Quantum optimal control for high-fidelity arbitrary quantum logic on a superconducting qudit

Quantum simulation is one of the most anticipated application of quantum computation, which often requires repeated applications of high-fidelity arbitrary quantum logic on the quantum hardware. Arbitrary quantum logic is often decomposed into a series of primitive standard quantum logics, each implemented as narrowband microwave pulses applied to the quantum system. This standard approach suffers from cumulative errors of pulse concatenation and device decoherence error. The alternative approach is quantum optimal control, which computes a single microwave pulse that directly realizes the arbitrary quantum logic based on quantum optimal control theory. We present experimental demonstration of this approach for implementing high-fidelity arbitrary quantum logic on a superconducting qudit. We describe our procedure for extracting the system Hamiltonian, calibrating the quantum and classical hardware chain, and evaluating the gate fidelity.