  Quantum simulators offer the potential to utilize the quantum nature of a
physical system to study another physical system. In contrast to conventional
simulation, which experiences an exponential increase in computational
complexity, quantum simulation cost increases only linearly with increasing
size of the problem, rendering it a promising tool for applications in quantum
chemistry. The variational-quantum-eigensolver algorithm is a particularly
promising application for investigating molecular electronic structures. For
its experimental implementation, spin-based solid-state qubits have the
advantage of long decoherence time and high-fidelity quantum gates, which can
lead to high accuracy in the ground-state finding. This study uses the
nitrogen-vacancy-center system in diamond to implement the
variational-quantum-eigensolver algorithm and successfully finds the eigenvalue
of a specific Hamiltonian without the need for error-mitigation techniques.
With a fidelity of 98.9% between the converged state and the ideal eigenstate,
the demonstration provides an important step toward realizing a scalable
quantum simulator in solid-state spin systems.
