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Towards spin-based quantum computing on liquid helium

S. A. Lyon, Guillaume Sabouret

Published Jan 1, 2007• 2 citations
OpenAlex

Abstract

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.

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Electrons floating on the surface of liquid helium are possible qubits for quantum information processing. Varying electric potentials do not modify spin states, which allows their transport on helium using a charge-coupled device (CCD)-like array of underlying gates. This scheme depends on an efficient intergate electron transfer and on the absence of electron traps. We will present a measurement of the charge transfer efficiency (CTE) of electrons clocked back and forth above a short CCD-like structure. The CTE obtained at low clocking frequencies is 0.999 with an electron density of about 4electrons∕μm2. We find no evidence for deep electron trapping.

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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.
Electrons floating on the surface of liquid helium are possible qubits for quantum information processing. Varying electric potentials do not modify spin states, which allows their transport on helium using a charge-coupled device (CCD)-like array of underlying gates. This scheme depends on an efficient intergate electron transfer and on the absence of electron traps. We will present a measurement of the charge transfer efficiency (CTE) of electrons clocked back and forth above a short CCD-like structure. The CTE obtained at low clocking frequencies is 0.999 with an electron density of about 4electrons∕μm2. We find no evidence for deep electron trapping.
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.
Electrons floating on the surface of superfluid helium have been suggested as promising mobile spin quantum bits (qubits). Transferring electrons extremely efficiently in a narrow channel structure with underlying gates has been demonstrated, showing no transfer error while clocking 10 9 pixels in a 3-phase charge coupled device (CCD). While on average, one electron per channel was clocked, it is desirable to reliably obtain a single electron per channel. We have designed an electron turnstile consisting of a narrow (0.8μm) channel and narrow underlying gates (0.5μm) operating across seventy-eight parallel channels. Initially, we find that more than one electron can be held above the small gates. Underlying gates in the turnstile region allow us to repeatedly split these electron packets. Results show a plateau in the electron signal as a function of the applied gate voltages, indicating quantization of the number of electrons per pixel, simultaneously across the seventy-eight parallel channels.
Electrons floating on the surface of liquid helium are possible spin qubits for quantum information processing. 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. This approach depends upon efficient intergate transfer of individual electrons. Measurements are presented here of the charge transfer efficiency of few electrons clocked back and forth above a short microscopic CCD-like structure. A charge transfer efficiency of 0.999 999 92 is obtained for a clocking frequency of 800kHz.
Unprecedented transport efficiency is demonstrated for electrons on the surface of micron-scale superfluid helium-filled channels by co-opting silicon processing technology to construct the equivalent of a charge-coupled device. Strong fringing fields lead to undetectably rare transfer failures after over a billion cycles in two dimensions. This extremely efficient transport is measured in 120 channels simultaneously with packets of up to 20 electrons, and down to singly occupied pixels. These results point the way towards the large scale transport of either computational qubits or electron spin qubits used for communications in a hybrid qubit system.
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.