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Quantum Inverse Algorithm via Adaptive Variational Quantum Linear Solver: Applications to General Eigenstates.

Takahiro Yoshikura1, Seiichiro L Ten-No1, Takashi Tsuchimochi1,2

  • 1Graduate School of System Informatics, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe, Hyogo 657-8501, Japan.

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Summary
This summary is machine-generated.

We introduce the Quantum Inverse Algorithm (QInverse) for directly finding quantum eigenstates. This singularity-free method accurately targets excited states, outperforming variational approaches for quantum energy level determination.

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Area of Science:

  • Quantum Computing
  • Quantum Algorithms
  • Computational Chemistry
  • Quantum Information Science

Background:

  • Determining general quantum eigenstates, especially excited states, is crucial for understanding molecular and material properties.
  • Existing variational methods often struggle with convergence and accuracy for excited states, frequently getting trapped in local minima.
  • The folded-spectrum method is a common approach but has limitations in reliably predicting target excited states.

Purpose of the Study:

  • To develop a novel quantum algorithm, Quantum Inverse (QInverse), for the direct determination of general quantum eigenstates.
  • To address the challenges of handling strongly entangled inverse power states and resultant excited states.
  • To provide a singularity-free and accurate method for targeting excited states near a specific energy shift.

Main Methods:

  • Proposed the Quantum Inverse Algorithm (QInverse) utilizing repeated application of the inverse power of a shifted Hamiltonian.
  • Solved the underlying linear equation variationally and adaptively using shallow quantum circuits to obtain faithful inverse power states.
  • Introduced a subspace expansion approach to accelerate convergence for eigenvalue determination.

Main Results:

  • QInverse successfully obtains target excited states with energies closest to the shift ω, overcoming limitations of variational methods.
  • The subspace expansion approach demonstrates effectiveness in determining the two nearest eigenvalues when they are equally close to ω.
  • QInverse shows systematically improvable success rates and accuracy compared to the folded-spectrum method, avoiding local minima issues.

Conclusions:

  • QInverse offers a robust and accurate method for directly calculating general quantum eigenstates, including challenging excited states.
  • The proposed variational and adaptive solutions for inverse power states enable faithful state preparation with shallow quantum circuits.
  • QInverse and the subspace expansion approach represent significant advancements in quantum computational chemistry and quantum simulation.