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Rishab Dutta1, Fei Gao2, Armin Khamoshi2

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Summary
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We present an efficient classical algorithm for the binary tree state (BTS) ansatz, enabling accurate approximations for complex quantum chemical calculations. This method simplifies permanents and ensures size-consistency in computations.

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Area of Science:

  • Quantum chemistry
  • Computational physics
  • Theoretical computer science

Background:

  • The antisymmetric product of interacting geminals (APIG) is computationally intractable for calculating permanents.
  • The binary tree state (BTS) ansatz offers a promising, size-consistent approximation method.
  • Efficient implementation of novel quantum computational methods is crucial.

Purpose of the Study:

  • To develop an efficient classical algorithm for the binary tree state (BTS) ansatz.
  • To demonstrate the computation of BTS overlap and reduced density matrices.
  • To explore correlated BTS approaches for enhanced accuracy.

Main Methods:

  • Algorithm development for BTS implementation on classical computers.
  • Efficient computation of BTS overlap and reduced density matrices.
  • Investigation of Jastrow coupled cluster and linear combinations of BTS for correlated methods.

Main Results:

  • An efficient algorithm for BTS implementation was successfully developed.
  • Methods for computing BTS overlap and reduced density matrices were established.
  • Correlated BTS approaches showed promise in benchmark applications.

Conclusions:

  • The developed BTS algorithm provides an efficient classical approach for approximating permanents.
  • Correlated BTS methods, including Jastrow coupled cluster and linear combinations, demonstrate potential for accurate quantum mechanical simulations.
  • The approach is validated through benchmark applications on reduced BCS and 1D XXZ Heisenberg Hamiltonians.