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arXiv:1906.11493 · Physical Review A

Resonant shortcuts for adiabatic rapid passage with only z -field control

Dionisis Stefanatos, Emmanuel Paspalakis

Published Jul 12, 2019• 27 citations
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Abstract

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.

DOI
10.1103/physreva.100.012111

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In this work we derive ultrafast shortcuts for adiabatic rapid passage for a qubit where the only control variable is the longitudinal zzz field, while the transverse xxx 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 \ensuremathπ/\ensuremathΩ\ensuremath{\pi}/\mathrm{\ensuremath{\Omega}}\ensuremathπ/\ensuremathΩ, where \ensuremathΩ\mathrm{\ensuremath{\Omega}}\ensuremathΩ is the constant transverse xxx 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 zzz 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.
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 Time-rescaling (TR) has been recently proposed as a method to engineer fast processes, also known as shortcuts to adiabaticity (STA), which enables the coherent control of quantum systems beyond the adiabatic regime (Bernardo 2020 Phys. Rev. Res. 2 013133). In this work, we revisit the technique and show that the obtained fast dynamics are transitionless, similar to the ones designed via the famous counterdiabatic (CD) approach. However, contrary to the CD approach, the TR method has the advantage of providing the Hamiltonians that generate the fast processes without requiring information about the instantaneous eigenstates of a reference protocol, and the convenience that experimental implementations dismiss additional coupling fields when compared with the reference adiabatic protocol. Here, we also show that the time evolution of the STA found via TR relates to that of the reference adiabatic protocol by a simple reparametrization of time. To illustrate our findings, we studied the paradigmatic problem of speeding up the stimulated Raman adiabatic passage and found out that TR revealed quantum dynamics more robust to parameter variations than those provided by the CD technique. These results motivate the application of TR to the control of larger quantum systems.
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.
In quantum information processing, the shortcut-to-adiabaticity (STA) protocol has been proposed to accelerate a system's adiabatic evolution by introducing an additional, counterdiabatic Hamiltonian. This protocol is particularly suitable for realizing the controlled-ZZZ ($C\phantom{\rule{0}{0ex}}Z$) gate, but a counterdiabatic Hamiltonian requires a variable, complex coupling of qubits. By introducing a representation transformation and a rescaling method, this work uses the STA protocol to obtain a high-fidelity $C\phantom{\rule{0}{0ex}}Z$ gate with two coupled transmon qubits. This method affords high flexibility in the evolution time and control waveform, and is expected to be directly useful in other quantum systems as well.
Accurate control of a quantum system is a fundamental requirement in many areas of modern science ranging from quantum information processing to high-precision measurements. A significantly important goal in quantum control is preparing a desired state as fast as possible, with sufficiently high fidelity allowed by available resources and experimental constraints. Stimulated Raman adiabatic passage (STIRAP) is a robust way to realize high-fidelity state transfer but it requires a sufficiently long operation time to satisfy the adiabatic criteria. Here we theoretically propose and then experimentally demonstrate a shortcut-to-adiabatic protocol to speed-up the STIRAP. By modifying the shapes of the Raman pulses, we experimentally realize a fast and high-fidelity stimulated Raman shortcut-to-adiabatic passage that is robust against control parameter variations. The all-optical, robust and fast protocol demonstrated here provides an efficient and practical way to control quantum systems.