This paper presents a hardware-efficient variational quantum eigensolver (VQE) for small molecules and quantum magnets. The approach uses a quantum processor with six superconducting qubits to solve for the ground state energy of molecular Hamiltonians, including $ BeH_2 $, and a quantum magnetism problem. The method involves encoding fermionic Hamiltonians into qubit-based Hamiltonians, using a parity mapping and a compact encoding scheme. The trial states are prepared using a hardware-efficient ansatz that is tailored to the available interactions on the quantum processor. The algorithm uses a robust stochastic optimization routine to find the optimal parameters for the trial states, which are then used to estimate the energy of the system. The VQE approach is compared with numerical simulations and experimental results, showing good agreement with a noisy model of the device. The results demonstrate that the method can be used to solve for the ground state energy of small molecules and quantum magnets, even in the presence of noise and decoherence. The approach is flexible and can be applied to a variety of problems, including quantum chemistry and quantum magnetism. The study highlights the importance of hardware-efficient algorithms for quantum computing, as they can be implemented on current quantum processors with limited qubit numbers and connectivity. The results also show that the method can be extended to larger systems, with the potential to achieve chemical accuracy with further improvements in coherence and sampling. The paper concludes that the hardware-efficient VQE is a promising approach for solving quantum problems on quantum computers.This paper presents a hardware-efficient variational quantum eigensolver (VQE) for small molecules and quantum magnets. The approach uses a quantum processor with six superconducting qubits to solve for the ground state energy of molecular Hamiltonians, including $ BeH_2 $, and a quantum magnetism problem. The method involves encoding fermionic Hamiltonians into qubit-based Hamiltonians, using a parity mapping and a compact encoding scheme. The trial states are prepared using a hardware-efficient ansatz that is tailored to the available interactions on the quantum processor. The algorithm uses a robust stochastic optimization routine to find the optimal parameters for the trial states, which are then used to estimate the energy of the system. The VQE approach is compared with numerical simulations and experimental results, showing good agreement with a noisy model of the device. The results demonstrate that the method can be used to solve for the ground state energy of small molecules and quantum magnets, even in the presence of noise and decoherence. The approach is flexible and can be applied to a variety of problems, including quantum chemistry and quantum magnetism. The study highlights the importance of hardware-efficient algorithms for quantum computing, as they can be implemented on current quantum processors with limited qubit numbers and connectivity. The results also show that the method can be extended to larger systems, with the potential to achieve chemical accuracy with further improvements in coherence and sampling. The paper concludes that the hardware-efficient VQE is a promising approach for solving quantum problems on quantum computers.