Work

Qudit Shadow Estimation Based on the Clifford Group and the Power of a Single Magic Gate

Year: 2025

Type: article

Abstract: Shadow estimation is a sample-efficient protocol for learning the properties of a quantum system using randomized measurements, but the current understanding of qudit shadow estimation is quite limited compared with the qubit setting. Here, we clarify the sample complexity of qudit shadow estimation based on the Clifford group, where the local dimension d is an odd prime. Notably, we show that the overhead of qudit shadow estimation over the qubit counterpart is only O(d), which is independent of the qudit number n, although the set of stabilizer states may deviate exponentially from a 3-design with respect to the third moment operator. Furthermore, by adding one layer of magic gates, we propose a simple circuit that can significantly boost the efficiency. Actually, a single magic gate can already eliminate the O(d) overhead in qudit shadow estimation and bridge the gap from the qubit setting.

Source: Physical Review Letters

DOI: 10.1103/physrevlett.134.160801

Authors: Chengsi Mao, Changhao Yi, Huangjun Zhu

Institutions: Fudan University, State Key Laboratory of Surface Physics, Shanghai Research Center for Quantum Sciences

Language: English

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,750

Funders: National Natural Science Foundation of China, Science and Technology Commission of Shanghai Municipality, National Key Research and Development Program of China