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Physical Review A

Robust quantum state transfer inspired by Dzyaloshinskii-Moriya interactions

Xuan Shi, Hao Yuan, X. Mao, Y. Ma, Hongquan Zhao

Published May 16, 2017• 12 citations
Publisher

Abstract

Quantum state transfer (QST) is a fundamental problem in quantum mechanics and is important for quantum information processing. In this paper we explore a fast, robust, and efficient QST in spin-based quantum dots. Differing from the usual method that only uses the exchange interactions to control the evolution of the spin system, here we treat the non-negligible Dzyaloshinskii-Moriya (DM) interactions that can be electrically and thermally controlled in quantum dots as an assisted driving to accelerate the population transfer. We demonstrate that the DM interactions are not an error source, but are beneficial for population evolution under certain condition because they can sufficiently eliminate the undesirable quantum transitions among adiabatic passages and strictly maintain the population evolution in a designed passage with high efficiency. We give a generic $N$-spin anisotropic Heisenberg spin model to describe the population evolution and take specific two- and three-spin systems as examples to demonstrate the advantages of the DM interactions for QST.

DOI
10.1103/physreva.95.052332

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Quantum state transfer (QST) is a fundamental problem in quantum mechanics and is important for quantum information processing. In this paper we explore a fast, robust, and efficient QST in spin-based quantum dots. Differing from the usual method that only uses the exchange interactions to control the evolution of the spin system, here we treat the non-negligible Dzyaloshinskii-Moriya (DM) interactions that can be electrically and thermally controlled in quantum dots as an assisted driving to accelerate the population transfer. We demonstrate that the DM interactions are not an error source, but are beneficial for population evolution under certain condition because they can sufficiently eliminate the undesirable quantum transitions among adiabatic passages and strictly maintain the population evolution in a designed passage with high efficiency. We give a generic NNN-spin anisotropic Heisenberg spin model to describe the population evolution and take specific two- and three-spin systems as examples to demonstrate the advantages of the DM interactions for QST.
Rapid preparation, manipulation, and correction of spin states with high fidelity are requisite for quantum information processing and quantum computing. In this paper, we propose a fast and robust approach for controlling two spins with Heisenberg and Ising interactions. By using the concept of shortcuts to adiabaticity, we first inverse design the driving magnetic fields for achieving fast spin flip or generating the entangled Bell state, and further optimize them with respect to the error and fluctuation. In particular, the designed shortcut protocols can efficiently suppress the unwanted transition or control error induced by anisotropic antisymmetric Dzyaloshinskii-Moriya exchange. Several examples and comparisons are illustrated, showing the advantages of our methods. Finally, we emphasize that the results can be naturally extended to multiple interacting spins and other quantum systems in an analogous fashion.
Accurate population transfer of uncoupled or weakly coupled spin states is crucial for many quantum-information-processing tasks. In this paper, we propose a fast and robust scheme for population transfer which combines invariant-based inverse engineering and geometric formalism for robust quantum control. Our scheme is not constrained by the adiabatic condition and therefore can be implemented quickly. It can also effectively suppress the dominant noise in spin systems, which together with the fast feature guarantees the accuracy of the population transfer. Moreover, the control parameters of the driving Hamiltonian in our scheme are easy to design because they correspond to the curvature and torsion of a three-dimensional visual space curve derived by using geometric formalism for robust quantum control. We test the efficiency of our scheme by numerically simulating the ground-state population transfer in 15N^{15}\mathrm{N}15N nitrogen-vacancy centers and comparing our scheme with stimulated Raman transition, stimulated Raman adiabatic passage, and conventional shortcuts to adiabaticity based schemes, three types of schemes popularly used for population transfer. The numerical results clearly show that our scheme is advantageous over these previous ones.
Adiabatic processes can keep the quantum system in its instantaneous eigenstate, which is robust to noises and dissipation. However, it is limited by sufficiently slow evolution. Here, we experimentally demonstrate the transitionless quantum driving (TLQD) of the shortcuts to adiabaticity in gate-defined semiconductor quantum dots (QDs) to greatly accelerate the conventional adiabatic passage for the first time. For a given efficiency of quantum state transfer, the acceleration can be more than twofold. The dynamic properties also prove that the TLQD can guarantee fast and high-fidelity quantum state transfer. In order to compensate for the diabatic errors caused by dephasing noises, the modified TLQD is proposed and demonstrated in experiment by enlarging the width of the counterdiabatic drivings. The benchmarking shows that the state transfer fidelity of 97.8% can be achieved. This work will greatly promote researches and applications about quantum simulations and adiabatic quantum computation based on the gate-defined QDs.
We construct short analytical quantum circuits for the exact evolution of a spin triangle with Dzyaloshinskii--Moriya (DM) interaction. We consider pure DM interaction with arbitrary real couplings and two Hamiltonian families with uniform Heisenberg exchange. For pure DM, a change of basis reduces the evolution to two single-qubit rotations. The circuits reproduce the full evolution operator at arbitrary time with a fixed gate count and admit implementations with both triangular and linear qubit connectivity. Experiments on a superconducting IBM quantum processor demonstrate directional quantum-state transfer and reproduce the amplitude and phase of transverse magnetization. In these experiments, the exact circuits reduce distortions relative to circuits based on the second-order Trotter formula. On a 12-spin kagome cluster, exact triangle blocks reduce the gate count at a prescribed accuracy. We also investigate the reduction of coherent errors by adjusting circuit angles and applying echo pulses to neighboring qubits.
We introduce an adiabatic transfer protocol for spin states in large quantum dot arrays that is based on time-dependent modulation of the Heisenberg exchange interaction in the presence of a magnetic field gradient. We refer to this protocol as spin-CTAP (coherent transport by adiabatic passage) in analogy to a related protocol developed for charge-state transfer in quantum dot arrays. The insensitivity of this adiabatic protocol to pulse imperfections has potential advantages for reading out extended spin qubit arrays. When the static exchange interaction varies across the array, a quantum-controlled version of spin-CTAP is possible, where the transfer process is conditional on the spin states in the middle of the array. This conditional operation can be used to generate NNN-qubit entangled GHZ states. Using a realistic noise model, we analyze the robustness of the spin-CTAP operations and find that high-fidelity (>95>95%>95) spin eigenstate transfer and GHZ state preparation is feasible in current devices.
The stimulated Raman adiabatic passage shows an efficient technique that accurately transfers population between two discrete quantum states with the same parity in three-level quantum systems based on adiabatic evolution. This technique has widely theoretical and experimental applications in many fields of physics, chemistry, and beyond. Here, we present a general approach to robust stimulated Raman shortcut-to-adiabatic passage with invariant-based optimal control. By controlling the dynamical process, we inversely design a family of Hamiltonians with non-divergent Rabi frequencies that can realize fast and accurate population transfer from the first to the third level, while the systematic errors are largely suppressed in general. Furthermore, a detailed trade-off relation between the population of the intermediate state and the amplitudes of Rabi frequencies in the transfer process is illustrated. These results provide an optimal route toward manipulating the evolution of three-level quantum systems in future quantum information processing.