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New Journal of Physics

Wiring up single electron traps to perform quantum gates

Jorge R. Zurita-Sánchez, Carsten Henkel

Published Aug 15, 2008• 14 citations
Publisher

Abstract

Two electrons in planar Penning traps can be coupled by connecting the trap electrodes with a metallic wire. The wire provides a capacitive and resistive link between the image charges that the electron oscillation (axial motion) is inducing in the electrodes. This can be operated as a quantum network to transfer excitation quanta between the traps and to entangle the two electrons. We give a detailed analysis of this system in the dispersive limit and assess the impact of resistive thermal noise. The latter is found to be remarkably small at temperatures below 4 K in miniaturized planar traps (sizes below 1 mm). The master equation for the two-electron system in the presence of resistive noise is solved exactly. We compute fidelities for basic quantum gates needed in quantum information processing.

DOI
10.1088/1367-2630/10/8/083021

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Two electrons in planar Penning traps can be coupled by connecting the trap electrodes with a metallic wire. The wire provides a capacitive and resistive link between the image charges that the electron oscillation (axial motion) is inducing in the electrodes. This can be operated as a quantum network to transfer excitation quanta between the traps and to entangle the two electrons. We give a detailed analysis of this system in the dispersive limit and assess the impact of resistive thermal noise. The latter is found to be remarkably small at temperatures below 4 K in miniaturized planar traps (sizes below 1 mm). The master equation for the two-electron system in the presence of resistive noise is solved exactly. We compute fidelities for basic quantum gates needed in quantum information processing.
We discuss quantum information processing with trapped electrons. After recalling the operation principle of planar Penning traps we sketch the experimental conditions to load, cool and detect single electrons. Here we present a detailed investigation of a scalable scheme including feasibility studies and the analysis of all important elements, relevant for the experimental stage. On the theoretical side, we discuss different methods to couple electron qubits. We estimate the relevant qubit coherence times and draw implications for the experimental setting. A critical assessment of quantum information processing with trapped electrons is concluding the article.
Quantum computers have the potential to solve problems far beyond the reach of classical computers by using the principles of superposition and entanglement. However, existing platforms face challenges such as short coherence times, interference from the environment, and difficulties in scaling up.Trapped electrons in a planar Penning trap offer a promising alternative. Unlike other qubits, electrons do not interact with nuclear spins, which helps maintain quantum states for much longer. Additionally, their strong confinement allows for fast and precise quantum operations. In our approach, electron spins serve as logical qubits, while their motional states are used for entanglement. Our setup consists of 2-dimensional array of micro-sized Penning traps fabricated on a ceramic chip, placed inside a 1T superconducting magnet and cooled in a dilution refrigerator to reach millikelvin temperatures. This extreme cooling reduces unwanted motion and makes it possible to entangle electron spins and perform quantum gates with high accuracy. At Inter-University Accelerator Centre (IUAC), New Delhi, India, we are developing a prototype planar Penning trap. This new system offers a stable, scalable, and high-coherence platform for quantum computing.
There has been much interest in developing methods for transferring quantum information. We discuss a way to transfer quantum information between two trapped ions through a wire. The motion of a trapped ion induces oscillating charges in the trap electrodes. By sending this current to the electrodes of a nearby second trap, the motions of ions in the two traps are coupled. We investigate the electrostatics of a setup where two separately trapped ions are coupled through an electrically floating wire. We also discuss experimental issues, including possible sources of decoherence.
We present a detailed account of the design choices required for planar Penning traps that feature a highly harmonic confining potential. High harmonicity is indispensable for a number of applications, particularly for confinement of single electrons as qubits in quantum-information processing. The present work extends previous studies [D. Goldmann and G. Gabrielse, Phys. Rev. A 81, 052335 (2010)] by a fully analytic treatment of finite electrode gaps and their relevance for small traps on the millimetre size scale and below, when relative gap sizes are non-negligible. We derive the overall trap potential with a particular focus on different models of finite-gap potentials and show how to find the optimum trap geometry and electrode voltages to minimize anharmonicities. The analytic calculations are compared with detailed finite-element simulations.
We investigate the generation of entanglement between the axial degrees of freedom of electrons confined in separated locations in planar Penning traps. We show that there are two different sources of entanglement: one is related with the mechanism of switching on and off the electrical coupling between the two electrons, and the other is due to the two-quanta-transition term of the coupling interaction. We show that the degree of entanglement can be controlled by adjusting the strength of the coupling between the traps and the time of interaction. We show that the coupled electrons behave as a temporal active interferometer.