Certified variational quantum algorithms for eigenstate preparation

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.

arXiv comment9 pages; 6 figures; REVTeX4-1

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• Numerical hardware-efficient variational quantum simulation of a soliton solution
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• Using non-convex optimization in quantum process tomography: Factored gradient descent is tough to beat
• Finding eigenvectors with a quantum variational algorithm
• Quantum algorithm for one-quasiparticle excitations in the thermodynamic limit via cluster-additive block diagonalization