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Meta-Quantum Simulation Framework via Universal Rough Operator Algebra (UROA): Subsuming Trotter Errors and Barren Plateaus

Seonggil Lee

Published Oct 4, 2026• 0 citations
Publisher

Abstract

The primary theoretical bottlenecks of practical quantum simulation—Trotter-Suzuki discretization errors [1, 2], massive fault-tolerant resource overhead, and VQE barren plateaus[3]—are deductively subsumed and algebraically elevated using the Seonggil Theory of Composite Torsion (STCT) and UROA. By redefining Hamiltonian evolution as a topological trajectory within an 8-Dimensional Non-commutative Tensor Space, classical approximation errors are geometrically saturated and variational gradients are mathematically preserved. This establishes a mathematically rigorous foundation for arbitrary-precision simulationwithin early fault-tolerant and hybrid analog-digital architectures.

DOI
10.5281/zenodo.23134870

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The primary theoretical bottlenecks of practical quantum simulation—Trotter-Suzuki discretization errors [1, 2], massive fault-tolerant resource overhead, and VQE barren plateaus[3]—are deductively subsumed and algebraically elevated using the Seonggil Theory of Composite Torsion (STCT) and UROA. By redefining Hamiltonian evolution as a topological trajectory within an 8-Dimensional Non-commutative Tensor Space, classical approximation errors are geometrically saturated and variational gradients are mathematically preserved. This establishes a mathematically rigorous foundation for arbitrary-precision simulationwithin early fault-tolerant and hybrid analog-digital architectures.
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Quantum simulation is a promising application for quantum computing. Quantum simulation algorithms may require the ability to control the time evolution unitary. Naive techniques to control a unitary can substantially increase the required computational resources. A standard approach to controlling Trotterized time evolution doubles the number of single-qubit arbitrary rotations. Here, we describe a compilation scheme that does not increase the number of arbitrary rotations for symmetric Trotterizations, which applies to second-order and higher Suzuki-Trotter decompositions. This halves the number of arbitrary rotations required to implement controlled, Trotterized time evolution compared to the standard approach. Arbitrary rotations contribute significantly to resource estimates in a fault-tolerant architecture due to the number of required magic states. Therefore, arbitrary rotations dominate the TTT-cost of fault-tolerant implementations of quantum simulation. This construction reduces the number of arbitrary rotations for controlled Trotter evolution to that of uncontrolled Trotter evolution, thereby reducing the cost of fault-tolerant quantum simulation.