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Faster Quantum Algorithm for Multiple Observables Estimation.

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This study introduces adaptive quantum gradient estimation (QGE) algorithms for faster estimation of quantum many-body system properties. These methods offer significant speedups for fermionic systems, improving practical quantum computing applications.

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Area of Science:

  • Quantum Computing
  • Quantum Many-Body Systems
  • Quantum Information Science

Background:

  • Estimating collective properties of quantum many-body systems is crucial for quantum computing.
  • The quantum gradient estimation (QGE) algorithm offers theoretical advantages but practical benefits are unclear.
  • Fermionic systems present unique challenges in quantum property estimation.

Purpose of the Study:

  • To develop a generalized adaptive QGE framework for efficient estimation of fermionic system properties.
  • To propose novel QGE variants achieving minimal cost for practical quantum algorithms.
  • To demonstrate quadratic speedups in fermionic partial tomography.

Main Methods:

  • Generalized adaptive quantum gradient estimation (QGE) framework.
  • Two novel QGE variants: one utilizing target state symmetry, another using a single-shot parallel scheme.
  • Numerical simulations for estimating 2-body fermionic reduced density matrices.

Main Results:

  • Proposed adaptive QGE variants offer the smallest cost among existing quantum algorithms for fermionic systems.
  • Achieved a quadratic speedup compared to prior QGE algorithms in fermionic partial tomography.
  • Demonstrated significant improvements in query numbers for estimating reduced density matrices (4.4x for FeMo cofactor, 7.8x for 200-site Fermi-Hubbard model).

Conclusions:

  • The proposed adaptive QGE methods provide practical advantages for estimating collective properties of fermionic systems.
  • These algorithms enhance the efficiency and applicability of quantum computing for complex quantum systems.
  • Significant speedups achieved pave the way for more complex quantum simulations and calculations.