Classical shadows based on locally-entangled measurements
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 lear...
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2024-03-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2024-03-21-1293/pdf/ |
| _version_ | 1797253806632730624 |
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| author | Matteo Ippoliti |
| author_facet | Matteo Ippoliti |
| author_sort | Matteo Ippoliti |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-24T21:39:55Z |
| format | Article |
| id | doaj.art-e07f19738e3549e2a46e8b15df59314d |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-04-24T21:39:55Z |
| publishDate | 2024-03-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-e07f19738e3549e2a46e8b15df59314d2024-03-21T10:22:59ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2024-03-018129310.22331/q-2024-03-21-129310.22331/q-2024-03-21-1293Classical shadows based on locally-entangled measurementsMatteo IppolitiWe 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.https://quantum-journal.org/papers/q-2024-03-21-1293/pdf/ |
| spellingShingle | Matteo Ippoliti Classical shadows based on locally-entangled measurements Quantum |
| title | Classical shadows based on locally-entangled measurements |
| title_full | Classical shadows based on locally-entangled measurements |
| title_fullStr | Classical shadows based on locally-entangled measurements |
| title_full_unstemmed | Classical shadows based on locally-entangled measurements |
| title_short | Classical shadows based on locally-entangled measurements |
| title_sort | classical shadows based on locally entangled measurements |
| url | https://quantum-journal.org/papers/q-2024-03-21-1293/pdf/ |
| work_keys_str_mv | AT matteoippoliti classicalshadowsbasedonlocallyentangledmeasurements |