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Quantum Information and Computation

Quantum computing with electrons floating on liquid helium

M. I. Dykman, P. M. Platzman

Published Dec 1, 2001• 8 citations
Publisher

Abstract

Electrons on a helium surface form a quasi two-dimensional system which displays the highest mobility reached in condensed matter physics. We propose to use this system as a set of interacting quantum bits. We will briefly describe the system and discuss how the qubits can be addressed and manipulated. The working frequency of the proposed quantum computer is ~ 1GHz. Careful analysis shows that the relaxation rate can be at least 5 orders of magnitude smaller, for low temperatures.

DOI
10.26421/qic1.s-10

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•Jan 1, 2007•2 citations
Electrons on a helium surface form a quasi two-dimensional system which displays the highest mobility reached in condensed matter physics. We propose to use this system as a set of interacting quantum bits. We will briefly describe the system and discuss how the qubits can be addressed and manipulated. The working frequency of the proposed quantum computer is ~ 1GHz. Careful analysis shows that the relaxation rate can be at least 5 orders of magnitude smaller, for low temperatures.
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.
Quantum computing promises new ways of solving some mathematical problems by making use of the state superposition properties of quantum bits (qubits) to compute in parallel all the results of a mathematical expression, which, in some cases, provides a computational advantage over classical computing. Various physical systems have been suggested as possible qubits. All of them have met significant challenges in their implementation into a quantum computer, in part because the usefulness of quantum computing is tied to its scalability. Electrons floating above superfluid helium are potential qubits because the exceptional lack of interaction with their surroundings should translate into extended quantum coherence times. Varying electric potentials are not expected to modify spin states, which allows their transport on helium using a charge-coupled device (CCD)-like array of underlying gates. That transport could move single qubits between memory, interaction and read-out gates that would constitute a quantum computer. The scalability of this scheme depends critically on efficient inter-gate electron transfer. This dissertation starts by presenting Shor's prime factorization algorithm as a motivation for quantum computing, justifying the use of electron spins on liquid helium as qubits and explaining the inner-workings of this type of quantum computer. But the essence of this work is experimental. Our setup had to be built from scratch. We then measured the inter-gate charge transfer efficiency (CTE) on thick (∼ 0.9 mm) helium and on helium in shallow (∼ 3 µm deep) channels. On thick helium, at low frequencies, we measured a CTE of 0.9990 (at a density of 4 electrons/µm2) that was governed by the diffusion of electrons through our millimeter-size CCD gates. In channels (12 × 10 µm gates), the CTE was found to be 0.99999992 ±6 × 10-8 for about one electron per gate and probably limited by shallow fabrication-related potential traps. This ability to reliably clock few charges for long distances is an important step towards a proof of the scalability of electron spins on helium as a quantum computing scheme.