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Variational quantum algorithms aim at harnessing the power of noisyintermediate-scale quantum computers, by using a classical optimizer to train aparameterized quantum circuit to solve tractable quantum problems. Thevariational quantum eigensolver is one of the aforementioned algorithmsdesigned to determine the ground-state of many-body Hamiltonians. Here, weapply the variational quantum eigensolver to study the ground-state propertiesof $N$-component fermions. With such knowledge, we study the persistent currentof interacting SU($N$) fermions, which is employed to reliably map out thedifferent quantum phases of the system. Our approach lays out the basis for acurrent-based quantum simulator of many-body systems that can be implemented onnoisy intermediate-scale quantum computers.

Variational Quantum Eigensolver for SU($N$) Fermions