Adiabatic evolution along the instantaneous eigenstate of a time-dependent Hamiltonian is used for robust and high fidelity state transfer in atomic and molecular physics. Shortcuts to adiabaticity (STA) are systematic approaches to accomplish the same final state transfer in a faster manner. This article presents an introduction to STA and reviews different theoretical approaches and applications of STA to a range of scientific and engineering tasks in quantum physics and beyond.

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Shortcuts to adiabaticity: Concepts, methods, and applications

Quantum biology is an emerging field of research that concerns itself with the experimental and theoretical exploration of non-trivial quantum phenomena in biological systems. In this tutorial overview we aim to bring out fundamental assumptions and questions in the field, identify basic design principles and develop a key underlying theme – the dynamics of quantum dynamical networks in the presence of an environment and the fruitful interplay that the two may enter. At the hand of three biological phenomena whose understanding is held to require quantum mechanical processes, namely excitation and charge transfer in photosynthetic complexes, magneto-reception in birds and the olfactory sense, we demonstrate that this underlying theme encompasses them all, thus suggesting its wider relevance as an archetypical framework for quantum biology.

Vibrations, quanta and biology

Quantum biology is an emerging field of research that concerns itself with the experimental and theoretical exploration of non-trivial quantum phenomena in biological systems. In this tutorial overview we aim to bring out fundamental assumptions and questions in the field, identify basic design principles and develop a key underlying theme -- the dynamics of quantum dynamical networks in the presence of an environment and the fruitful interplay that the two may enter. At the hand of three biological phenomena whose understanding is held to require quantum mechanical processes, namely excitation and charge transfer in photosynthetic complexes, magneto-reception in birds and the olfactory sense, we demonstrate that this underlying theme encompasses them all, thus suggesting its wider relevance as an archetypical framework for quantum biology.

Vibrations, Quanta and Biology

An open quantum system refers to a system that is further coupled to a bath system consisting of surrounding radiation fields, atoms, molecules, or proteins. The bath system is typically modeled by an infinite number of harmonic oscillators. This system-bath model can describe the time-irreversible dynamics through which the system evolves toward a thermal equilibrium state at finite temperature. In nuclear magnetic resonance and atomic spectroscopy, dynamics can be studied easily by using simple quantum master equations under the assumption that the system-bath interaction is weak (perturbative approximation) and the bath fluctuations are very fast (Markovian approximation). However, such approximations cannot be applied in chemical physics and biochemical physics problems, where environmental materials are complex and strongly coupled with environments. The hierarchical equations of motion (HEOM) can describe the numerically "exact" dynamics of a reduced system under nonperturbative and non-Markovian system-bath interactions, which has been verified on the basis of exact analytical solutions (non-Markovian tests) with any desired numerical accuracy. The HEOM theory has been used to treat systems of practical interest, in particular, to account for various linear and nonlinear spectra in molecular and solid state materials, to evaluate charge and exciton transfer rates in biological systems, to simulate resonant tunneling and quantum ratchet processes in nanodevices, and to explore quantum entanglement states in quantum information theories. This article presents an overview of the HEOM theory, focusing on its theoretical background and applications, to help further the development of the study of open quantum dynamics.

Numerically "exact" approach to open quantum dynamics: The hierarchical equations of motion (HEOM).

Experimental perspective on three-dimensional topological semimetals

An extended hierarchy equation of motion (HEOM) is proposed and applied to study the dynamics of the spin-boson model. In this approach, a complete set of orthonormal functions are used to expand an arbitrary bath correlation function. As a result, a complete dynamic basis set is constructed by including the system reduced density matrix and auxiliary fields composed of these expansion functions, where the extended HEOM is derived for the time derivative of each element. The reliability of the extended HEOM is demonstrated by comparison with the stochastic Hamiltonian approach under room-temperature classical ohmic and sub-ohmic noises and the multilayer multiconfiguration time-dependent Hartree theory under zero-temperature quantum ohmic noise. Upon increasing the order in the hierarchical expansion, the result obtained from the extended HOEM systematically converges to the numerically exact answer.

