Abstract
This paper shows that generic high-depth variational circuits can approximate the ground state of any given one-dimensional quantum many-body Hamiltonian by carrying out the local gradient search of the circuit parameters.
Highlights
We explore the effectiveness of variational quantum circuits in simulating the ground states of quantum manybody Hamiltonians
The variational quantum eigensolver (VQE) [1,2] is one of the most promising hybrid quantum-classical (HQC) algorithms, which may offer a precise approximation of the ground state of quantum systems
CIRCUIT ANSATZE Our focus in this paper is to demonstrate the efficiency of high-depth layered circuits in a typical VQE problem, i.e., to approximate the ground state of a given Hamiltonian
Summary
The variational quantum eigensolver (VQE) [1,2] is one of the most promising hybrid quantum-classical (HQC) algorithms, which may offer a precise approximation of the ground state of quantum systems. When the layered circuit reaches a certain depth such that it evolves to an approximate 2-design, a numerical experiment [4] has shown the exponential decay of the variance of energy gradients ∇θE (θ) with respect to the number n of qubits—for random circuit states obtained by uniformly sampling from the parameter space. The main goal of this paper is to demonstrate the inherent capability of variational circuits as universal and accurate eigensolvers for generic Hamiltonians—if they can even approximate close-to-random states To this end, we will put aside the barren plateau problem by sufficiently increasing the classical computation capacity.
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