Time-optimal universal control of two-level systems under strong driving

Abstract

We report on a theoretical and experimental study of time-optimal construction of arbitrary singlequbit rotations under a single strong driving field of finite amplitude. Using radiation-dressed states of nitrogen vacancy centers in diamond we realize a strongly-driven two-level system, with driving frequencies four times larger than its precession frequency. We implement time optimal universal rotations on this system, characterize their performance using quantum process tomography, and demonstrate a dual-axis multi-pulse control sequence where the qubit is rotated on time scales faster than its precession period. Our results pave the way for applying fast qubit control and high-density pulse schemes in the fields of quantum information processing and quantum metrology.

Breaking the rotating wave approximation for a strongly driven dressed single-electron spin

“…This level splitting is much smaller than the level splitting of the undressed electron spin ν e (= ν L ), which allows reaching the strong driving regime with moderate microwave powers 25,26 . Furthermore, the dressed qubit can be driven using frequency modulation (FM) of the MW source 23 , which does not add any heating to that of the MW power used for dressing.…”

“…The ease with which we can reach this regime and the level of control that we have over the driving fields, make the dressed electron spin a model system for investigating the strong driving regime, where the RWA breaks down and Bloch-Siegert shifts become important 25,27,28 . The development of deterministic quantum control beyond the RWA can have a significant advantage for quantum computation by allowing much faster gate operations to be performed 26,29,30 .…”

Fast control of semiconductor qubits beyond the rotating-wave approximation

“…It is emphasized that the optimization of quantum gates or evolution operators [on SU (2), or diffeomorphic to the S 3 space] [16,[58][59][60][61][62] are different than that of the state transfer which is only parametrized by two real numbers on the Bloch sphere [63,64]. In the weak-driving RWA regime, the minimal times to achieve the Hadamard and ( Ω is the bound of the control field), respectively, by resorting to Pontryagin maximum principle [61,65] and minimizing the action [60].…”

Pulse design without the rotating-wave approximation

“…For a constant transition (angular) frequency, ω 0 , taking into account Eqs. (7) and (29), setting ϕ(0) = π/2 and integrating, the phase of the pulse is given by…”

“…This is a simple alternative to a more sophisticated optimal-control-theory approach [28] or bang-bang methods [29]. In a numerical example we first set the reference parameters, t f = 0.1 µs, ω 0 = 2π × 5 GHz, A = (2π) 2 × 506.606 MHz 2 , a = (2π) 2 × 254.648 MHz 2 , and Ω 0 = 2π × 2 GHz, for which the Hamiltonian within and without the RWA give similar dynamics with unsuccessful population inversions, see Fig.…”