Auxiliary-free replica shadow estimation

• URL: http://arxiv.org/abs/2407.20865v1
• Date: Tue, 30 Jul 2024 14:40:29 GMT
• Title: Auxiliary-free replica shadow estimation
• Authors: Qing Liu, Zihao Li, Xiao Yuan, Huangjun Zhu, You Zhou,
• Abstract summary: We propose an efficient auxiliary-free replica shadow (AFRS) framework, which leverages the power of the joint entangling operation on a few input replicas. We rigorously prove that AFRS can offer exponential improvements in estimation accuracy compared with the conventional shadow method. We introduce an advanced local-AFRS variant tailored to estimating local observables with even constant-depth local quantum circuits.
• Score: 9.129051558668854
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Efficiently measuring nonlinear properties, like the entanglement spectrum, is a significant yet challenging task from quantum information processing to many-body physics. Current methodologies often suffer from an exponential scaling of the sampling cost or require auxiliary qubits and deep quantum circuits. To address these limitations, we propose an efficient auxiliary-free replica shadow (AFRS) framework, which leverages the power of the joint entangling operation on a few input replicas while integrating the mindset of shadow estimation. We rigorously prove that AFRS can offer exponential improvements in estimation accuracy compared with the conventional shadow method, and facilitate the simultaneous estimation of various nonlinear properties, unlike the destructive swap test. Additionally, we introduce an advanced local-AFRS variant tailored to estimating local observables with even constant-depth local quantum circuits, which significantly simplifies the experimental realization compared with the general swap test. Our work paves the way for the application of AFRS on near-term quantum hardware, opening new avenues for efficient and practical quantum measurements.

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