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Chinese Physics Letters

Controlled Phase Gate Based on an Electron Floating on Helium

Yan-Li Shi, Feng Mei, Ya-Fei Yu, Zhi‐Ming Zhang

Published May 1, 2011• 0 citations
Publisher

Abstract

We propose a scheme to generate the controlled phase gate by using an electron floating on liquid helium. The electron is also driven by a classical laser beam and by an oscillating magnetic field. In the process, the vibration of the electron is used as the qubus to couple the energy level qubit (1D Stark-shifted hydrogen) and spin qubit. Ultimately, the controlled phase gate can be generated.

DOI
10.1088/0256-307x/28/5/050302

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We propose a scheme to generate the controlled phase gate by using an electron floating on liquid helium. The electron is also driven by a classical laser beam and by an oscillating magnetic field. In the process, the vibration of the electron is used as the qubus to couple the energy level qubit (1D Stark-shifted hydrogen) and spin qubit. Ultimately, the controlled phase gate can be generated.
Numerous physical systems have been proposed for constructing quantum computers, but formidable obstacles stand in the way of making even modest systems with a few hundred quantum bits (qubits). Several approaches utilize the spin of an electron as the qubit. Here it is suggested that the spin of electrons floating on the surface of liquid helium will make excellent qubits. These electrons can be electrostatically held and manipulated much like electrons in semiconductor heterostructures, but being in a vacuum the spins on helium suffer much less decoherence. In particular, the spin-orbit interaction is reduced so that moving the qubits with voltages applied to gates has little effect on their coherence. Remaining sources of decoherence are considered, and it is found that coherence times for electron spins on helium can be expected to exceed 100s100\phantom{\rule{0.3em}{0ex}}\mathrm{s}100s. It is shown how to obtain a controlled-NOT operation between two qubits using the magnetic dipole-dipole interaction.
Jaynes-Cummings model is a typical model in quantum optics and has been realized with various physical systems [e.g, cavity quantum electrodynamics (QED), trapped ions, circuit QED, etc.] of two-level atoms interacting with quantized bosonic fields. Here, we propose an implementation of this model by using a single classical laser beam to drive an electron floating on liquid helium. Two lowest levels of the vertical motion of the electron act as a two-level ``atom'' and the quantized vibration of the electron along one of the parallel directions, e.g., xxx direction, serves as the bosonic mode. These two degrees of freedom of the trapped electron can be coupled together by using a classical laser field. If the frequencies of the applied laser fields are properly set, the desirable Jaynes-Cummings models could be effectively realized.
In this review, we introduce a developing qubit platform: floating-electron-based qubits. Electrons floating in a vacuum above the surface of liquid helium or solid neon emerge as promising candidates for qubits, especially due to their expected long coherence times. Despite being in the early stages, a variety of recent experiments from different groups have shown substantial potential in this role. We survey a range of theoretical proposals and recent experiments, primarily focusing on the use of the spin state as the qubit state, wherein the spin and charge states are hybridized. Throughout these proposals and experiments, the charge state is coupled to an LC resonator, which facilitates both the control and readout mechanisms for the spin state via an artificially introduced spin–charge coupling.
Abstract Surface-state electrons floating on liquid Helium have been served as one of the great potential experimental platforms to implement quantum computation, wherein the qubits are usually encoded by either the lowest two levels of the vertical vibrations (i.e., Hydrogen-like atoms) or the electronic spins. Given the relevant operations require additional techniques, such as the corresponding millimeter-wave or magnetic field manipulations, here we investigate how to implement the scalable quantum computation with a trapped electron array by alternatively using the usual centimeter-wave manipulating techniques. This is because the eigenfrequency of the present qubit, encoded by the two lowest levels of the lateral vibration of the trapped electron, is limited in the centimeter-wave band. We show that, by biasing the electrodes properly and driving the coplanar waveguide transmission line resonator, the electrons can be individually trapped in a series of anharmonic potentials on liquid Helium. Therefore, the well-developed circuit quantum electrodynamics technique for the implementation of superconducting quantum computation can be conveniently utilized here in the present quantum computing platform (proposed firstly in Phys Rev Lett 105:040503, 2010, to implement the fundamental logic gates, typically such as the single-qubit rotations of the individually addressable trapped electrons, the switchable two-qubit manipulations between the electrons trapped in the distant traps, and also the high-fidelity readouts of the target qubits. The feasibility of the proposal is also discussed by numerical simulations.