Invested and Potential Magic Resources in Measurement-Based Quantum Computation
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arXiv
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| Main Authors: | , , , , , , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912757025079296 |
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| author | Li, Gongchu Chen, Lei Zhang, Si-Qi Hong, Xu-Song Xu, Huaqing Liu, Yuancheng Zhou, You Chen, Geng Li, Chuan-Feng Hamma, Alioscia Guo, Guang-Can |
| author_facet | Li, Gongchu Chen, Lei Zhang, Si-Qi Hong, Xu-Song Xu, Huaqing Liu, Yuancheng Zhou, You Chen, Geng Li, Chuan-Feng Hamma, Alioscia Guo, Guang-Can |
| contents | Magic states and magic gates are crucial for achieving universal quantum computation, but important questions about how magic resources should be implemented to attain maximal quantum advantage have remained unexplored, especially in the context of measurement-based quantum computation (MQC). This work bridges the gap between MQC and the resource theory of magic by introducing the key concepts of "invested" and "potential" magic resources. The former quantifies the magic cost associated with MQC, serving as both a resource witness and a feasible upper bound for the practical realization, and is gate-order independent; The latter represents the maximal achievable magic resource in a given graph structure defining MQC. We utilize both concepts to analyze the quantum Fourier transform (QFT) and provide a fresh perspective on the universality of MQC, highlighting the crucial role of non-Pauli measurements in injecting magic. In particular, we theoretically prove that high-dimensional graphs can generate an exponential advantage of MQC compared to classical computing. We demonstrate experimentally our theoretical findings in a high-fidelity four-photon setup, surpassing conventional magic state injection (MSI) methods in both qubit efficiency and resource utilization. Our findings pave the way for future research exploring magic resource optimization and novel distillation schemes within the MQC framework, advancing fault-tolerant universal quantum computation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_01980 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Invested and Potential Magic Resources in Measurement-Based Quantum Computation Li, Gongchu Chen, Lei Zhang, Si-Qi Hong, Xu-Song Xu, Huaqing Liu, Yuancheng Zhou, You Chen, Geng Li, Chuan-Feng Hamma, Alioscia Guo, Guang-Can Quantum Physics Magic states and magic gates are crucial for achieving universal quantum computation, but important questions about how magic resources should be implemented to attain maximal quantum advantage have remained unexplored, especially in the context of measurement-based quantum computation (MQC). This work bridges the gap between MQC and the resource theory of magic by introducing the key concepts of "invested" and "potential" magic resources. The former quantifies the magic cost associated with MQC, serving as both a resource witness and a feasible upper bound for the practical realization, and is gate-order independent; The latter represents the maximal achievable magic resource in a given graph structure defining MQC. We utilize both concepts to analyze the quantum Fourier transform (QFT) and provide a fresh perspective on the universality of MQC, highlighting the crucial role of non-Pauli measurements in injecting magic. In particular, we theoretically prove that high-dimensional graphs can generate an exponential advantage of MQC compared to classical computing. We demonstrate experimentally our theoretical findings in a high-fidelity four-photon setup, surpassing conventional magic state injection (MSI) methods in both qubit efficiency and resource utilization. Our findings pave the way for future research exploring magic resource optimization and novel distillation schemes within the MQC framework, advancing fault-tolerant universal quantum computation. |
| title | Invested and Potential Magic Resources in Measurement-Based Quantum Computation |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2408.01980 |