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Trapped-ion entangling gates with bichromatic pair of microwave fields and magnetic field gradient

R. T. Sutherland

Published Dec 4, 2023• 0 citations
OpenAlex

Abstract

A trapped-ion quantum logic gate and a method of operating the trapped-ion quantum logic gate are provided. The trapped-ion quantum logic gate includes at least one ion having two internal states and forming a qubit having a qubit transition frequency ω00, a magnetic field gradient, and two microwave fields. Each of the two microwave fields has a respective frequency that is detuned from the qubit transition frequency ω0 by frequency difference δ. The at least one ion has a Rabi frequency Ωμ due to the two microwave fields and a Rabi frequency Ωg due to the magnetic field gradient. The method includes applying the magnetic field gradient and the two microwave fields to the at least one ion such that a quantity Ωg/δ is in a range between zero and 5×10−2.

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A trapped-ion quantum logic gate and a method of operating the trapped-ion quantum logic gate are provided. The trapped-ion quantum logic gate includes at least one ion having two internal states and forming a qubit having a qubit transition frequency ω00, a magnetic field gradient, and two microwave fields. Each of the two microwave fields has a respective frequency that is detuned from the qubit transition frequency ω0 by frequency difference δ. The at least one ion has a Rabi frequency Ωμ due to the two microwave fields and a Rabi frequency Ωg due to the magnetic field gradient. The method includes applying the magnetic field gradient and the two microwave fields to the at least one ion such that a quantity Ωg/δ is in a range between zero and 5×10−2.
Oscillating magnetic fields and field gradients can be used to implement single-qubit rotations and entangling multiqubit quantum gates for trapped-ion quantum information processing (QIP). With fields generated by currents in microfabricated surface-electrode traps, it should be possible to achieve gate speeds that are comparable to those of optically induced gates for realistic distances between the ion crystal and the electrode surface. Magnetic-field-mediated gates have the potential to significantly reduce the overhead in laser-beam control and motional-state initialization compared to current QIP experiments with trapped ions and will eliminate spontaneous scattering, a fundamental source of decoherence in laser-mediated gates.
A platform for trapping atomic ions includes a substrate and a plurality of metallization layers that overlie the substrate. The metallization layer farthest from the substrate is a top layer patterned with electrostatic control trap electrodes and radio-frequency trap electrodes. Another metallization layer is a microwave layer patterned to define a microwave circuit. The microwave layer lies below the top layer. The microwave circuit is adapted to generate, in use, a microwave magnetic field above the electrostatic control and radio-frequency trap electrodes. The top metallization layer includes slots that, in use, are penetrated by microwave energy from the microwave circuit.
We present a general theory for laser-free entangling gates with trapped-ion hyperfine qubits, using either static or oscillating magnetic-field gradients combined with a pair of uniform microwave fields symmetrically detuned about the qubit frequency. By transforming into a 'bichromatic' interaction picture, we show that either or geometric phase gates can be performed. The gate basis is determined by selecting the microwave detuning. The driving parameters can be tuned to provide intrinsic dynamical decoupling from qubit frequency fluctuations. The gates can be implemented in a novel manner which eases experimental constraints. We present numerical simulations of gate fidelities assuming realistic parameters.
An ion trap chip, which may be used for quantum information processing and the like, includes an integrated microwave antenna. The antenna is formed as a radiator connected by one of its ends to the center trace of a microwave transmission line and connected by its other end to a current return path through a ground trace of the microwave transmission line. The radiator includes several parallel, coplanar radiator traces connected in series. The radiator traces are connected such that they all carry electric current in the same direction, so that collectively, they simulate a single, unidirectionally flowing sheet of current. In embodiments, induced currents in underlying metallization planes are suppressed by parallel slots that extend in a direction perpendicular to the radiator traces.
Microwave-driven quantum logic gates in trapped-ion systems offer a scalable and laser-free alternative to optical control, with the potential for robust integration into surface-electrode trap architectures. In this work, we present a systematic design guideline for planar ion traps optimized for fast two-qubit microwave gates using chip-integrated conductors. We investigate two electrode configurations, one employing a single microwave line for driving σ transitions, and another with two symmetric lines for π transitions. Through finite-element simulations, we analyze ion height, magnetic field gradients, heating effects, and gate durations under realistic cryogenic conditions. Our results show that both configurations can achieve two-qubit gate times in the order of 10 μs for Be+9 and Ca+40 ions.
A method for preparing an entangled quantum state of an atomic ensemble is provided. The method includes loading each atom of the atomic ensemble into a respective optical trap; placing each atom of the atomic ensemble into a same first atomic quantum state by impingement of pump radiation; approaching the atoms of the atomic ensemble to within a dipole-dipole interaction length of each other; Rydberg-dressing the atomic ensemble; during the Rydberg-dressing operation, exciting the atomic ensemble with a Raman pulse tuned to stimulate a ground-state hyperfine transition from the first atomic quantum state to a second atomic quantum state; and separating the atoms of the atomic ensemble by more than a dipole-dipole interaction length.