined-generator layers generally outperform separable ones, so layer organization matters alongside interaction range. Finally, a quasiparticle analysis shows finite depth leaves an unresolved window of width $ξ_D^{-1}$ around the low-energy modes responsible for long-distance correlations. The emergent correlation length thus acts as an infrared resolution scale, providing a benchmark for critical-state preparation and a guide for designing resource-efficient variational architectures.

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