  First-quantized eigensolver (FQE) is a recently proposed framework of quantum
computation for obtaining the ground state of an interacting electronic system
based on probabilistic imaginary-time evolution. In this study, we propose a
method for introducing a uniform magnetic field to an FQE calculation. We
demonstrate via resource estimation that the additional circuit responsible for
the magnetic field can be implemented with a liner depth in terms of the number
of qubits assigned to each electron, giving rise to no impact on the leading
order of whole computational cost. We confirm the validity of our method via
numerical simulations for ground and excited states by employing the filtration
circuits for energy eigenstates. We also provide the generic construction of
derivative circuits together with measurement-based formulae. As a special case
of them, we can obtain the electric-current density in an electronic system to
get insights into the microscopic origin of magnetic response.
