Deterministic Generation of Arbitrary Fock States via Resonant Subspace Engineering

• URL: http://arxiv.org/abs/2602.12156v1
• Date: Thu, 12 Feb 2026 16:36:58 GMT
• Title: Deterministic Generation of Arbitrary Fock States via Resonant Subspace Engineering
• Abstract summary: We introduce resonant subspace engineering (RSE), a protocol that analytically confines the infinite-dimensional bosonic dynamics to a two-dimensional invariant subspace.<n>RSE achieves $O(n1/4)$ scaling in both evolution time and gate depth, showing a fundamental improvement over existing deterministic schemes.<n>RSE provides a scalable and analytically transparent framework for large-scale bosonic state engineering and gate synthesis.
• Score: 9.529916381983394
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Deterministic preparation of high-excitation Fock states is a central challenge in bosonic quantum information, with control complexity that generically explodes as the Hilbert space dimension grows. Here we introduce resonant subspace engineering (RSE), a protocol that analytically confines the infinite-dimensional bosonic dynamics to a two-dimensional invariant subspace spanned by an initial coherent state and the target state. State transfer then reduces to a geodesic rotation on a synthetic Bloch sphere, governed by resonance and phase-matching conditions we derive in closed form. For single Fock states, RSE achieves $O(n^{1/4})$ scaling in both evolution time and gate depth, showing a fundamental improvement over existing deterministic schemes. The construction generalizes to $K$-component superpositions via a $(K{+}1)$-dimensional invariant subspace with full $\mathrm{SU}(K{+}1)$ controllability, requiring only 3-5 iterations of operations for superpositions spanning photon numbers 70--100. RSE provides a scalable and analytically transparent framework for large-scale bosonic state engineering and gate synthesis across single- and multimode platforms.

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