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arXiv:2303.03688 · Physical Review Applied

Blueprint for quantum computing using electrons on helium

Erika Kawakami, Jiabao Chen, Mónica Benito, Denis Konstantinov

Published Nov 9, 2023• 30 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevapplied.20.054022

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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.
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.
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.
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.
Hybridizing different degrees of freedom or physical platforms potentially offers various advantages in building scalable quantum architectures. We study the hybrid quantum system of a single electron trapped on a solid neon surface, where the motional states of an electron interact with microwave photons in an on-chip superconducting cavity. By applying a nonuniform magnetic field with a gradient along the vibrational axis, the spin-orbit coupling of the electron's spin degree of freedom and its lateral motion can be engineered. We show that the electron's spin states with ultralong coherence time as a quantum memory can be explored to store the quantum information of a superconducting qubit. As an extension, we also propose to implement high-quality quantum state transfer between the spin states of two electrons trapped in spatially separated superconducting cavities. The present work may have practical applications for realizing floating-electron-based hybrid quantum computation.
The promise of quantum computing has driven a persistent quest for new qubit platforms with long coherence, fast operation, and large scalability. Electrons, ubiquitous elementary particles of nonzero charge, spin, and mass, have commonly been perceived as paradigmatic local quantum information carriers. Despite superior controllability and configurability, their practical performance as qubits via either motional or spin states depends critically on their material environment. Here we report our experimental realization of a new qubit platform based upon isolated single electrons trapped on an ultraclean solid neon surface in vacuum. By integrating an electron trap in a circuit quantum electrodynamics architecture, we achieve strong coupling between the motional states of a single electron and a single microwave photon in an on-chip superconducting resonator. Qubit gate operations and dispersive readout are implemented to measure the energy relaxation time T1T_1T1​ of 15μ\muμs and phase coherence time T2T_2T2​ over 200ns. These results indicate that the electron-on-solid-neon qubit already performs near the state of the art as a charge qubit.
We propose a scheme to read out the spin of a single electron quantum bit in a surface Paul trap using oscillating magnetic-field gradients. The readout sequence is composed of cooling, driving, amplification, and detection of the electron's motion. We study the scheme in the presence of noise and trap anharmonicities at liquid-helium temperatures. An analysis of the four procedures shows short measurement times ($25\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{s}$) and high fidelities (99.799.7%99.7) are achievable with realistic experimental parameters. Our scheme performs the function of fluorescence detection in ion trapping schemes, highlighting the potential to build all-electric quantum computers based on trapped electron-spin qubits.