Electric-Circuit Simulation of Quantum Fast Hitting with Exponential Speedup

The ultimate goal of developing quantum algorithms and constructing quantum computers is to achieve faster information processing than using current classical computers. Quantum walks are powerful kernels in quantum computing protocols and possess strong capabilities in speeding up various simulation and optimization tasks. One striking example is provided by quantum walkers evolving on unbalanced trees, which demonstrate faster hitting performances than classical random walk. However, direct experimental construction of unbalanced trees to prove quantum advantage with exponential speedup remains a great challenge due to the highly complex arrangements of the structure. This study attempts to simulate quantum algorithm by classical circuit. Inspired by the quantum algorithm, the classical circuit networks are designed and fabricated with unbalanced tree structures. It is then demonstrated, both theoretically and experimentally, that the quantum algorithm for the fast hitting problem can be simulated in the structure. It is shown that the hitting efficiency of electric signals in the circuit networks with unbalanced tree structures is exponentially faster than the corresponding cases of classical random walks. Because classical circuit networks possess good scalability and stability, the results open up a scalable new path toward quantum speedup in complex problems.