Genetic Algorithm for Searching Single-Flux-Quantum Pulse Sequences for Two-Qubit Quantum Operation

Today, most superconducting quantum processors are based on transmons, the modifications of charge qubits. Traditional transmon control schemes for implementing high-fidelity quantum gates are based on the analog microwave signals. Current problems with this type of control are bulkiness, high cost, and unwanted feedback from the microwave equipment, which increases with the number of qubits involved. A promising breakthrough is the use of superconducting digital circuits operating with picosecond (single flux quantum or SFQ) pulses. In our previous work, we have shown how to use SFQ control sequences to implement the rotation of a qubit at rest on the Bloch sphere around the Y-axis by an angle $$\pi/2$$ with fidelity better than 99.99 $$\%$$ . The next important step is to implement two-qubit operations. Here we present the Genetic Algorithm for SFQ Control Sequence Search, which implements the original control protocol using the ZX operation as an example. The algorithm also takes into account the leakage to the higher energy states of the system. Its parallel implementation can find the appropriate sequence for arbitrary system parameters from a practical range in a reasonable time. As a result of numerical experiments, control sequences were found that implement the ZX operation with 0.999 target level population.