# Minimal Time Robust Control for Two Superconducting Qubits

## TL;DR

This paper develops robust optimal control strategies to perform high-fidelity, fast quantum gates on superconducting qubits within minimal times, accounting for realistic uncertainties and noise.

## Contribution

It introduces experimentally feasible robust control pulses that achieve minimal operation times with high fidelity despite system uncertainties.

## Key findings

- Achieved >0.99 fidelity within 64 ns with 10% uncertainty robustness.
- Extended control to 71 ns for >0.999 fidelity with 3% uncertainty.
- Demonstrated robustness against static and dynamic errors with 100 ns pulses.

## Abstract

High-fidelity quantum gates are crucial for achieving fault-tolerant quantum computing; however, decoherence significantly reduces gate fidelities during long operation times. Although optimal control techniques can theoretically minimize these operation times, they often neglect realistic uncertainties in system parameters. In this work, we demonstrate that by using robust optimal control strategies, the cross-resonance gate in superconducting systems can be operated within 64 ns, achieving fidelities of F > 0.99 while maintaining robustness against up to 10% uncertainty in a single parameter. Alternatively, by extending the control time to 71 ns, we achieve fidelities of F > 0.999 with robustness against up to 3% uncertainty. Our results identify the minimal control times attainable with experimentally feasible pulses and system parameters, as well as the maximum allowable static parameter error for high-fidelity operations. Furthermore, we demonstrate simultaneous robustness against both static and time-dependent errors by generating 100 ns control pulses (F > 0.99) that maintain robustness against 10% static parameter error and time-dependent parameter fluctuations two orders of magnitude stronger than typical experimental noise. These findings demonstrate a viable open-loop strategy for implementing fast, high-fidelity quantum gates in the presence of realistic system uncertainties that would otherwise degrade conventional control pulses.