Dual unitaries as maximizers of the distance to local product gates
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866913238097068032 |
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| author | Brahmachari, Shrigyan Rajmohan, Rohan Narayan Rather, Suhail Ahmad Lakshminarayan, Arul |
| author_facet | Brahmachari, Shrigyan Rajmohan, Rohan Narayan Rather, Suhail Ahmad Lakshminarayan, Arul |
| contents | TThe problem of finding the resource free, closest local unitary, to any bipartite unitary gate $U$ is addressed. Previously discussed as a measure of nonlocality, the distance $K_D(U)$ to the nearest product unitary has implications for circuit complexity and related quantities. Dual unitaries, currently of great interest in models of complex quantum many-body systems, are shown to have a preferred role as these are maximally and equally away from the set of local unitaries. This is proved here for the case of qubits and we present strong numerical and analytical evidence that it is true in general. An analytical evaluation of $K_D(U)$ is presented for general two-qubit gates. For arbitrary local dimensions, that $K_D(U)$ is largest for dual unitaries, is substantiated by its analytical evaluations for an important family of dual-unitary and for certain non-dual gates. A closely allied result concerns, for any bipartite unitary, the existence of a pair of maximally entangled states that it connects. We give efficient numerical algorithms to find such states and to find $K_D(U)$ in general. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2210_13307 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Dual unitaries as maximizers of the distance to local product gates Brahmachari, Shrigyan Rajmohan, Rohan Narayan Rather, Suhail Ahmad Lakshminarayan, Arul Quantum Physics Statistical Mechanics Mathematical Physics TThe problem of finding the resource free, closest local unitary, to any bipartite unitary gate $U$ is addressed. Previously discussed as a measure of nonlocality, the distance $K_D(U)$ to the nearest product unitary has implications for circuit complexity and related quantities. Dual unitaries, currently of great interest in models of complex quantum many-body systems, are shown to have a preferred role as these are maximally and equally away from the set of local unitaries. This is proved here for the case of qubits and we present strong numerical and analytical evidence that it is true in general. An analytical evaluation of $K_D(U)$ is presented for general two-qubit gates. For arbitrary local dimensions, that $K_D(U)$ is largest for dual unitaries, is substantiated by its analytical evaluations for an important family of dual-unitary and for certain non-dual gates. A closely allied result concerns, for any bipartite unitary, the existence of a pair of maximally entangled states that it connects. We give efficient numerical algorithms to find such states and to find $K_D(U)$ in general. |
| title | Dual unitaries as maximizers of the distance to local product gates |
| topic | Quantum Physics Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2210.13307 |