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Gradient-Descent Quantum Process Tomography by Learning Kraus Operators.

Shahnawaz Ahmed1, Fernando Quijandría1,2, Anton Frisk Kockum1

  • 1Department of Microtechnology and Nanoscience, Chalmers University of Technology, 412 96 Gothenburg, Sweden.

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|April 28, 2023
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This summary is machine-generated.

We developed gradient-descent quantum process tomography (GD-QPT) to efficiently characterize quantum systems. This method reconstructs quantum processes using fewer measurements and scales to larger systems, reducing computational costs.

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Area of Science:

  • Quantum Information Science
  • Quantum Computing
  • Quantum Control

Background:

  • Quantum process tomography (QPT) is essential for characterizing quantum systems.
  • Existing QPT methods like compressed-sensing (CS) and projected least-squares (PLS) have limitations in measurement requirements or scalability.
  • Efficient and scalable QPT is crucial for advancing intermediate-scale quantum technologies.

Purpose of the Study:

  • To introduce a novel gradient-descent quantum process tomography (GD-QPT) method.
  • To develop a QPT technique that combines the strengths of CS and PLS methods.
  • To enable efficient and scalable quantum process characterization for discrete- and continuous-variable systems.

Main Methods:

  • Utilized Kraus operators to represent quantum processes, ensuring complete positivity.
  • Employed a constrained gradient-descent (GD) optimization on the Stiefel manifold for trace-preserving reconstructions.
  • Developed an ansatz using a minimal set of Kraus operators for low-rank quantum processes.

Main Results:

  • GD-QPT demonstrated performance comparable to CS and PLS in two-qubit benchmarks.
  • Reconstructed quantum processes from a small number of random measurements, similar to CS.
  • Successfully scaled to larger systems (up to five qubits), outperforming CS and matching PLS scalability.

Conclusions:

  • GD-QPT offers a practical and data-driven approach for quantum process characterization.
  • This method significantly reduces the cost and computational effort for QPT.
  • GD-QPT is a promising tool for characterizing intermediate-scale quantum systems.