Improving success probability of imaginary-time evolution on a quantum computer*

Quantum algorithms based on the imaginary-time evolution (ITE) method are actively researched due to their characteristics of the exponential decay of high-energy states. One proposal realizes the action of the ITE operator by introducing an ancilla qubit with some probability, called its probabilistic ITE (PITE) method. The advantage of the PITE method over other types of the ITE method on a quantum computer is the unnecessity of many evaluations of quantum circuits to obtain the next imaginary-time steps. However, the probabilistic nature of the PITE method brings us the drawback that a success probability, the probability of obtaining the state acted on by the ITE operator, exponentially decreases along with an increase of imaginary time. Here, we cope with the undesirable nature by using quantum amplitude amplification. The developed quantum circuits for PITE combined with quantum amplitude amplification (QAA) succeeded in the reduction of the circuit depth and improvement of the success probability. We present the simulation results employed by the proposed technique with a discussion of the computational overhead of the amplification circuits.