Using Grover's search algorithm to test a three-level quantum system

In the present work, Grover's search algorithm is modified and studied for application to a three-level “qutrit” quantum device. The modified algorithm constructs the superposition of all states via the discrete Fourier transform instead of the standard Hadamard gate. Then, the analogous Grover's diffusion operator is applied m times. The probability of determining the correct answer as a function of m is derived and shown to be very close to unity for specific choices of m. In a real device, the measured probability will deviate from theoretical predictions due to decoherence effects, and, since different energy levels of the qutrit have different decoherence properties, this can potentially affect the performance of the algorithm depending on the marked state. To address these issues, the algorithm has been specifically designed for implementation on the LLNL Quantum Design and Integration Testbed (QuDIT) hardware platform. This device is based on superconducting circuit architecture where the first three-levels of a transmon are used to define the qutrit.