Classical shadows based on locally-entangled measurements
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866913284078174208 |
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| author | Ippoliti, Matteo |
| author_facet | Ippoliti, Matteo |
| contents | We study classical shadows protocols based on randomized measurements in $n$-qubit entangled bases, generalizing the random Pauli measurement protocol ($n = 1$). We show that entangled measurements ($n\geq 2$) enable nontrivial and potentially advantageous trade-offs in the sample complexity of learning Pauli expectation values. This is sharply illustrated by shadows based on two-qubit Bell measurements: the scaling of sample complexity with Pauli weight $k$ improves quadratically (from $\sim 3^k$ down to $\sim 3^{k/2}$) for many operators, while others become impossible to learn. Tuning the amount of entanglement in the measurement bases defines a family of protocols that interpolate between Pauli and Bell shadows, retaining some of the benefits of both. For large $n$, we show that randomized measurements in $n$-qubit GHZ bases further improve the best scaling to $\sim (3/2)^k$, albeit on an increasingly restricted set of operators. Despite their simplicity and lower hardware requirements, these protocols can match or outperform recently-introduced "shallow shadows" in some practically-relevant Pauli estimation tasks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_10723 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Classical shadows based on locally-entangled measurements Ippoliti, Matteo Quantum Physics Statistical Mechanics We study classical shadows protocols based on randomized measurements in $n$-qubit entangled bases, generalizing the random Pauli measurement protocol ($n = 1$). We show that entangled measurements ($n\geq 2$) enable nontrivial and potentially advantageous trade-offs in the sample complexity of learning Pauli expectation values. This is sharply illustrated by shadows based on two-qubit Bell measurements: the scaling of sample complexity with Pauli weight $k$ improves quadratically (from $\sim 3^k$ down to $\sim 3^{k/2}$) for many operators, while others become impossible to learn. Tuning the amount of entanglement in the measurement bases defines a family of protocols that interpolate between Pauli and Bell shadows, retaining some of the benefits of both. For large $n$, we show that randomized measurements in $n$-qubit GHZ bases further improve the best scaling to $\sim (3/2)^k$, albeit on an increasingly restricted set of operators. Despite their simplicity and lower hardware requirements, these protocols can match or outperform recently-introduced "shallow shadows" in some practically-relevant Pauli estimation tasks. |
| title | Classical shadows based on locally-entangled measurements |
| topic | Quantum Physics Statistical Mechanics |
| url | https://arxiv.org/abs/2305.10723 |