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arXiv:1907.00166 · Journal of Physics A Mathematical and Theoretical

Speeding up adiabatic passage with an optimal modified Roland–Cerf protocol

Dionisis Stefanatos, Emmanuel Paspalakis

Published Feb 7, 2020• 21 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1751-8121/ab7423

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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.
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 $\ensuremath{\pi}/\mathrm{\ensuremath{\Omega}}$, where $\mathrm{\ensuremath{\Omega}}$ 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.
We consider a two-level system with a fixed energy spacing (detuning) between the two levels and a single transverse control field which can take values between zero and a maximum amplitude. Using Pontryagin's maximum principle, we completely solve the problem of generating in minimum time a uniform superposition of the two quantum states when starting from one of them, for all the values of the ratio between the maximum control amplitude and the detuning. For each value of this ratio we find the optimal pulse sequence to have the bang-bang form and calculate the durations of the pulses composing it. The suggested framework is not only restricted to the problem at hand, but it can be also exploited in the problem of fast charging a quantum battery based on a two-level system, as well as for the optimization of pulse sequences used for the controlled preparation of the excited state in a quantum emitter, which is a prerequisite for its usage as a single-photon source.
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.
We determine the optimal quantum manipulation protocols for implementing high-fidelity, fast single-qubit gates. We demonstrate that the time-optimal pulse sequence is a ``bang-bang'' sequence: discrete pulses of either positive or negative maximum amplitude or zero. The non-adiabatic bang-bang pulse sequence minimizes gate duration providing a speedup for low-frequency architectures. We first derive the protocol for a transversally driven two-level system, extracting exact analytic expressions for minimum gate times. We then extend this framework to general multilevel architectures, identifying conditions that enable the coherent suppression of leakage errors. Using the fluxonium circuit as a representative case study, we optimize X/2X/2X/2 and Y/2Y/2Y/2 gates through a combination of discrete bang sequences and continuous waveform smoothing. This approach preserves near-optimal execution speeds while mitigating transitions outside the computational subspace. Open-system simulations demonstrate that these sequences outperform commensurate and resonant pulse schemes across different fluxonium regimes, achieving low-error manipulation significantly faster than standard resonant control, even in the presence of 1/f1/f1/f flux noise and dissipation.
Adiabatic protocols are employed across a variety of quantum technologies, from implementing state preparation and individual operations that are building blocks of larger devices, to higher-level protocols in quantum annealing and adiabatic quantum computation. The problem of speeding up these processes has garnered a large amount of interest, resulting in a menagerie of approaches, most notably quantum optimal control and shortcuts to adiabaticity. The two approaches are complementary: optimal control manipulates control fields to steer the dynamics in the minimum allowed time while shortcuts to adiabaticity aim to retain the adiabatic condition upon speed-up. We outline a new method which combines the two methodologies and takes advantage of the strengths of each. The new technique improves upon approximate local counterdiabatic driving with the addition of time-dependent control fields. We refer to this new method as counterdiabatic optimised local driving (COLD) and we show that it can result in a substantial improvement when applied to annealing protocols, state preparation schemes, entanglement generation and population transfer on a lattice. We also demonstrate a new approach to the optimisation of control fields which does not require access to the wavefunction or the computation of system dynamics. COLD can be enhanced with existing advanced optimal control methods and we explore this using the chopped randomised basis method and gradient ascent pulse engineering.