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We developed a new quantum state learning scheme using randomized measurements and random quantum circuits. This method offers efficient and accurate estimation of quantum properties with fewer measurements.

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Area of Science:

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

Background:

  • Learning properties of quantum states is crucial for quantum information processing.
  • Existing methods like classical shadows have limitations in sample complexity and experimental feasibility.
  • Efficiently characterizing quantum states with minimal measurements remains a key challenge.

Purpose of the Study:

  • To present a novel, practical, and powerful scheme for learning quantum state properties.
  • To develop a randomized measurement scheme modulated by the depth of a random quantum circuit.
  • To interpolate between existing classical shadows schemes for improved performance and feasibility.

Main Methods:

  • Utilizing a depth-modulated randomized measurement scheme in one spatial dimension.
  • Analyzing the scheme in the regime where circuit depth scales logarithmically with system size.
  • Employing tools from shadow estimation, random circuits, and tensor networks.
  • Developing methods for estimating expectation values and bounding the shadow norm.

Main Results:

  • The proposed scheme retains desirable sample complexity properties of extremal classical shadows schemes.
  • The method is shown to be experimentally feasible.
  • Rigorous guarantees on the accuracy of output estimates are provided by computing upper bounds on the depth-modulated shadow norm.

Conclusions:

  • The depth-modulated randomized measurement scheme offers an efficient and accurate approach to quantum state learning.
  • This work bridges the gap between theoretical efficiency and experimental practicality in quantum state characterization.
  • The findings contribute to the advancement of quantum state tomography and characterization techniques.