Path-independent gates for error-corrected quantum computing: Theory

Universal control of a quantum system can usually not be achieved by direct control of the system. To realize the missing unitary gates for universal control, we can couple an ancilla system with more complete functionality to the logical system and jointly control both systems. However, the ancilla often suffers much stronger noise than the logical system. Here, we propose a general class of quantum gates on the logical system that is path independent (PI) of Markovian ancilla error trajectories, including both ancilla relaxation and dephasing errors. By fixing the initial and final ancilla states, the designed gates can be PI of infinite-order ancilla dephasing errors, finite-order ancilla relaxation errors, and the combination of both. The PI gates can also be made error-transparent to the first-order logical system errors. As an example, we show that the photon-number selective arbitrary phase (SNAP) gates in circuit QED belong to such a class of PI gates. This proposal provides a hardware-efficient approach toward fault-tolerant quantum computation with system-specific error models.