Trapped-Ion Qubits

calendar_today April 14, 2026 article 627 words access_time 4 min replay Modified April 28, 2026

Table of Contents

Optical Vs Hyperfine Qubits

Optical qubit
The ionization of Ca+ allows it to be manipulated via electromagnetic fields
Structure of the electron shell orbitals is determined by the Pauling Diagram
- The principal quantum numbers determine the electron configuration
The bandgap between the ket vectors are in the 400~790 THz range in the visible light spectrum

Hyperfine atom
Dipole-dipole interactions create hyperfine splitting states which are natural Bell states
Triplet state: the states are either aligned or symmetrically coupled (Bell state)
The energy bandgap is only 1 THz; but a smaller energy difference corresponds to a higher coherence time due to the Heisenberg uncertainty principle!
- 10 min coherence (vs 1 second)
- Tradeoff: harder to manipulate individual atoms

Uses a static magnetic field to trap ions in the environment
4 qubits, with each having a ground state $\ket{g_{k}}$ and excited state $\ket{e_k}$
- When $\Delta E$ is equal to the electronic transition energy, can become excited
Quantized phonon modes
- Allow as a “bus-qubit” allowing quantum information to travel across the chain of ions for quantum computation
- Each phonon mode has a ground and excited state per ion
The phonon state is conserved in carrier transition
Edge case: the laser frequency is increased/decreased by a vibrational quantum
- Produces blue/red sidebands
The computational Hilbert space is typically only the first two phonon modes
Phonon mediatead coupling
- The red laser induces lowering of the electronic state when the phonon bus is at $\ket{0_p}$
- This action depends entirely on whether the qubit is in its ground state or excited state
This is the foundation for universal quantum gates and multi-qubit operations

In Ca+, the states are atomic orbitals
- In the ground state, the highest energy level is the $4S_{1/2}$ orbital and represented as $\ket{0}$
- The excited $3D_{5/2}$ state is $\ket{1}$
- There is technically another energy level higher than $3D_{5/2}$, but it has such a low lifetime of just 7 ns, but it does appear relatively frequently.
  - Electron dipole transitions are much more common than quadrapoles and other dipole interactions on the outer shell, hence why we use $3D_{5/2}$ instead of that one

How to initialize all the qubits to $\ket{0}$?
- Optical pumping
  - Drive the Ca+ to an auxiliary state that decays to the $4S_{1/2}$ orbital; can be repeated to make sure

If it jumps from $\ket{0}$ to the really high 4P state, there is a fluorescent light beam that emits; and vice-versa (no light) if it’s from $\ket{1}$ to really high 4P
- This fluorescent light can be easily detected, hence we have our readout

They have to do with vibrations
There are equilibrium positions, but the objects oscillate around those equilibrium positions
Similar to solid (strongly-coupled) state of matter!
- In solids, you actually have a lattice of singly-charged ions that are constantly exchanging electrons with one another, effectively canceling each other out
- Each constriction of those ions cause waves of constrictions felt throughout the lattice that are also felt by the electrons that are being exchanged
  - These vibrations are quantized and thus referred to as phonons
You need to have a vacuum. You can’t do these in the air
- Air is mostly made of diatomic nitrogen/oxygen, which has an average speed of ~170 m/s, so it’s not really measurable in that space. In the words of the instructor: “It’s like hitting an ant with a truck”

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