Abstract We derive shortcuts to adiabaticity for a two-level system using the detuning as sole control parameter while the Rabi frequency is kept fixed. We work in the adiabatic basis while we also employ a time-rescaling. The control function that we use is the time-derivative of the magnetic field angle relative to the z-axis. We find that a constant control attains adiabatic passage with perfect fidelity only at particular durations, which we call resonances. We also find that, if we use a control with appropriate on-off modulation, a perfect adiabatic passage is achieved for all durations exceeding the bound π/Ω, with Ω being the constant Rabi frequency. The advantage of the proposed methodology over previous works is that the detuning control obtained is continuous and monotonic. The present work may find applications in the field of quantum information. As an example we mention the problem of designing a CZ gate, which can be formulated as the problem of adiabatically controlling a two-level system using only the detuning.
Abstract We derive shortcuts to adiabaticity for a two-level system using the detuning as sole control parameter while the Rabi frequency is kept fixed. We work in the adiabatic basis while we also employ a time-rescaling. The control function that we use is the time-derivative of the magnetic field angle relative to the z-axis. We find that a constant control attains adiabatic passage with perfect fidelity only at particular durations, which we call resonances. We also find that, if we use a control with appropriate on-off modulation, a perfect adiabatic passage is achieved for all durations exceeding the bound π/Ω, with Ω being the constant Rabi frequency. The advantage of the proposed methodology over previous works is that the detuning control obtained is continuous and monotonic. The present work may find applications in the field of quantum information. As an example we mention the problem of designing a CZ gate, which can be formulated as the problem of adiabatically controlling a two-level system using only the detuning.
In this work we derive ultrafast shortcuts for adiabatic rapid passage for a qubit where the only control variable is the longitudinal z field, while the transverse x field remains constant. This restrictive framework is pertinent to some important tasks in quantum computing, for example, the design of a high fidelity controlled-phase gate can be mapped to the adiabatic quantum control of such a qubit. We study this problem in the adiabatic reference frame and with appropriately rescaled time, using as control input the derivative of the total field polar angle (with respect to rescaled time). We first show that a constant pulse can achieve perfect adiabatic rapid passage at only specific times, corresponding to resonant shortcuts to adiabaticity. We next show that, by using ``on-off-on-...-on-off-on'' pulse sequences with appropriate characteristics (amplitude, timing, and number of pulses), a perfect fidelity can be obtained for every duration larger than the limit $\ensuremath{\pi}/\mathrm{\ensuremath{\Omega}}$, where $\mathrm{\ensuremath{\Omega}}$ is the constant transverse x field. We provide equations from which these characteristics can be calculated. The proposed methodology for generalized resonant shortcuts exploits the advantages of composite pulses in the rescaled time, while the corresponding control z field varies continuously and monotonically in the original time. Of course, as the total duration approaches the lower limit, the changes in the control signal become more abrupt. These results are not restricted only to quantum information processing applications, but is also expected to impact other areas, where adiabatic rapid passage is used.
Abstract In this article we propose a novel method to accelerate adiabatic passage in a two-level system with only longitudinal field (detuning) control, while the transverse field is kept constant. The suggested method is a modification of the Roland–Cerf protocol, during which the parameter quantifying local adiabaticity is held constant. Here, we show that with a simple ‘on–off’ modulation of this local adiabaticity parameter, a perfect adiabatic passage can be obtained for every duration larger than the lower bound , where is the constant transverse field. For a fixed maximum amplitude of the local adiabaticity parameter, the timings of the ‘on–off’ pulse-sequence which achieves perfect fidelity in minimum time are obtained using optimal control theory. The corresponding detuning control is continuous and monotonic, a significant advantage compared to the detuning variation at the quantum speed limit which includes non-monotonic jumps. The proposed methodology can be applied in several important core tasks in quantum computing, for example to the design of a high fidelity controlled-phase gate, which can be mapped to the adiabatic quantum control of such a qubit. Additionally, it is expected to find applications across all physics disciplines which exploit the adiabatic control of such a two-level system.
We propose a simple scheme for generating a high-fidelity controlled-Z (CZ) gate in a three-component qubit/bus/qubit device. The corresponding tune/detune pulse is single-step, with a near-resonant constant undershoot between the 200 and 101 states. During the pulse, the frequency of the first qubit is kept fixed, while the frequency of the second qubit is varied in such a way as to bring the 200 and 101 states close to resonance. As a result, the phase of the 101 state is accumulated via the corresponding second-order anticrossing. For experimentally realistic qubit frequencies and a 75 MHz coupling (150 MHz splitting), a 45 ns gate time can be realized with >99.99% intrinsic fidelity, with errors arising due to the non-adiabaticity of the ramps. The CZ pulse is characterized by two adjustable parameters: the undershoot magnitude and undershoot duration. The pulse does not load an excitation into the bus. This by-passes the previously proposed need for two additional qubit-to-bus and bus-to-qubit MOVE operations. Combined with the recently predicted high-fidelity idling operation in the RezQu architecture [A. Galiautdinov, J. Martinis, A. Korotkov (unpublished)], this controlled-Z scheme may prove useful for implementations on the first generation quantum computers.
Abstract We consider a generic two-level quantum system with control parameters as the coupling between the two states, taking values in a bounded positive interval, and the detuning, restricted in a symmetric interval around zero. Using Stokes theorem, we prove that the optimal path for fast quasi-adiabatic dynamics lies mainly on the border of parameter space, as it was numerically found in a recent study regarding coupled elastic waveguides, modelled as a two-level system. We calculate analytically the adiabaticity parameter as a function of the protocol duration and compare with the finite-time Landau–Zener protocol, where the coupling is kept constant while the detuning varies linearly with time. The optimized-path protocol shows superior performance even for shorter durations, where the Landau–Zener protocol fails. The present study may be useful in different fields with systems modelled as the investigated generic two-level quantum system.
Shortcuts to adiabaticity in various quantum systems have attracted much attention with their wide applications in quantum information processing and quantum control. In this paper, we concentrate on a stimulated Raman shortcut-to-adiabatic passage in quantum three-level systems. To implement counterdiabatic driving but without additional coupling, we first reduce the quantum three-level systems to effective two-level problems at large intermediate-level detuning, or on resonance, apply counterdiabatic driving along with the unitary transformation and eventually modify the pump and Stokes pulses for achieving fast and high-fidelity population transfer. The required laser intensity and stability against parameter variation are further discussed, to demonstrate the advantage of shortcuts to adiabaticity.
Abstract Quantum control methods, like rapid adiabatic passage, stimulated Raman adiabatic passage, shortcuts to adiabaticity and optimal control, have become an integral part of modern quantum technologies, for example quantum computation and sensing, where they are exploited in order to find the optimal pulse sequences which drive quantum systems to the desired target state in minimum time or with maximum fidelity, overcoming decoherence and dissipation. In this perspective, we use the basic example of adiabatic population inversion in a two-level system in order to present these methods and review the latest developments in the field, while we touch upon the emerging method of reinforcement learning.