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Invested and Potential Magic Resources in Measurement-Based Quantum Computation.

Gong-Chu Li1,2,3,4, Lei Chen1,2,3,4, Si-Qi Zhang1,2,3,4

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This study introduces invested and potential magic resources for measurement-based quantum computation (MQC). High-dimensional graphs show exponential MQC advantage, demonstrated experimentally.

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Area of Science:

  • Quantum Information Science
  • Quantum Computation

Background:

  • Magic states and gates are essential for universal quantum computation.
  • Optimal implementation of magic resources for quantum advantage in measurement-based quantum computation (MQC) remains underexplored.

Purpose of the Study:

  • Introduce and define "invested" and "potential" magic resources within the MQC framework.
  • Analyze the Quantum Fourier Transform (QFT) using these new resource concepts.
  • Investigate the role of non-Pauli measurements in magic injection and MQC universality.

Main Methods:

  • Developed a resource theory of magic tailored for MQC, defining invested (cost) and potential (achievable) magic.
  • Analyzed the Quantum Fourier Transform (QFT) using invested and potential magic.
  • Theoretically proved exponential advantage for MQC using high-dimensional graphs.
  • Experimentally validated findings using a four-photon setup.

Main Results:

  • Quantified magic cost and maximal achievable magic in MQC graph structures.
  • Demonstrated that non-Pauli measurements are crucial for injecting magic.
  • Proved theoretically that high-dimensional graphs offer exponential MQC advantage.
  • Experimental results in a four-photon system surpassed conventional methods in efficiency and resource use.

Conclusions:

  • Invested and potential magic resources provide a new framework for MQC analysis.
  • High-dimensional graphs and non-Pauli measurements are key to unlocking MQC's potential.
  • Experimental demonstration confirms theoretical predictions, advancing practical MQC.