Ion Quantum Computing & Simulation

Ions are excellent quantum systems for both quantum computing and quantum simulation. They can be ultimately controlled in all of their quantum states (electronic and motional) and well isolated from the environment to provide excellent qubits.

To prepare ions for quantum computing and quantum simulation applications, atoms are ionized, laser-cooled and electromagnetically trapped in so-called Paul or Penning-type traps. The ion traps can be three-dimensional or complex "two-dimensional" chip-based surface traps. Such ion traps are often designed and manufactured in institutes but also nowadays commercially available from companies such as Alpine Quantum Technologies (AQT) or Infineon. The trapping of the ions is done within ultra high-vacuum systems, sometimes even in cryogenic environment, and requires specialized laser systems for ionization, cooling and repumping. In addtion, one needs rf fields, low-noise voltages, and magnetic fields to realize the ion traps.

• Single-qubit gates are realized by coherently driving a transition between the two qubit states |0> and |1> of one ion for a well defined time with well defined phase. The methods depend on the involved qubit states:
• For optical quits, one usually uses a laser directly addressing the optical clock transition. Typically, one needs high-power low-noise lasers with linewidths on the order of few Hz that are frequency-stabilized to the optical clock transition with accuracy on the order of few Hz. 
• Hyperfine and nuclear qubits are addressed in two ways. Either one applies
• coherent radiofrequency or microwave fields resonant to the energy difference of the involved qubit states, or
• two lasers with optical frequencies that differ by the energy difference of the involved qubit states, that have a well-defined relative phase, and that are each close to a common upper quantum state for a well defined time with well defined phase.
• Two-qubit gates are realized in many different ways. 
  A simplified picture for one of them (a version of the so-called Cirac-Zoller-Gate) using the optical qubit is the following: All ions (eg. ion 1 and ion 2) are prepared in the motional ground state within the trapping potential. Then one shines in a laser that is resonant to the transition of one qubit state, e.g. |0>, to the other qubit state |1> on ion 1 but in such a way that ion 1 is transferred to |1> and at the same time both ions 1 and 2, which are coupled to each other by the Coulomb interaction of the charged ions, are excited to a higher motional state. This requires an optical frequency of the excitation laser that corresponds to the transition frequency of resting ions plus the frequency of the motional excitation, which is on the order of the ion trap frequency around a few MHz. If the second ion 2 is subsequently locally addressed with a laser resonant to the optical transition of resting ions minus the frequency of the motional excitation, it is also excited to |1> and both ions are again at rest. If, however the first ion 1 had been in state |1> and not in |0> at the beginning of the pulse sequence, no excitation of ion 2 would occur. This is a two-qubit gate, because the final state of ion 2 depends on the initial state of ion 1.
  

To read out the result of the computation performed by gate sequences, one reads out the final quantum state of the ions by shining in quantum-state-selective lasers, which are resonant to transitions that scatter many photons onto photodectors and/or cameras. The detection step might require additional repumping and prior optical pumping or coherent transfer.

Instead of applying gate sequences like in (digtial) quantum computing, for quantum simulation (analog quantum computing) one applies

• designed artificial potentials (optical, electric or magnetic fields), or
• uses spin exchange (magnetic) interactions between the ions

to realize certain "Hamiltonians" withing the system. One then observes the time dependent evolution of the ions' quantum states or the finally realized quantum state under the influence of this Hamiltonian. Detection is again achieved via fluorescence detection and imaging.

Laser play a key role in ion quantum computing and simulation. All of our products designed for quantum technologies are not only suited for this application but also integrated in scientific and many commercial solutions. TOPSELLERs and customized versions comprise:

• Tunable diode laser systems
• Clock Laser Systems
• Cw fiber amplifiers and Raman fiber amplifiers
• Optical Frequency Combs
• Wavelength meters
• Frequency and phase stabilization electronic modules
• Complete laser rack systems containing the above mentioned products

Please contact our sales and application experts for consultation of the best suited solutions.