02 · Trapped ions

Trapped ions

Shared motion. Selected pairs.

SCHEMATIC GEOMETRY

CALCULATED · IDEAL MODEL

RXX(θ) = cos(θ/2)I − i sin(θ/2)X⊗X; C = |sin θ|; d³ = 2kₑe²/(mωz²); ωCOM = ωz; ωstretch = √3ωz

Assumptions and limits

Only the selected pair is a simulated quantum register. It starts in |00⟩, in basis order 00, 01, 10, 11. The other four numbered ions provide architecture context.
The gate angle is in radians, not elapsed hardware time. Transport progress changes the drawing only and does not apply a logical SWAP or alter the modeled state.
The motion inset uses isolated equal-mass singly charged ions with illustrative mass 171u and a harmonic axial trap. Frequencies are MHz; displayed separation follows Coulomb equilibrium.
The inset shows enlarged classical normal-mode displacements about equilibrium, not literal ground-state trajectories. Its M1/M2 markers are separate from Q1–Q6.
Ideal unitary dynamics exclude motional heating, imperfect cooling, leakage, pulse errors, crosstalk and readout errors. Probabilities are analytical model outputs, not hardware measurements.
Architecture positions and regrouping paths are conceptual and not to scale. Electrodes provide confinement; the drawing omits optical hardware, detailed trap voltages, ion reordering and spectator motion.

Sources · 11 references

IonQ · Trapped-ion technologyUndated · Checked 5 September 2026 · Ion-chain architecture, laser control and fluorescence readout.
IonQ · Native gatesUndated · Checked 5 September 2026 · Aria MS and Forte ZZ gate distinctions; Aria marked retired.
Quantinuum · H2 operationUndated · Checked 5 September 2026 · Ion transport, gate scheduling and RZZ/RXX basis conversion.
Pino et al. · QCCD architecture (2021)Nature 592, 209–213 (2021) · Integrated ion transport, small crystals and optical addressing.
Wineland et al. · Trapped-ion quantum control (1998)May–June 1998 · Coulomb equilibrium, collective motion and two-ion axial normal modes.
Grzesiak et al. · Entangling gates (2020)11 June 2020 · Collective-mode coupling, designed pulses and constrained simultaneous entangling operations.
Maldacena & Susskind · Cool horizons for entangled black holes (2013)3 June 2013 · The ER = EPR conjecture, cited for the Frontier chapter.
Maldacena · Eternal black holes in AdS (2001)JHEP 0304, 021 (2003) · The thermofield double behind the ER = EPR conjecture.
Kobrin, Schuster & Yao · Comment on "Traversable wormhole dynamics on a quantum processor" (2023)15 February 2023 · Contests the 2022 processor "wormhole" claim; the original paper carries a later author correction.
Yao, Potter, Potirniche et al. · Discrete time crystals: rigidity, criticality, and realizations (2016)Phys. Rev. Lett. 118, 030401 (2017) · Floquet time-crystal theory, cited for the Frontier chapter; not simulated here.
Zhang, Hess, Kyprianidis et al. · Observation of a discrete time crystal (2016)Nature 543, 217–220 (2017) · First observation, on a ten-ion chain.

Starting 3D…