Fidelity Between Unitary Operators and the Generation of Gates Robust Against Off-Resonance Perturbations

Abstract

We perform a functional expansion of the fidelity between two unitary matrices in order to find the necessary conditions for the robust implementation of a target gate. Comparison of these conditions with those obtained from the Magnus expansion and Dyson series shows that they are equivalent in first order. By exploiting techniques from robust design optimization, we account for issues of experimental feasibility by introducing an additional criterion to the search for control pulses. This search is accomplished by exploring the competition between the multiple objectives in the implementation of the NOT gate by means of evolutionary multi-objective optimization.

References in corpus (7)

• The Magnus expansion and some of its applications
• Fault-Tolerant Quantum Dynamical Decoupling
• Tackling Systematic Errors in Quantum Logic Gates with Composite Rotations
• Arbitrarily accurate composite pulses
• Arbitrary precision composite pulses for NMR quantum computing
• Advantages of Randomization in Coherent Quantum Dynamical Control
• A precise CNOT gate in the presence of large fabrication induced variations of the exchange interaction strength

Cited by in corpus (5)

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• Robustness of Controlled Quantum Dynamics
• Preparation of quantum states of two spin-$\frac{1}{2}$ particles in the form of the Schmidt decomposition
• Retrieving space-dependent polarization transformations via near-optimal quantum process tomography
• Barenco gate implementation using driven two- and three-qubit spin chains