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. 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 π 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 and nears the quantum speed limit without requiring complicated pulse shaping or optimal control sequences.

Achieving high-fidelity single-qubit gates in a strongly driven silicon-quantum-dot hybrid qubit

“…For a system like a double dot coherently coupled to a microwave resonator [30][31][32][33], it is essential to use a dressedstate model [34] in which the qubit electron(s) and the resonator photon(s) are both treated quantum mechanically [35][36][37][38][39]. If, instead, the quantum dot is driven via a classical field, one may employ either a semiclassical [40,41,42] or a fully quantum model. Both approaches are capable of describing corrections to the RWA, and have been used to describe strong driving in superconducting qubit systems [43][44][45][46].…”

Dynamical second-order noise sweetspots in resonantly driven spin qubits

“…The exchange interaction, as a virtual tunneling process, is similarly modified by the ac driving [33,34]. Several qubit platforms employing a resonant exchange interaction have been studied both theoretically and experimentally [35][36][37][38]. Resonant exchange qubits based on double quantum dots in both GaAs/AlGaAs heterostructures [39] and Silicon [40], as well as on triple quantum dots [41,42] have been developed.…”

Invariant‐Based Pulse Design for Three‐Level Systems Without the Rotating‐Wave Approximation

“…The previous schemes with STA focused on the physical systems under the rotating‐wave approximation (RWA). However, many recent schemes about superconducting systems, optomechanical systems, semiconducting systems, Bose‐Einstein condensates, and NV centers have shown that, RWA may be invalid in the cases of ultra‐fast operations and ultra‐strong couplings. For example, Liu et al .…”

“…have demonstrated in a NV center that, when using a magnetic field with a frequency of 30MHz, RWA can not be used for a qubit control if the Rabi frequency larger than 15MHz. From these examples, RWA may be invalid in fast quantum information processing, thus the applications of previous schemes with STA would be limited. Therefore, it is worthwhile to study STA without RWA so that pulse design for fast quantum information processing could be more effective.…”