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In the Shadow of the Hadamard Test: Using the Garbage State for Good and Further Modifications.

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This study enhances the Hadamard test by integrating classical shadows, improving quantum state analysis for intermediate quantum devices. This novel approach extracts more information from quantum systems, advancing quantum algorithm development.

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Area of Science:

  • Quantum Information Science
  • Quantum Computing Algorithms

Background:

  • The Hadamard test is crucial for quantum algorithms but typically ignores system register information.
  • Classical shadows offer efficient quantum state representation, developed independently of the Hadamard test.

Purpose of the Study:

  • To improve the Hadamard test by integrating classical shadows for enhanced quantum state analysis.
  • To leverage classical shadows on the work register to extract additional information during the Hadamard test.

Main Methods:

  • Combining the Hadamard test with classical shadows on the n-qubit work register.
  • Utilizing measurements of an auxiliary qubit and classical shadows for comprehensive state characterization.

Main Results:

  • Substantial improvements to the Hadamard test by exploiting classical shadows.
  • Access to additional quantum state features like fidelity, energy, and purity using classical shadows.
  • Demonstrated application in statistical phase estimation and potential for broader algorithm use.

Conclusions:

  • The combined Hadamard test and classical shadows framework offers significant advantages for intermediate quantum applications.
  • This integrated approach enhances information extraction from quantum systems, settling exploitation for current quantum devices.
  • The framework is general and applicable to various quantum algorithms, augmenting capabilities with anticontrolled unitaries.