Exact Fock-State Preparation with $n^{1/4}$ Circuit Depth

• URL: http://arxiv.org/abs/2608.23389v1
• Date: Mon, 24 Aug 2026 15:35:08 GMT
• Title: Exact Fock-State Preparation with $n^{1/4}$ Circuit Depth
• Abstract summary: We map Fock-state preparation in an infinite-dimensional Hilbert space onto two-dimensional amplitude amplification.<n>Phase matching guarantees unit fidelity in the ideal model; remarkably, preparing $|106rangle$ requires only 39 iterations.<n>This framework provides a broadly applicable route to highly excited bosonic states on platforms supporting these elementary controls.
• Score: 0.18049490005680832
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Efficient, deterministic, and high-fidelity preparation of large Fock states is essential for scaling bosonic quantum technologies and exploring quantum phenomena at large excitation energies. We introduce a deterministic one-parameter (D1p) protocol that maps Fock-state preparation in an infinite-dimensional Hilbert space onto two-dimensional amplitude amplification. Starting from a coherent state with $|α|\simeq\sqrt{n}$, the initial target-state population scales as $n^{-1/2}$, yielding an iteration count and circuit depth of $\mathcal{O}(n^{1/4})$. Phase matching guarantees unit fidelity in the ideal model; remarkably, preparing $|{10^6}\rangle$ requires only 39 iterations. The protocol uses only displacements and number-selective phase operations, requires no numerical optimization, and further extends to state transfer, general superpositions, finite-dimensional systems, and multipartite entangled states. In the large-amplitude regime, its multi-target form prepares $L$-legged cat states with an iteration count determined only by $L$; cats with up to ten legs require only two iterations, independent of the coherent-state amplitude. This framework provides a broadly applicable route to highly excited bosonic states on platforms supporting these elementary controls.

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