Trapped Ion MOC

Curated map of Zoo entries in the Trapped Ion family.

Entries

Entry	Type	Status
cirac-zoller-gate	gate	demonstrated
molmer-sorenson-gate	gate	demonstrated
shuttling-ion-trap-qubit	infrastructure	demonstrated
trapped-ion-qubit	qubit	demonstrated
ytterbium-hyperfine-qubit	qubit	demonstrated

Composition

• gate: 2
• infrastructure: 1
• qubit: 2

Conceptual anchors

• motional-mode-coupling-in-ion-traps is the key evergreen note tying the modality to its entangling-gate layer.
• coherence-time-hierarchy is the right lens for comparing long hyperfine memory times to much faster gate and readout cycles.

Curated synthesis

The most useful way to read this family is as a three-layer stack rather than three unrelated notes.

1. trapped-ion-qubit is the modality baseline

   • Start there when the question is why ions are still canonical: identical qubits, minute-scale coherence, high-fidelity readout, and shared-mode connectivity.
   • It owns the broad platform tradeoff against superconducting and neutral-atom systems.

2. cirac-zoller-gate is the historical mechanism note

   • It explains the original phonon-bus idea in its most literal form: map spin information into motion, apply a conditional phase, map back.
   • Read it when the important question is where trapped-ion entangling gates came from conceptually, not which pulse family dominates today.

3. shuttling-ion-trap-qubit is the scaling architecture note

   • It exists because the same shared-motion resource that gives all-to-all connectivity also stops scaling cleanly in very long chains.
   • QCCD is therefore best understood as an architectural response to motional-mode crowding, not as a new qubit modality.

Modern operational stack

• ytterbium-hyperfine-qubit is the memory-and-readout anchor: clock-state storage, fluorescence detection, and long coherence margins.
• molmer-sorenson-gate is the modern entanglement anchor: virtual-phonon XX interactions, robustness beyond the strict Cirac-Zoller ground-state requirement, and pulse shaping toward 99.9%+ two-qubit fidelity.
• Together they expose the practical systems bottleneck: motional-mode engineering and calibration, not the existence of a clean atomic memory.

Gate-to-architecture decision map

The two gate notes and the shuttling note answer different questions. The first two choose how internal states borrow the phonon bus inside one interaction zone; QCCD chooses how many ions should share that bus before routing replaces longer-range collective motion.

Route	How motion is used	Closure condition	What it buys	Dominant systems debt	Read it when…
cirac-zoller-gate	Sequential sideband pulses map a qubit excitation into a real phonon, apply a conditional phase through a second ion and auxiliary level, then map the phonon back	The selected mode must begin near its ground state and end disentangled from both ions	The cleanest literal picture of a phonon as a quantum data bus and the historical route to trapped-ion universality	Ground-state preparation, auxiliary-level control, and sensitivity to heating during a multi-pulse sequence	the question is how the original bus-mediated gate works or why sideband resolution matters
molmer-sorenson-gate	A bichromatic spin-dependent force drives a closed trajectory in motional phase space and leaves an effective XX interaction	Every significantly driven mode must return to its starting phase-space point at the gate end; ground-state cooling is not required, but the Lamb-Dicke and mode-closure conditions remain	The modern operational default: direct entanglement, multi-ion reach, and better tolerance of imperfect motional preparation	Spectator-mode coupling, detuning and phase calibration, heating, and pulse-shape complexity as modes crowd	the question is how present-day ion processors execute high-fidelity entangling gates
shuttling-ion-trap-qubit	Ions are transported between short-chain memory, interaction, and readout zones; a local MS or related gate still supplies entanglement inside each zone	Transport must preserve internal coherence and deliver a sufficiently cold, well-characterized motional state for the next local gate	Keeps local mode spectra tractable while scaling processor connectivity beyond one long Coulomb crystal	Junction routing, scheduling, transport-induced excitation, recooling, and calibration across many zones	the question has shifted from one gate pulse to machine-scale connectivity and throughput

This map prevents two common category errors. MS gates are less sensitive to the initial phonon occupation than Cirac-Zoller gates, but they are not independent of motion: residual phase-space displacement still leaves spin and motion entangled. Likewise, QCCD does not replace the phonon-bus gate; it repeatedly reconstructs a small, controllable local bus after transport. Read all three through motional-mode-coupling-in-ion-traps to track where motional complexity moves rather than assuming it disappears.

Coherence evidence ladder

Trapped-ion coherence records are easy to flatten into a single platform number, but they answer different architectural questions. Route a claim by the protection resource it consumes before comparing it with another result.

Evidence layer	What is being protected	Resource that creates the margin	What the headline does not establish
Passive clock-state encoding	One ion’s internal-state splitting	First-order magnetic-field insensitivity of a hyperfine clock transition, as in ytterbium-hyperfine-qubit	That the same coherence survives laser exposure, transport, repeated measurement, or a full processor duty cycle
Dynamically decoupled memory	One stored ion over a long idle interval	A sustained refocusing sequence suppresses residual magnetic and oscillator noise	A bare $T_2^{\ast }$, or a memory that remains simultaneously available for arbitrary gates
Sympathetically cooled memory	Internal-state coherence plus usable motional/readout conditions	A second species removes heating without directly scattering from the data ion; long-memory demonstrations may combine this with dynamical decoupling	That cooling itself suppresses magnetic dephasing, or that the result is a property of the qubit species alone
Decoherence-free encoded memory	A logical state distributed across multiple ions	Symmetry cancels collective noise inside a protected subspace; see decoherence-free-subspace	Protection against differential noise, gate faults, leakage, or the physical-qubit overhead of the encoding

The comparison discipline is therefore: use coherence-time-hierarchy to name the measured timescale, then name the active or encoded resource that produced it. In particular, the ten-minute ${}^{171}{\mathrm{Yb}}^{+}$ memory result should be read as a stack—clock-state storage, dynamical decoupling, and sympathetic cooling—not attributed to any one ingredient in isolation. This keeps memory demonstrations informative for architecture without silently turning them into bare-species or processor-wide specifications.

Routing rule: when to stay here versus hand off

• Stay in this MOC for the full modality stack: optical and hyperfine encodings, Cirac-Zoller and Mølmer-Sørensen gates, shared motion, and QCCD scaling.
• Enter ytterbium-hyperfine-qubit or molmer-sorenson-gate directly for the modern Yb + MS implementation slice.
• Hand off to neutral-atom-moc when the comparison shifts from Coulomb-crystal buses to tweezer-rearranged atomic arrays with transient Rydberg interactions.

Scope boundary

This is the authoritative trapped-ion platform map. Species-specific entries are reserved for materially distinct encodings or milestones rather than one page per isotope.