Trapped-ion quantum computer

A trapped-ion quantum computer (TIQC) is one proposed approach to a large-scale quantum computer. Ions, or charged atomic particles, can be confined and suspended in free space using electromagnetic fields. Qubits are stored in stable electronic states of each ion, and quantum information can be transferred through the collective quantized motion of the ions in a shared trap (interacting through the Coulomb force). Lasers are applied to induce coupling between the qubit states (for single qubit operations) or coupling between the internal qubit states and the external motional states (for entanglement between qubits). The fundamental operations of a quantum computer have been demonstrated experimentally with the highest accuracy in trapped-ion systems. Promising schemes in development to scale the system to arbitrarily large numbers of qubits include transporting ions to spatially distinct locations in an array of ion traps, building large entangled states via photonically connected networks of remotely entangled ion chains, and combinations of these ideas. This makes the trapped-ion quantum computer system one of the most promising architectures for a scalable, universal quantum computer. As of December 2023, the largest number of particles to be controllably entangled is 32 trapped ions.

History The first implementation scheme for a controlled-NOT quantum gate was proposed by Ignacio Cirac and Peter Zoller in 1995, specifically for the trapped-ion system. The same year, a key step in the controlled-NOT gate was experimentally realized at NIST Ion Storage Group, and research in quantum computing began to accelerate worldwide.

In 2021, researchers from the University of Innsbruck presented a quantum computing demonstrator that fits inside two 19-inch server racks, the world's first quality standards-meeting compact trapped-ion quantum computer.

Paul trap

The electrodynamic quadrupole ion trap now used in trapped-ion quantum computing research was invented in the 1950s by Wolfgang Paul (who received the Nobel Prize for his work in 1989). Charged particles cannot be trapped in 3D by only electrostatic forces because of Earnshaw's theorem. Instead, an electric field oscillating at radio frequency (RF) is applied, forming a potential with the shape of a saddle spinning at the RF frequency. If the RF field has the right parameters (oscillation frequency and field strength), the charged particle becomes effectively trapped at the saddle point by a restoring force, with the motion described by a set of Mathieu equations. This saddle point is the point of minimized energy magnitude, | E ( x ) | {\displaystyle |E(\mathbf {x} )|} , for the ions in the potential field. The Paul trap is often described as a harmonic potential well that traps ions in two dimensions (assume x ^ {\displaystyle {\hat {x}}} and y ^ {\displaystyle {\widehat {y}}} without loss of generality) and does not trap ions in the z ^ {\displaystyle {\widehat {z}}} direction. When multiple ions are at the saddle point and the system is at equilibrium, the ions are only free to move in z ^ {\displaystyle {\widehat {z}}} . Therefore, the ions will repel each other and create a vertical configuration in z ^ {\displaystyle {\widehat {z}}} , the simplest case being a linear strand of only a few ions. Coulomb interactions of increasing complexity will create a more intricate ion configuration if many ions are initialized in the same trap. Furthermore, the additional vibrations of the added ions greatly complicate the quantum system, which makes initialization and computation more difficult. Once trapped, the ions should be cooled such that k B T ≪ ℏ ω z {\displaystyle k_{\rm {B}}T\ll \hbar \omega _{z}} (see Lamb Dicke regime). This can be achieved by a combination of Doppler cooling and resolved sideband cooling. At this very low temperature, vibrational energy in the ion trap is quantized into phonons by the energy eigenstates of the ion strand, which are called the center of mass vibrational modes. A single phonon's energy is given by the relation ℏ ω z {\displaystyle \hbar \omega _{z}} . These quantum states occur when the trapped ions vibrate together and are isolated from the external environment. If the ions are not properly isolated, noise can result from ions interacting with external electromagnetic fields, which creates random movement and destroys the quantized energy states.

Requirements for quantum computation

The full requirements for a functional quantum computer are not entirely known, but there are many generally accepted requirements. David DiVincenzo outlined several of these criteria for quantum computing.

Qubits Any two-level quantum system can form a qubit, and there are two predominant ways to form a qubit using the electronic states of an ion:

Two ground state hyperfine levels (these are called "hyperfine qubits") A ground state level and an excited level (these are called the "optical qubits") Hyperfine qubits are extremely long-lived (decay time of the order of thousands to millions of years) and phase/frequency stable (traditionally used for atomic frequency standards). Optical qubits are also relatively long-lived (with a decay time of the order of a second), compared to the logic gate operation time (which is of the order of microseconds). The use of each type of qubit poses its own distinct challenges in the laboratory.

… excerpt ends here. Continue reading the full article.