Certified variational quantum algorithms for eigenstate preparation
- URL: http://arxiv.org/abs/2006.13222v2
- Date: Mon, 9 Nov 2020 15:42:54 GMT
- Title: Certified variational quantum algorithms for eigenstate preparation
- Authors: Andrey Kardashin and Alexey Uvarov and Dmitry Yudin and Jacob Biamonte
- Abstract summary: We develop a means to certify the termination of variational algorithms.
We demonstrate our approach by applying it to three models: the transverse field Ising model, the model of one-dimensional spinless fermions with competing interactions, and the Schwinger model of quantum electrodynamics.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Solutions to many-body problem instances often involve an intractable number
of degrees of freedom and admit no known approximations in general form. In
practice, representing quantum-mechanical states of a given Hamiltonian using
available numerical methods, in particular those based on variational Monte
Carlo simulations, become exponentially more challenging with increasing system
size. Recently quantum algorithms implemented as variational models have been
proposed to accelerate such simulations. The variational ansatz states are
characterized by a polynomial number of parameters devised in a way to minimize
the expectation value of a given Hamiltonian, which is emulated by local
measurements. In this study, we develop a means to certify the termination of
variational algorithms. We demonstrate our approach by applying it to three
models: the transverse field Ising model, the model of one-dimensional spinless
fermions with competing interactions, and the Schwinger model of quantum
electrodynamics. By means of comparison, we observe that our approach shows
better performance near critical points in these models. We hence take a
further step to improve the applicability and to certify the results of
variational quantum simulators.
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