A Lightweight Protocol for Matchgate Fidelity Estimation
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915577817202688 |
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| author | Burkat, Jędrzej Strelchuk, Sergii |
| author_facet | Burkat, Jędrzej Strelchuk, Sergii |
| contents | We present a low-depth randomised algorithm for the estimation of entanglement fidelity between an $n$-qubit matchgate circuit $\mathcal{U}$ and its noisy implementation $\mathcal{E}$. Our procedure makes use of a modified Pauli-Liouville representation of quantum channels, with Clifford algebra elements as a basis. We show that this choice of representation leads to a block-diagonal compound matrix structure of matchgate superoperators which enables construction of efficient protocols for estimating the fidelity, achieving a $1/\sqrt{n}$ speedup over protocols of Flammia & Liu [PRL 106, 230501]. Finally, we offer simple extensions of our protocol which (without additional overhead) benchmark matchgate circuits intertwined by Clifford circuits, and circuits composed of exclusively nearest-neighbour $XY(θ)$ gates or Givens rotations - forming the first known method for direct benchmarking of matchgate subgroups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_07974 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Lightweight Protocol for Matchgate Fidelity Estimation Burkat, Jędrzej Strelchuk, Sergii Quantum Physics We present a low-depth randomised algorithm for the estimation of entanglement fidelity between an $n$-qubit matchgate circuit $\mathcal{U}$ and its noisy implementation $\mathcal{E}$. Our procedure makes use of a modified Pauli-Liouville representation of quantum channels, with Clifford algebra elements as a basis. We show that this choice of representation leads to a block-diagonal compound matrix structure of matchgate superoperators which enables construction of efficient protocols for estimating the fidelity, achieving a $1/\sqrt{n}$ speedup over protocols of Flammia & Liu [PRL 106, 230501]. Finally, we offer simple extensions of our protocol which (without additional overhead) benchmark matchgate circuits intertwined by Clifford circuits, and circuits composed of exclusively nearest-neighbour $XY(θ)$ gates or Givens rotations - forming the first known method for direct benchmarking of matchgate subgroups. |
| title | A Lightweight Protocol for Matchgate Fidelity Estimation |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2404.07974 |