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Variational approaches are among the most powerful techniques toapproximately solve quantum many-body problems. These encompass bothvariational states based on tensor or neural networks, and parameterizedquantum circuits in variational quantum eigensolvers. However,self-consistent evaluation of the quality of variational wavefunctionsis a notoriously hard task. Using a recently developed Hamiltonianreconstruction method, we propose a multi-faceted approach to evaluatingthe quality of neural-network based wavefunctions. Specifically, weconsider convolutional neural network (CNN) and restricted Boltzmannmachine (RBM) states trained on a square latticespin-1/2 J_1\!-\!J_2 Heisenberg model. We find that the reconstructed Hamiltonians aretypically less frustrated, and have easy-axis anisotropy near the highfrustration point. In addition, the reconstructed Hamiltonians suppressquantum fluctuations in the largeJ_2 limit. Our results highlight the critical importance of thewavefunction’s symmetry. Moreover, the multi-faceted insight from theHamiltonian reconstruction reveals that a variational wave function canfail to capture the true ground state through suppression of quantumfluctuations.
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Efficient symmetry-preserving state preparation circuits for the variational quantum eigensolver algorithm
Abstract The variational quantum eigensolver is one of the most promising approaches for performing chemistry simulations using noisy intermediate-scale quantum (NISQ) processors. The efficiency of this algorithm depends crucially on the ability to prepare multi-qubit trial states on the quantum processor that either include, or at least closely approximate, the actual energy eigenstates of the problem being simulated while avoiding states that have little overlap with them. Symmetries play a central role in determining the best trial states. Here, we present efficient state preparation circuits that respect particle number, total spin, spin projection, and time-reversal symmetries. These circuits contain the minimal number of variational parameters needed to fully span the appropriate symmetry subspace dictated by the chemistry problem while avoiding all irrelevant sectors of Hilbert space. We show how to construct these circuits for arbitrary numbers of orbitals, electrons, and spin quantum numbers, and we provide explicit decompositions and gate counts in terms of standard gate sets in each case. We test our circuits in quantum simulations of the$${H}_{2}$$ and$$LiH$$ molecules and find that they outperform standard state preparation methods in terms of both accuracy and circuit depth.
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- Award ID(s):
- 1839136
- PAR ID:
- 10154197
- Publisher / Repository:
- Nature Publishing Group
- Date Published:
- Journal Name:
- npj Quantum Information
- Volume:
- 6
- Issue:
- 1
- ISSN:
- 2056-6387
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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