Representation-Induced Symmetry Trapping in Adaptive Variational Quantum Simulations of Multi-Reference Topologies

• URL: http://arxiv.org/abs/2606.13387v1
• Date: Thu, 11 Jun 2026 14:16:11 GMT
• Title: Representation-Induced Symmetry Trapping in Adaptive Variational Quantum Simulations of Multi-Reference Topologies
• Abstract summary: We evaluate a spin-conserved SUSD operator pool across highly stretched configurations.<n>We show that the preservation of point-group symmetry structurally protects the optimization landscape.<n> exploiting structural overlap within our pool, we introduce a co-variance-driven, adaptive shot-allocation filter.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Evaluating the trainability of adaptive quantum chemistry algorithms under multi-reference static correlation requires understanding how representation topologies intertwine with molecular geometry. We systematically expose a deep physical dependence on point-group symmetry by evaluating a spin-conserved SUSD operator pool across highly stretched configurations (2 x Re) of asymmetric LiH, symmetric BeH2, and asymmetric H2O. Under asymmetric distortions, the non-local mapping constraints of the Bravyi-Kitaev transformation create an optimization trapping effect--an encodement-locked manifestation of the broader barren plateau crisis. Crucially, by comparing these to the symmetrical stretching baseline of BeH2, we demonstrate that the preservation of point-group symmetry structurally protects the optimization landscape, proving that ansatz symmetry restrictions are necessary but insufficient without accounting for the underlying fermion-to-qubit representation. While current methods rely on numerical pruning to throttle pool sizes, our structural approach establishes that the mapping representation remains a critical factor in maintaining landscape trainability. Furthermore, exploiting structural overlap within our pool, we introduce a covariance-driven, adaptive shot-allocation filter. Diverging from static energy-variance minimization frameworks, our allocation engine operates as a dynamic runtime diagnostic tool. By continuously monitoring the gradient precision threshold epsilon, it aggressively prunes dead symmetry channels and triggers an automated circuit-termination sequence upon detecting representation-induced flat-lined states (dE/dtheta approx 0). This integration of algebraic measurement reuse with topology-aware statistical filtering provides a promising, resource-efficient strategy for executing deep variational algorithms on early fault-tolerant architectures.

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