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Low Temperature Physics

Quantum computing with bits made of electrons on a helium surface

Arnold J. Dahm

Published Jun 1, 2003• 3 citations
Publisher

Abstract

We describe a quantum computer based on electrons supported by a helium film and localized laterally by small electrodes. Each quantum bit (qubit) is made of combinations of the ground and first excited state of an electron trapped in the image potential well at the surface. Mechanisms for preparing the initial state of the qubit, operations with the qubits, and a proposed readout are described. This system is, in principle, capable of 105 operations in a decoherence time.

DOI
10.1063/1.1542534

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We describe a quantum computer based on electrons supported by a helium film and localized laterally by small electrodes. Each quantum bit (qubit) is made of combinations of the ground and first excited state of an electron trapped in the image potential well at the surface. Mechanisms for preparing the initial state of the qubit, operations with the qubits, and a proposed readout are described. This system is, in principle, capable of 105 operations in a decoherence time.
A quantum computer based on the manipulation and detection of coherent states of electrons localized above a helium film is described. Each quantum logic element (qubit) is made of a combination of the ground and first excited states of an electron trapped in the image potential well at the surface. Potentials applied to micro-electrodes located beneath each electron confine the lateral motion of the electron and are used to operate gates. Mechanisms for one- and two-qubit logic operations and a readout of the final state are discussed. The principle decay channel for the excited state is via the emission of one phonon into the bulk liquid. Dechoherence times are calculated to be of order of 100 μs and allow greater than 104 serial operations.
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
A quasi-two-dimensional set of electrons (1 < N < 10(9)) in vacuum, trapped in one-dimensional hydrogenic levels above a micrometer-thick film of liquid helium, is proposed as an easily manipulated strongly interacting set of quantum bits. Individual electrons are laterally confined by micrometer-sized metal pads below the helium. Information is stored in the lowest hydrogenic levels. With electric fields, at temperatures of 10(-2) kelvin, changes in the wave function can be made in nanoseconds. Wave function coherence times are 0.1 millisecond. The wave function is read out with an inverted dc voltage, which releases excited electrons from the surface.
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.
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.