Robust and efficient verification of graph states in blind measurement-based quantum computation

Abstract

Blind quantum computation (BQC) is a secure quantum computation method that protects the privacy of clients. Measurement-based quantum computation (MBQC) is a promising approach for realizing BQC. To obtain reliable results in blind MBQC, it is crucial to verify whether the resource graph states are accurately prepared in the adversarial scenario. However, previous verification protocols for this task are too resource consuming or noise susceptible to be applied in practice. Here, we propose a robust and efficient protocol for verifying arbitrary graph states with any prime local dimension in the adversarial scenario, which leads to a robust and efficient protocol for verifying the resource state in blind MBQC. Our protocol requires only local Pauli measurements and is thus easy to realize with current technologies. Nevertheless, it can achieve the optimal scaling behaviors with respect to the system size and the target precision as quantified by the infidelity and significance level, which has never been achieved before. Notably, our protocol can exponentially enhance the scaling behavior with the significance level.

14+32 pages, 8+5 figures, and 1 table; published in npj Quantum Information

References in corpus (8)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Quantum computational advantage using photons
• Quantum secret sharing with qudit graph states
• Theoretical and Experimental Perspectives of Quantum Verification
• Group theoretical study of LOCC-detection of maximally entangled state using hypothesis testing
• Efficient verification of Affleck-Kennedy-Lieb-Tasaki states
• Experimental optimal verification of three-dimensional entanglement on a silicon chip
• Efficient verification of arbitrary entangled states with homogeneous local measurements

Cited by in corpus (8)

• Efficient Verification of Ground States of Frustration-Free Hamiltonians
• Symmetric quantum states: a review of recent progress
• Learning Properties of Quantum States Without the I.I.D. Assumption
• Measuring quantum relative entropy with finite-size effect
• Experimental Verification of Entangled States in the Adversarial Scenario
• Universal and Efficient Quantum State Verification via Schmidt Decomposition and Mutually Unbiased Bases
• Blind quantum computing with different qudit resource state architectures
• Phase Transitions and Noise Robustness of Quantum Graph States