Trapped Ion Quantum Computers

Trapped Ion Quantum Computers

How Trapped Ions Work

Trapped ion quantum computers use individual atoms as qubits. Typically ytterbium (Yb+) or barium (Ba+) ions are trapped in electromagnetic (Paul) traps in ultra-high vacuum. The qubit states are encoded in the electronic energy levels of the ion.

Transitions between states are driven by carefully tuned laser pulses or microwave radiation. The frequency must match the energy gap between levels with extraordinary precision.

The Paul Trap

A Paul trap uses oscillating electric fields (radio frequency) to confine charged particles in 3D. The ions line up in a chain along the trap axis due to mutual Coulomb repulsion.

The normal modes are the bus that enables two-qubit gates: by exciting shared phonon modes, two distant ions can interact.

Single-Qubit Gates

Single-qubit gates are implemented by targeting an individual ion with a focused laser beam. The laser frequency is tuned to the qubit transition frequency, and the pulse duration controls the rotation angle.

Gate fidelity: >99.9% single-qubit fidelity is routinely achieved on trapped ion systems.

Two-Qubit Gates: The Molmer-Sorensen Gate

The workhorse two-qubit gate for trapped ions is the Molmer-Sorensen (MS) gate. It uses two simultaneous laser beams that couple the electronic states of both ions to shared phonon modes (collective motion).

The MS gate implements: $e^{-i\chi {\sigma }_x\otimes {\sigma }_x}$ (an XX interaction between the two ions). For $\chi =\pi /4$, this is equivalent to a maximally entangling gate (equivalent to CNOT up to single-qubit rotations).