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Unified framework for matchgate classical shadows.

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This study unifies classical shadows protocols for estimating quantum fermionic properties by proving the equivalence of different Fermionic Gaussian Unitaries (FGUs) ensembles. It introduces an optimal sampling scheme for matchgates circuits, enhancing computational efficiency.

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Area of Science:

  • Quantum Information Science
  • Computational Physics
  • Electronic Systems Modeling

Background:

  • Estimating quantum fermionic properties is computationally intensive but vital for electronic systems.
  • Classical shadows protocols using Fermionic Gaussian Unitaries (FGUs) offer a promising approach.
  • Existing protocols utilize diverse sub-ensembles of the orthogonal group O(2n).

Purpose of the Study:

  • To unify and prove the equivalence of existing classical shadows protocols for FGUs.
  • To derive an optimal sampling scheme for efficient quantum fermionic property estimation.
  • To generalize known results on FGU moments and address open questions in the field.

Main Methods:

  • Demonstration of equal first three moments for FGU ensembles associated with SO(2n) and its Clifford group intersection.
  • Mathematical proof establishing the equivalence between different FGU-based classical shadows protocols.
  • Derivation of an optimal sampling scheme based on a small sub-ensemble of matchgates circuits.

Main Results:

  • The first three moments of the FGU ensemble associated with SO(2n) and its Clifford intersection are equal.
  • All previously analyzed FGU ensembles yield equivalent classical shadows protocols.
  • An optimal sampling scheme using a minimal set of matchgates circuits is proposed.

Conclusions:

  • A unified framework for classical shadows protocols in fermionic systems is presented.
  • The proposed optimal sampling scheme enhances computational efficiency for quantum property estimation.
  • This work provides theoretical guarantees for the performance of the new sampling strategy.