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This study introduces a new method to improve Variational Quantum Eigensolver (VQE) performance by optimizing quantum computations in a reduced subspace, leading to more accurate results with fewer resources. The approach enhances VQE accuracy and speeds up convergence for quantum algorithms.

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Area of Science:

  • Quantum Computing
  • Computational Chemistry
  • Optimization Algorithms

Background:

  • Variational Quantum Eigensolver (VQE) is challenged by hardware noise, barren plateaus, and local traps.
  • These issues hinder accurate and efficient quantum computations, particularly in chemistry-inspired applications.

Purpose of the Study:

  • To develop a general formalism to optimize VQE hardware resource utilization and accuracy.
  • To mitigate the detrimental effects of noise and local minima in VQE optimization landscapes.

Main Methods:

  • Projecting VQE optimizations onto a reduced-dimensional subspace.
  • Partitioning the ansatz into principal and auxiliary subspaces based on temporal hierarchy.
  • Utilizing adiabatic approximation to restrict optimization to the principal subspace.
  • Reconstructing auxiliary subspace parameters without variational optimization.
  • Applying auxiliary subspace corrections (ASC) to the cost-function.

Main Results:

  • Achieved one to two orders of magnitude better estimation of minima when integrated with chemistry-inspired ansatze.
  • Demonstrated a 'plummeting effect' in the energy landscape towards more optimal minima.
  • Introduced a novel initialization strategy for accelerated convergence of gradient-informed dynamic quantum algorithms.
  • Provided heuristic evidence of alleviating local trap effects.

Conclusions:

  • The proposed method enhances VQE accuracy and resource utilization without additional quantum hardware.
  • The approach effectively mitigates noise and local minima issues, facilitating convergence to better solutions.
  • Novel initialization strategy accelerates convergence and improves robustness of quantum algorithms.