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arXiv:cond-mat/0510757

Quantum computing with single electron bubbles in helium

Weijun Yao

Published Oct 27, 2005• 0 citations
arXivHTMLPDF

Abstract

An electron inside liquid helium forms a bubble of 17 Åin radius. In an external magnetic field, the two-level system of a spin 1/2 electron is ideal for the implementation of a qubit for quantum computing. The electron spin is well isolated from other thermal reservoirs so that the qubit should have very long coherence time. By confining a chain of single electron bubbles in a linear RF quadrupole trap, a multi-bit quantum register can be implemented. All spins in the register can be initialized to the ground state either by establishing thermal equilibrium at a temperature around 0.1 K and at a magnetic field of 1 T or by sorting the bubbles to be loaded into the trap with magnetic separation. Schemes are designed to address individual spins and to do two-qubit CNOT operations between the neighboring spins. The final readout can be carried out through a measurement similar to the Stern-Gerlach experiment.

DOI
10.48550/arxiv.cond-mat/0510757

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An electron inside liquid helium forms a bubble of 17 Åin radius. In an external magnetic field, the two-level system of a spin 1/2 electron is ideal for the implementation of a qubit for quantum computing. The electron spin is well isolated from other thermal reservoirs so that the qubit should have very long coherence time. By confining a chain of single electron bubbles in a linear RF quadrupole trap, a multi-bit quantum register can be implemented. All spins in the register can be initialized to the ground state either by establishing thermal equilibrium at a temperature around 0.1 K and at a magnetic field of 1 T or by sorting the bubbles to be loaded into the trap with magnetic separation. Schemes are designed to address individual spins and to do two-qubit CNOT operations between the neighboring spins. The final readout can be carried out through a measurement similar to the Stern-Gerlach experiment.
We present a blueprint for building a fault-tolerant quantum computer using the spin states of electrons on the surface of liquid helium. We propose to use ferromagnetic micropillars to trap single electrons on top of them and to generate a local magnetic field gradient. Introducing a local magnetic field gradient hybridizes charge and spin degrees of freedom, which allows us to benefit from both the long coherence time of the spin state and the long-range Coulomb interaction that affects the charge state. We present concrete schemes to realize single- and two-qubit gates and quantum nondemolition readout. In our framework, the hybridization of charge and spin degrees of freedom is large enough to perform fast qubit gates and small enough not to degrade the coherence time of the spin state significantly, which leads to the realization of high-fidelity qubit gates.
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.
The system of electrons on liquid helium is an interesting candidate to implement quantum computation, due to the long coherence times of the qubits encoded by the electronic spins. In order to implement the quantum logic operations between the spins, we propose here a configuration, similarly to the cooled ions in a trap, to couple the distant electrons via manipulating their center of mass (CM) vibrations. First, we show that the electrons could be confined in a common harmonic oscillator potential by using an electrostatic field. Then, with a single current pulse (applied on the micro-electrode below the liquid helium) the distant electronic spins can be coupled simultaneously to the CM mode. Finally, by adiabatically eliminating the CM mode, effective interaction between the distant spins is induced for implementing the desired quantum computing.
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.
It has been proposed in literature that a quantum computer can be made utilizing the electronic states of electrons bound to the surface of liquid helium. One can model a single electron on the surface as a 1d hydrogenic atom, providing a set of quantum electronic states which are easily tunable, with an untuned energy gap of 0.488\\,meV (̃120 GHz) between the ground state and the first excited state, and it is these two energy levels that are proposed as the 0 and 1 state of a qubit. To that end, three microfabricated devices are needed: a low temperature electron source of low energy electrons, a detector capable of detecting single electrons, and a microstructure capable of trapping and Stark shifting the energy levels of individual electrons in proximity close enough to perform multiple qubit operations. This dissertation contains a description of the devices microfabricated for these purposes. An electron source based on porous silicon was fabricated, tested, and proven to provide low energy electrons. Other more conventional techniques based on a thoriated tungsten filament were also explored. For electron detection, we have fabricated a transition edge superconducting microbolometer. Tests have shown it is capable of detecting a few eV of energy. For the microstructure, we fabricated a series of columns 200 nm in diameter, 1.5[mu]m in height, separated by 500 nm. For later tests, a microelectrode exposed through a 10[mu]m diameter hole in a ground plane was used. Initial experiments describing bolometer designs and electron confinement are discussed, as well as proposed microfabrication redesign to continue this work. Numerical time series computations of both single (NOT, PHASE) and two qubit (SWAP, [square root]SWAP, CNOT) gates are also presented