Projection algorithm for state preparation on quantum computers

Understand

We present an efficient method to prepare states of a many-body system on quantum hardware, first isolating individual quantum numbers and then using time evolution to isolate the energy.

• Our method in its simplest form requires only one additional auxiliary qubit.
• The total time evolved for an accurate solution is proportional to the ratio of the spectrum range of the trial state to the gap to the lowest excited state, and the accuracy increases exponentially with the time evolved.
• Isolating the quantum numbers is efficient because of the known eigenvalues, and increases the gap thus shortening the propagation time required.