Extended hierarchy equation of motion for the spin-boson model

Following the calculation of optimal energy transfer in thermal environment in our first paper [J. L. Wu, F. Liu, Y. Shen, J. S. Cao, and R. J. Silbey, New J. Phys. 12, 105012 (2010)], full quantum dynamics and leading-order "classical" hopping kinetics are compared in the seven-site Fenna-Matthews-Olson (FMO) protein complex. The difference between these two dynamic descriptions is due to higher-order quantum corrections. Two thermal bath models, classical white noise (the Haken-Strobl-Reineker (HSR) model) and quantum Debye model, are considered. In the seven-site FMO model, we observe that higher-order corrections lead to negligible changes in the trapping time or in energy transfer efficiency around the optimal and physiological conditions (2% in the HSR model and 0.1% in the quantum Debye model for the initial site at BChl 1). However, using the concept of integrated flux, we can identify significant differences in branching probabilities of the energy transfer network between hopping kinetics and quantum dynamics (26% in the HSR model and 32% in the quantum Debye model for the initial site at BChl 1). This observation indicates that the quantum coherence can significantly change the distribution of energy transfer pathways in the flux network with the efficiency nearly the same. The quantum-classical comparison of the average trapping time with the removal of the bottleneck site, BChl 4, demonstrates the robustness of the efficient energy transfer by the mechanism of multi-site quantum coherence. To reconcile with the latest eight-site FMO model which is also investigated in the third paper [J. Moix, J. L. Wu, P. F. Huo, D. F. Coker, and J. S. Cao, J. Phys. Chem. Lett. 2, 3045 (2011)], the quantum-classical comparison with the flux network analysis is summarized in Appendix C. The eight-site FMO model yields similar trapping time and network structure as the seven-site FMO model but leads to a more disperse distribution of energy transfer pathways.

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Efficient energy transfer in light-harvesting systems: Quantum-classical comparison, flux network, and robustness analysis

Based on a 'shortcut-to-adiabaticity' (STA) scheme, we theoretically design and experimentally realize a set of high-fidelity single-qubit quantum gates in a superconducting Xmon qubit system. Through a precise microwave control, the qubit is driven to follow a fast 'adiabatic' trajectory with the assistance of a counter-diabatic field and the correction of derivative removal by adiabatic gates. The experimental measurements of quantum process tomography and interleaved randomized benchmarking show that the process fidelities of our STA quantum gates are higher than 94.9% and the gate fidelities are higher than 99.8%, very close to the state-of-art gate fidelity of 99.9%. An alternate of high-fidelity quantum gates is successfully achieved under the STA protocol.

https://iopscience.iop.org/article/10.1088/1367-2630/aac9e7/pdf

The experimental realization of high-fidelity ‘shortcut-to-adiabaticity’ quantum gates in a superconducting Xmon qubit

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-$Z$ ($C\phantom{\rule{0}{0ex}}Z$) 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.

Experimental Realization of a Fast Controlled- Z Gate via a Shortcut to Adiabaticity

The significance of topological phases has been widely recognized in thecommunity of condensed matter physics. The well controllable quantum systemsprovide an artificial platform to probe and engineer various topologicalphases. The adiabatic trajectory of a quantum state describes thechange of the bulk Bloch eigenstates with the momentum, and this adiabatic simulation method is however practicallylimited due to quantum dissipation. Here we apply the “shortcut to adiabaticity” (STA)protocol to realize fast adiabatic evolutions in the system of a superconducting phase qubit.The resulting fast adiabatic trajectories illustratethe change of the bulk Bloch eigenstates in the Su-Schrieffer-Heeger (SSH) model. A sharp transitionis experimentally determined for the topological invariant of a winding number.Our experiment helps identify the topological Chern number of a two-dimensionaltoy model, suggesting the applicability of the fast adiabatic simulationmethod for topological systems.

Jianlan Wu

Papers

Extended hierarchy equation of motion for the spin-boson model

Efficient energy transfer in light-harvesting systems: Quantum-classical comparison, flux network, and robustness analysis

The experimental realization of high-fidelity ‘shortcut-to-adiabaticity’ quantum gates in a superconducting Xmon qubit

Experimental Realization of a Fast Controlled- Z Gate via a Shortcut to Adiabaticity

Simulating a topological transition in a superconducting phase qubit by fast adiabatic trajectories