Cirac-Zoller gate for trapped ion qubits

Figure

Description

The key idea of the Cirac–Zoller proposal is to mediate the interaction between two long-lived ion qubits through the joint motion of the complete chain of trapped ions. The first quantum computer proposal.

Motivation

A quantum computer can be implemented with cold ions confined in a linear trap and interacting with laser beams. The quantized vibrations of the ions in the trap (“phonons”) can serve as a quantum bus, enabling highly controllable interactions between ions.

References

• https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.74.4091
• https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.75.4714
• https://www.nature.com/articles/nature01494

Linked Papers

• cirac-zoller-1995-trapped-ion-gate

Related Entries

• molmer-sorenson-gate

Seed Metadata

• date_published: 2015-05-15

Physics

Two-qubit gate for trapped ions using the shared motional (phonon) mode as a quantum bus. The qubit is encoded in two internal electronic states of each ion. Gate sequence:

1. Red sideband $\pi$-pulse on ion $j$: maps $\alpha |g⟩+\beta |e⟩$ onto phonon mode $\alpha |0⟩+\beta |1⟩$
2. Conditional phase gate on ion $k$ (2$\pi$ pulse on $|e,1⟩$ transition): acquires phase conditional on phonon + qubit state
3. Reverse red sideband on ion $j$: restores phonon to $|0⟩$

Requires ground-state cooling of motional mode ($\bar{n}\approx 0$) and Lamb-Dicke regime ($\eta =k\sqrt{\hslash /2M\nu }\ll 1$).

Key Metrics

Metric	Value	Notes	Fidelity reference
Qubit coherence $T_1$	>1000 s	Hyperfine qubits (e.g., ${}^{171}$Yb${}^{+}$)	Cirac & Zoller 1995
Qubit coherence $T_2$	1–600 s	With dynamical decoupling	Wang et al. 2021
Gate fidelity (1Q)	99.9999%	Record: Harty et al. 2014	Harty et al. 2014
Gate fidelity (2Q)	99.5–99.9%	Mølmer-Sørensen or CZ variant	Ballance et al. 2016
Gate time (1Q)	1–10 μs	Microwave or Raman	—
Gate time (2Q)	10–200 μs	Laser-mediated	—
Readout fidelity	99.9%+	Fluorescence detection	Myerson et al. 2008
Qubit footprint	~5 μm ion spacing	In linear Paul trap	—
Operating temperature	Room temp (trap) / 4K (cryo)	Vacuum chamber	—
Connectivity	All-to-all (small chains)	Via shared phonon modes	—

Related Qubits

• loss-divincenzo-qubit — semiconductor analogue