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arXiv · 2602.19250

Eigenstate-assisted realization of general quantum controlled unitaries with a fixed cost

Carlos Navas-Merlo·Juan Carlos García-Escartín
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Abstract

Controlled unitary gates are a basic element in many quantum algorithms. Converting a general unitary $U$ with a known decomposition into its controlled version, controlled-$U$, can introduce a large overhead in terms of the depth of the circuit. We present a general method to take any unitary $U$ into controlled-$U$ using a fixed circuit with 4 CNOT gates and 2 Toffoli gates per qubit. For $n$-qubit unitaries and one control qubit, we require $2n+1$ qubits and a circuit that can generate an eigenstate of $U$, for which there are many cost-effective known algorithms. The method also works for any black block implementation of $U$, achieving a constant-depth realization independent of its decomposition. We illustrate its use in the Hadamard test and discuss applications to variational and quantum machine-learning algorithms.

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Carlos Navas-Merlo, Juan Carlos García-Escartín. 2026-02-22. Eigenstate-assisted realization of general quantum controlled unitaries with a fixed cost. https://arxiv.org/abs/2602.19250

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