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Amplitude Reordering Accelerates the Adaptive Variational Quantum Eigensolver Algorithms.

Zhihao Lan1, WanZhen Liang1

  • 1State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and Department of Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, Fujian Province, Peoples' Republic of China.

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Summary

We developed an amplitude reordering (AR) strategy to speed up adaptive quantum algorithms (AAs) for quantum chemistry simulations. This method accelerates calculations by over ten times without losing accuracy, making quantum simulations more efficient.

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Area of Science:

  • Quantum Computing
  • Computational Chemistry
  • Quantum Algorithms

Background:

  • Variational Quantum Eigensolver (VQE) is a promising algorithm for quantum chemistry simulations on noisy-intermediate-scale quantum devices.
  • The accuracy and cost of VQE depend on the ansatz, necessitating compact and accurate ansatz generation.
  • Adaptive algorithms (AAs) like ADAPT-VQE create efficient ansatzes but suffer from low computational efficiency due to extensive measurements.

Purpose of the Study:

  • To propose an amplitude reordering (AR) strategy to accelerate computationally expensive adaptive algorithms (AAs).
  • To introduce AR into ADAPT-VQE (AR-ADAPT-VQE) and AES-VQE (AR-AES-VQE) algorithms.
  • To evaluate the performance of AR-equipped adaptive algorithms (AR-AAs) in quantum chemistry simulations.

Main Methods:

  • Developed an amplitude reordering (AR) strategy to add operators in a batched, quasi-optimal order, reducing measurement overhead.
  • Integrated the AR strategy into the adaptive derivative-assembled pseudo-Trotter VQE (ADAPT-VQE) algorithm, creating AR-ADAPT-VQE.
  • Incorporated AR into the energy-sorting VQE (ES-VQE) algorithm, forming AR-AES-VQE, and tested on LiH, BeH2, and H6 molecular dissociation curves.

Main Results:

  • AR-equipped adaptive algorithms (AR-AAs) significantly reduced the number of iterations, accelerating calculations by over ten times.
  • The AR strategy achieved this speedup without a noticeable loss in computational accuracy.
  • Final ansatzes generated by AR-AAs maintained accuracy and avoided increased circuit depth, sometimes outperforming original AAs.

Conclusions:

  • The amplitude reordering (AR) strategy effectively accelerates adaptive quantum algorithms for VQE simulations.
  • AR-AAs provide a significant speedup in quantum chemistry calculations, making them more practical for noisy quantum devices.
  • This approach enhances the efficiency of VQE simulations without compromising accuracy or increasing circuit complexity.