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Noise in quantum computers creates barren plateaus, hindering Variational Quantum Algorithms (VQAs) training. This study proves noise-induced barren plateaus (NIBPs) limit VQA performance on NISQ devices.

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Area of Science:

  • Quantum Computing
  • Quantum Information Science
  • Computational Physics

Background:

  • Variational Quantum Algorithms (VQAs) are promising for achieving quantum advantage on Noisy Intermediate-Scale Quantum (NISQ) devices.
  • The impact of noise on the performance and trainability of VQAs is a critical research question.
  • Barren plateaus, characterized by vanishing gradients, pose a significant challenge to VQA training.

Purpose of the Study:

  • To rigorously investigate the effect of noise on VQA training landscapes.
  • To prove the existence of noise-induced barren plateaus (NIBPs) in noisy quantum computations.
  • To differentiate NIBPs from previously identified noise-free barren plateaus.

Main Methods:

  • Theoretical analysis of VQA training dynamics under local Pauli noise.
  • Mathematical proof of exponentially vanishing gradients for linearly growing ansatz depth.
  • Formulation of results for a generic ansatz, applicable to specific VQAs like QAOA and UCCA.
  • Numerical simulations using realistic hardware noise models.

Main Results:

  • A rigorous proof demonstrates that local Pauli noise induces barren plateaus in VQAs.
  • The gradient vanishes exponentially with the number of qubits when ansatz depth scales linearly with qubits.
  • Noise-induced barren plateaus are shown to be distinct from barren plateaus caused by random initialization.
  • Numerical evidence confirms the NIBP phenomenon for the Quantum Alternating Operator Ansatz under realistic noise.

Conclusions:

  • Quantum noise fundamentally limits VQA performance by creating barren plateaus.
  • NIBPs present a significant obstacle for training VQAs on current NISQ hardware.
  • Understanding and mitigating NIBPs is crucial for realizing the potential of VQAs and achieving quantum advantage.