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We experimentally study the time-optimal construction of arbitrary single-qubit 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 and achieve driving frequencies four times larger than its Larmor frequency. We implement time optimal universal rotations on this system, characterize their performance using quantum process tomography, and demonstrate a dual-axis ac magnetometry sequence with pulses at sub-Larmor time scales. 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.
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A remarkably simple result is derived for the minimal time $T_{rm min}$ required to drive a general initial state to a final target state by a Landau-Zener type Hamiltonian or, equivalently, by time-dependent laser driving. The associated protocol is also derived. A surprise arises for some states when the interaction strength is assumed to be bounded by a constant $c$. Then, for large $c$, the optimal driving is of type bang-off-bang and for increasing $c$ one recovers the unconstrained result. However, for smaller $c$ the optimal driving can suddenly switch to bang-bang type. We discuss the notion of quantum speed limit time.
We consider the dynamics of a two-level system (qubit) driven by strong and short resonant pulses in the framework of Floquet theory. First we derive analytical expressions for the quasienergies and Floquet states of the driven system. If the pulse amplitude varies very slowly, the system adiabatically follows the instantaneous Floquet states, which acquire dynamical phases that depend on the evolution of the quasienergies over time. The difference between the phases acquired by the two Floquet states corresponds to a qubit state rotation, generalizing the notion of Rabi oscillations to the case of large driving amplitudes. If the pulse amplitude changes very fast, the evolution is non-adiabatic, with transitions taking place between the Floquet states. We quantify and analyze the nonadiabatic transitions during the pulse by employing adiabatic perturbation theory and exact numerical simulations. We find that, for certain combinations of pulse rise and fall times and maximum driving amplitude, a destructive interference effect leads to a remarkably strong suppression of transitions between the Floquet states. This effect provides the basis of a quantum control protocol, which we name Floquet Interference Efficient Suppression of Transitions in the Adiabatic basis (FIESTA), that can be used to design ultra-fast high-fidelity single-qubit quantum gates.
We present a model describing the use of ultra-short strong pulses to control the population of the excited level of a two-level quantum system. In particular, we study an off-resonance excitation with a few cycles pulse which presents a smooth phase jump i.e. a change of the pulses phase which is not step-like, but happens over a finite time interval. A numerical solution is given for the time-dependent probability amplitude of the excited level. The control of the excited levels population is obtained acting on the shape of the phase transient, and other parameters of the excitation pulse.
We study an Otto heat machine whose working substance is a single two-level system interacting with a cold thermal reservoir and with a squeezed hot thermal reservoir. By adjusting the squeezing or the adiabaticity parameter (the probability of transition) we show that our two-level system can function as a universal heat machine, either producing net work by consuming heat or consuming work that is used to cool or heat environments. Using our model we study the performance of these machine in the finite-time regime of the isentropic strokes, which is a regime that contributes to make them useful from a practical point of view.
Manipulate and control of the complex quantum system with high precision are essential for achieving universal fault tolerant quantum computing. For a physical system with restricted control resources, it is a challenge to control the dynamics of the target system efficiently and precisely under disturbances. Here we propose a multi-level dissipative quantum control framework and show that deep reinforcement learning provides an efficient way to identify the optimal strategies with restricted control parameters of the complex quantum system. This framework can be generalized to be applied to other quantum control models. Compared with the traditional optimal control method, this deep reinforcement learning algorithm can realize efficient and precise control for multi-level quantum systems with different types of disturbances.
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