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Area of Science:

  • Quantum computing
  • Computational chemistry
  • Artificial intelligence

Background:

  • Noisy Intermediate-Scale Quantum (NISQ) devices present challenges for Variational Quantum Eigensolver (VQE) accuracy due to inherent noise.
  • Iterative error amplification in VQE exacerbates inaccuracies on NISQ hardware.
  • Deep Neural Networks (DNNs) have been explored to mitigate VQE errors, but primarily in noiseless simulations.

Purpose of the Study:

  • To evaluate the efficacy of two DNN-VQE approaches (DNN1 and DNNF) for predicting molecular ground state energies on noisy quantum devices.
  • To compare the accuracy and performance of DNN1, DNNF, and standard VQE across various quantum circuits, ansatzes, qubit counts, and circuit depths.
  • To identify the most suitable DNN-VQE method for accurate and efficient ground state energy calculations on current quantum hardware.

Main Methods:

  • Trained DNN models for DNN1 and DNNF approaches using various quantum circuits.
  • Tested DNN1, DNNF, and VQE on noisy simulators and real quantum hardware.
  • Evaluated accuracy across different ansatzes, qubit counts, and circuit depths (e.g., depth 15 vs. depth 83).

Main Results:

  • Both DNN1 and DNNF consistently outperformed standard VQE in predicting more accurate ground state energies in noisy quantum environments.
  • DNN-VQE methods provided meaningful results only at lower circuit depths (depth = 15, gates = 21); accuracy significantly degraded at higher depths (depth = 83, gates = 112).
  • DNNF did not offer a speed advantage over VQE, while DNN1 demonstrated potential for quicker calculations.

Conclusions:

  • DNN-VQE methods offer improved accuracy over standard VQE for molecular ground state energy calculations on noisy quantum hardware.
  • The DNN1 approach is recommended as the preferred method for efficient and accurate results on current quantum hardware, especially for circuits with lower depth and fewer qubits.
  • Further research is needed to address accuracy limitations at higher circuit depths.