On the Feasibility of Exact Unitary Transformations for Many-body Hamiltonians

• URL: http://arxiv.org/abs/2510.10957v1
• Date: Mon, 13 Oct 2025 03:09:43 GMT
• Title: On the Feasibility of Exact Unitary Transformations for Many-body Hamiltonians
• Authors: Praveen Jayakumar, Tao Zeng, Artur F. Izmaylov,
• Abstract summary: We show that exact unitary transformations arise whenever the adjoint action of a unitary's generator defines a linear map within a finite-dimensional operator space.<n>This perspective brings together previously disparate examples of exact transformations under a single unifying principle.<n>We illustrate this framework for unitary coupled-cluster and involutory generators, identifying cases in which a single commutator suffices.
• Score: 2.7522708287669495
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Exact unitary transformations play a central role in the analysis and simulation of many-body quantum systems, yet the conditions under which they can be carried out exactly and efficiently remain incompletely understood. We show that exact transformations arise whenever the adjoint action of a unitary's generator defines a linear map within a finite-dimensional operator space. In this regime, the Cayley-Hamilton theorem ensures the existence of a finite-degree polynomial that annihilates the adjoint map, rendering the Baker-Campbell-Hausdorff expansion finite. This perspective brings together previously disparate examples of exact transformations under a single unifying principle and clarifies how algebraic relations between generators and transformed operators determine the polynomial degree of the transformation. We illustrate this framework for unitary coupled-cluster and involutory generators, identifying cases in which a single commutator suffices. The result establishes clear algebraic criteria for when exact unitary transformations are possible and provides new strategies for reducing their computational cost in quantum simulation.

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