Classical shadows based on locally-entangled measurements

• URL: http://arxiv.org/abs/2305.10723v3
• Date: Sun, 17 Mar 2024 23:03:11 GMT
• Title: Classical shadows based on locally-entangled measurements
• Authors: Matteo Ippoliti,
• Abstract summary: We study classical shadows protocols based on randomized measurements in $n$-qubit entangled bases. We show that entangled measurements enable nontrivial and potentially advantageous trade-offs in the sample complexity of learning Pauli expectation values.
• Score: 0.03922370499388702
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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