Reconfigurable Quantum Hutchinson with Real-Time Evolution

Recently, quantum algorithms leveraging dynamical evolution under the many-body Hamiltonian of interest have proven exceptionally effective in pinpointing individual eigenvalues near the edge of Hamiltonian spectrum, for example the ground state energy. This work delves into the potential of real-time evolution to evaluate the aggregate of eigenvalues across the entire spectrum. In particular, we introduce a simple near-term algorithm designed to compute the trace of a wide class of operators, including functions of the target Hamiltonian. Using stochastic real-time evolution, we transform the task of trace estimations to straightforward state-vector simulations on quantum computer. For numerical illustration, we highlight important applications, such as density of states and free energy calculations, relevant in physical, chemical, and materials sciences.