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arXiv:1811.07566 · Journal of Physics A Mathematical and Theoretical

Universal speeded-up adiabatic geometric quantum computation in three-level systems via counterdiabatic driving

Jin‐Lei Wu, Shi‐Lei Su

Published Jun 18, 2019• 26 citations
arXivHTMLPDF

Abstract

Abstract Universal speeded-up adiabatic geometric quantum computation is studied in a system with different coupling cases including time-dependent detuning, large detuning, and one-photon resonance couplings. The counterdiabatic driving method is used to speed up the universal quantum computation. These schemes are feasible in experiment because additional unaccessible ground-state coupling is not needed. Only the shapes and phases of the reference adiabatic classical-field pulse are modified with the aid of effective two-level systems. The speed and robustness against system decay and control errors are discussed, and the performance of the scheme is compared for different coupling cases.

DOI
10.1088/1751-8121/ab2a92

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Abstract Universal speeded-up adiabatic geometric quantum computation is studied in a system with different coupling cases including time-dependent detuning, large detuning, and one-photon resonance couplings. The counterdiabatic driving method is used to speed up the universal quantum computation. These schemes are feasible in experiment because additional unaccessible ground-state coupling is not needed. Only the shapes and phases of the reference adiabatic classical-field pulse are modified with the aid of effective two-level systems. The speed and robustness against system decay and control errors are discussed, and the performance of the scheme is compared for different coupling cases.
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 We propose a general approach to speed up quantum adiabatic processes for fast quantum information transfer in a three-level system. In the approach, by using an intermediate Hamiltonian which is assumed to be formed by the original Hamiltonian H 0 ( t ) and its counterdiabatic driving Hamiltonian H cd ( t ) with a simple linear relationship, we design exact dynamics following the eigenstates of the intermediate Hamiltonian to speed up the desired population processes. We apply the present approach to a three-level system to show that by suitably choosing the parameters, not only the population processes could be sped up, but also the existence of the undesired off-diagonal terms, the populations of the intermediate states, and even the shapes of the pulses would be controllable in the speeding up scheme.
We show that geodesic motion in the Riemannian manifold of quantum states provides a direct route to time-independent counterdiabatic driving. Using the relation between the counterdiabatic Hamiltonian and the quantum metric tensor, we prove that a constant-speed geodesic makes the Hilbert-Schmidt norm of the counterdiabatic Hamiltonian constant. For effective two-level systems whose counterdiabatic correction has a fixed operator direction, this further implies that the full counterdiabatic Hamiltonian itself is time independent. We illustrate this result with the Landau-Zener model, three-level Stimulated Raman adiabatic passage and a collectively driven Rydberg ensemble in the blockade regime. Limitations of this approach in realistic many-body systems are discussed, where the two-level reduction is only emergent and leakage out of the effective subspace bounds the achievable speedup. In all cases, time-independent counterdiabatic driving achieves unit-fidelity state preparation on timescales substantially shorter than conventional adiabatic protocols while replacing temporally shaped auxiliary controls by fixed-amplitude fields.
Efficient adiabatic control schemes, where one steers a quantum system along an adiabatic path ensuring minimal excitations while achieving a desired final state, that enable fast, high-fidelity operations are essential for any practical quantum computation. However, current optimization protocols are not universally tractable due to stringent requirements imposed by the microscopic systems encoding the qubit, including complex energy level structures and unwanted transitions, and generally require a trade-off between speed and fidelity of the operation. Here, we address these challenges by developing a general framework for optimal control based on the quantum metric tensor. This framework allows for fast and high-fidelity adiabatic pulses, even for a dense energy spectrum, based solely on the Hamiltonian of the system instead of the time evolution propagator and independent of the size of the underlying Hilbert space. Furthermore, our framework suppresses diabatic transitions and state-dependent crosstalk effects without the need for additional control fields. As an example, we study the adiabatic charge transfer in a double quantum dot to find optimal control pulses with improved performance. We show that for the geometric protocol, the transfer fidelities are lower bounded F>99%\mathcal{F}>99\%F>99% for ultrafast $20~\mbox{ns}$ pulses, regardless of the size of the anti-crossing, while being robust against miscalibration errors and quasistatic noise.
Abstract We review a scheme for the systematic design of quantum control protocols based on shortcuts to adiabaticity in few-level quantum systems. The adiabatic dynamics is accelerated by introducing high-frequency modulations in the control Hamiltonian, which mimic a time-dependent counterdiabatic correction. We present a number of applications for the high-fidelity realization of quantum state transfers and quantum gates based on effective counterdiabatic driving, in platforms ranging from superconducting circuits to Rydberg atoms.
Adiabatic quantum control is a powerful tool for quantum engineering and a key component in some quantum computation models, where accurate control over the timing of the involved pulses is not needed. However, the adiabatic condition requires that the process be very slow and thus limits its application in quantum computation, where quantum gates are preferred to be fast due to the limited coherent times of the quantum systems. Here, we propose a feasible scheme to implement universal holonomic quantum computation based on non-Abelian geometric phases with superadiabatic quantum control, where the adiabatic manipulation is sped up while retaining its robustness against errors in the timing control. Consolidating the advantages of both strategies, our proposal is thus both robust and fast. The cavity QED system is adopted as a typical example to illustrate the merits where the proposed scheme can be realized in a tripod configuration by appropriately controlling the pulse shapes and their relative strength. To demonstrate the distinct performance of our proposal, we also compare our scheme with the conventional adiabatic strategy.