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This study introduces a modified Hybrid Harrow-Hassidim-Lloyd (HHL) algorithm for quantum linear algebra, making it more compatible with current quantum hardware. The enhanced algorithm successfully demonstrated its efficacy in solving portfolio optimization problems on a trapped-ion quantum computer.

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Area of Science:

  • Quantum Computing
  • Quantum Algorithms
  • Quantum Linear Algebra

Background:

  • Current quantum hardware limitations restrict the scale of quantum algorithmic demonstrations and application-oriented benchmarking.
  • The Harrow-Hassidim-Lloyd (HHL) algorithm, a key quantum linear algebra primitive, is largely inaccessible to noisy intermediate-scale quantum (NISQ) devices, necessitating hybrid classical-quantum approaches.

Purpose of the Study:

  • To bridge the gap between near-term friendly HHL implementations and executable quantum circuits on current noisy hardware.
  • To enhance the compatibility of the Hybrid HHL algorithm with existing quantum devices.
  • To enable larger-scale experimental demonstrations of HHL for practical applications.

Main Methods:

  • Proposed two modifications to the Hybrid HHL algorithm: a novel method for determining a scaling factor for the linear system matrix to optimize ancillary qubit usage in phase estimation, and a heuristic for circuit compression.
  • Implemented and executed the modified Hybrid HHL algorithm on Quantinuum System Model H-series trapped-ion quantum computers.

Main Results:

  • Successfully demonstrated the efficacy of the modified Hybrid HHL algorithm on real quantum hardware.
  • Addressed the challenge of limited ancillary qubits in HHL's phase estimation component.
  • Achieved the largest experimental demonstrations of HHL for an application (portfolio optimization) to date.

Conclusions:

  • The proposed modifications significantly improve the practicality of the HHL algorithm for current quantum hardware.
  • The enhanced Hybrid HHL algorithm is more compatible with NISQ devices, facilitating broader application-oriented benchmarking.
  • This work represents a significant step towards utilizing quantum linear algebra primitives for real-world problems on available quantum computers.