Toffoli gates solve the tetrahedron equations
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909211038842880 |
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| author | Sinha, Akash Padmanabhan, Pramod Korepin, Vladimir |
| author_facet | Sinha, Akash Padmanabhan, Pramod Korepin, Vladimir |
| contents | The circuit model of quantum computation can be interpreted as a scattering process. In particular, factorised scattering operators result in integrable quantum circuits that provide universal quantum computation and are potentially less noisy. These are realized through Yang-Baxter or 2-simplex operators. A natural question is to extend this construction to higher qubit gates, like the Toffoli gates, which also lead to universal quantum computation but with shallower circuits. We show that unitary families of such operators are constructed by the 3-dimensional generalizations of the Yang-Baxter operators known as tetrahedron or 3-simplex operators. The latter satisfy a spectral parameter-dependent tetrahedron equation. This construction goes through for $n$-Toffoli gates realized using $n$-simplex operators. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_16477 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Toffoli gates solve the tetrahedron equations Sinha, Akash Padmanabhan, Pramod Korepin, Vladimir Quantum Physics Statistical Mechanics High Energy Physics - Theory Mathematical Physics The circuit model of quantum computation can be interpreted as a scattering process. In particular, factorised scattering operators result in integrable quantum circuits that provide universal quantum computation and are potentially less noisy. These are realized through Yang-Baxter or 2-simplex operators. A natural question is to extend this construction to higher qubit gates, like the Toffoli gates, which also lead to universal quantum computation but with shallower circuits. We show that unitary families of such operators are constructed by the 3-dimensional generalizations of the Yang-Baxter operators known as tetrahedron or 3-simplex operators. The latter satisfy a spectral parameter-dependent tetrahedron equation. This construction goes through for $n$-Toffoli gates realized using $n$-simplex operators. |
| title | Toffoli gates solve the tetrahedron equations |
| topic | Quantum Physics Statistical Mechanics High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2405.16477 |