Adaptive quantum control via direct fidelity estimation and indirect model-based parametric process tomography

The single and two-qubit logic gates which are universal for building a quantum computer are not, as yet, produced “naturally” - error correction and fault tolerant constructions are required, and making these requires control. To meet the requisite stringent performance goals places resource demands both spatially (ancilla qubits for error correction) and temporally (complex well timed control signals). On-line adaptive tuning of initially good controls offers a possible means to significantly reduce these overhead requirements. Two methods are proposed for control tuning: (i) direct estimation of fidelity between the actual system and the desired (unitary) logic gate, and (ii) estimating model parameters via compressive sensing. Both methods are evaluated numerically for a single qubit system with Hamiltonian parameter uncertainty.