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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.19250 |
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| _version_ | 1866917286892273664 |
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| author | Navas-Merlo, Carlos García-Escartín, Juan Carlos |
| author_facet | Navas-Merlo, Carlos García-Escartín, Juan Carlos |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_19250 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Eigenstate-assisted realization of general quantum controlled unitaries with a fixed cost Navas-Merlo, Carlos García-Escartín, Juan Carlos Quantum Physics 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. |
| title | Eigenstate-assisted realization of general quantum controlled unitaries with a fixed cost |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2602.19250 |