Deterministic Generation of Arbitrary Fock States via Resonant Subspace Engineering

TL;DR

This paper introduces resonant subspace engineering (RSE), a method for deterministic high-excitation Fock state preparation that significantly improves efficiency and scalability in bosonic quantum systems.

Contribution

The authors develop RSE, an analytical protocol that confines bosonic dynamics to a low-dimensional subspace, enabling efficient state transfer and superposition generation with minimal operations.

Findings

Achieves $O(n^{1/4})$ scaling in time and gate depth for Fock states

Generalizes to superpositions with high photon numbers using a small number of operations

Provides a scalable, transparent framework for large-scale bosonic state engineering

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.