We study the performance of composite pulses in the presence of time-varying control noise on a single qubit. These protocols, originally devised only to correct for static, systematic errors, are shown to be robust to time-dependent non-Markovian noise in the control field up to frequencies as high as $\ensuremath{\sim}10%$ of the Rabi frequency. Our study combines a generalized filter-function approach with asymptotic dc-limit calculations to give a simple analytic framework for error analysis applied to a number of composite-pulse sequences relevant to nuclear magnetic resonance as well as quantum information experiments. Results include examination of recently introduced concatenated composite pulses and dynamically corrected gates, demonstrating equivalent first-order suppression of time-dependent fluctuations in amplitude and/or detuning, as appropriate for the sequence in question. Our analytic results agree well with numerical simulations for realistic
1/f noise spectra with a roll-off to
1/f2, providing independent validation of our theoretical insights.
The Hamiltonian control of n qubits requires precision control of both the strength and timing of interactions. Compensation pulses relax the precision requirements by reducing unknown but systematic errors. Using composite pulse techniques designed for single qubits, we show that systematic errors for n -qubit systems can be corrected to arbitrary accuracy given either two non-commuting control Hamiltonians with identical systematic errors or one error-free control Hamiltonian. We also examine composite pulses in the context of quantum computers controlled by two-qubit interactions. For quantum computers based on the XY interaction, single-qubit composite pulse sequences naturally correct systematic errors. For quantum computers based on the Heisenberg or exchange interaction, the composite pulse sequences reduce the logical single-qubit gate errors but increase the errors for logical two-qubit gates.
Abstract A frequently encountered source of systematic error in quantum computations is imperfections in the control pulses which are the classical fields that control qubit gate operations. From an analysis of the quantum-mechanical time-evolution operator of the spin wavefunction, it has been demonstrated that composite pulses can mitigate certain systematic errors and an appealing geometric interpretation was developed for the design of error-suppressing composite pulses. Here we show that these same pulse sequences can be obtained within a quasi-classical framework. This raises the question of whether error-correction procedures exist that exploit entanglement in a manner that can not be reproduced in the quasi-classical formulation.