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Thrifty Shadow Estimation: Reusing Quantum Circuits and Bounding Tails.

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We introduce thrifty shadow estimation, a practical method for quantum state analysis using circuit reuse. This approach enhances statistical efficiency for near-term quantum computing, especially with Haar random unitaries.

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Area of Science:

  • Quantum Information Science
  • Quantum Computing Algorithms

Background:

  • Classical shadows enable estimating numerous quantum state properties.
  • Current methods require fresh random quantum circuits for each measurement, limiting efficiency.

Purpose of the Study:

  • To improve the statistical efficiency of shadow estimation for near-term quantum computers.
  • To introduce a practical variant of shadow estimation through circuit reuse.

Main Methods:

  • Proposed 'thrifty shadow estimation' by reusing quantum circuits.
  • Analyzed the effectiveness of circuit reuse for different random unitary ensembles (Haar vs. Clifford).
  • Introduced an efficiently simulable family of quantum circuits as an alternative to the Clifford group.

Main Results:

  • Circuit reuse is most effective with Haar random unitaries and ineffective with Clifford group unitaries.
  • Demonstrated an intermediate family of quantum circuits that balances efficiency and simulability.
  • Investigated tail bounds and conditions for replacing median-of-means with standard mean estimation.

Conclusions:

  • Thrifty shadow estimation offers a more practical and statistically efficient approach for quantum state characterization.
  • The choice of random circuit family significantly impacts the efficacy of circuit reuse.
  • The proposed intermediate circuits provide a superior alternative to Clifford circuits for shadow estimation.