  Quantum computers have the potential to help solve a range of physics and
chemistry problems, but noise in quantum hardware currently limits our ability
to obtain accurate results from the execution of quantum-simulation algorithms.
Various methods have been proposed to mitigate the impact of noise on
variational algorithms, including several that model the noise as damping
expectation values of observables. In this work, we benchmark various methods,
including a new method proposed here. We compare their performance in
estimating the ground-state energies of several instances of the 1D mixed-field
Ising model using the variational-quantum-eigensolver algorithm with up to 20
qubits on two of IBM's quantum computers. We find that several error-mitigation
techniques allow us to recover energies to within 10% of the true values for
circuits containing up to about 25 ansatz layers, where each layer consists of
CNOT gates between all neighboring qubits and Y-rotations on all qubits.
