Fast control of semiconductor qubits beyond the rotating-wave approximation

Abstract

We present a theoretical study of single-qubit operations by oscillatory fields on various semiconductor platforms. We explicitly show how to perform faster gate operations by going beyond the universally-used rotating wave approximation (RWA) regime, while using only two sinusoidal pulses. No complicated pulse shaping or optimal control sequences are required. We first show for specific published experiments how much error is currently incurred by implementing pulses designed using standard RWA. We then show that an even modest increase in gate speed would cause problems in using RWA for gate design in the singlet-triplet (ST) and resonant-exchange (RX) qubits. We discuss the extent to which analytically keeping higher orders in the perturbation theory would address the problem. More strikingly, we give a new prescription for gating with strong coupling far beyond the RWA regime. We perform numerical calculations for the phases and the durations of two consecutive pulses to realize the key Hadamard and $\frac{\pi }{8}$ gates with coupling strengths up to several times the qubit splitting. Working in this manifestly non-RWA regime, the gate operation speeds up by two to three orders of magnitude.

Published version, with 15 pages and 9 figures

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• Fast pulse sequences for dynamically corrected gates in single-triplet qubits
• Pulse reverse-engineering for strong field-matter interaction
• Suppression of multiphoton resonances in driven quantum systems via pulse shape optimization
• Invariant-based pulse design for three-level systems without the rotating-wave approximation
• Coherent manipulation of nuclear spins in the strong driving regime
• An analytical double-unitary-transformation approach for strongly and periodically driven three-level systems
• Dynamical second-order noise sweetspots in resonantly driven spin qubits
• Quantum harvester enables energy transfer without randomness transfer or dissipation
• Insights from the exact analytical solution of periodically driven transverse field Ising chain
• openMMF: a library for multimode driven quantum systems
• Effective dynamics and quantum state engineering by periodic kicks