Quantum experiments on trapped atomic ions have demonstrated excellent coherence times and high-fidelity gate operations. This makes the platform well-suited for the engineering of quantum computing devices, but it also presents a set of challenges to the classical electronics that control these systems. Today, many trapped ion researchers use FPGAs to address some of the timing and synchronization challenges that they face. In this application note, we will demonstrate how a deeper integration between the control electronics and FPGAs can enable digital signal processing on hardware to solve challenges of long waveform upload times and wasted hardware memory across parameter scans, single experimental shots, and individual pulses.
Introduction to Trapped Ion Qubits
When a neutral atom loses an electron, a positively charged ion is created. Because of their large charge-to-mass ratio, ions interact strongly with electric and magnetic fields and can be trapped in free space either through a combination of static electric and magnetic fields in a Penning trap or, more commonly, through dynamic electric fields in a Paul trap.
Atomic species selected for trapped-ion applications tend to have a relatively simple energy level structure, where two states are selected as the qubit states |0⟩ and |1⟩ to carry quantum information. The energy splitting between these levels can fall either into the microwave or optical regimes, and we refer to the resulting qubits as microwave qubits or optical qubits, respectively.
Additionally, couplings to other atomic energy levels are used to perform many operations such as laser cooling, state initialization, and certain logical operations between the qubit levels. Because these couplings are in the optical regime for both microwave and optical qubits, laser control is an essential component of the control system for all trapped ion systems.
An indispensable tool for electronic control of laser systems is the Acousto-Optic Modulator (AOM). This device modulates the frequency of an input laser beam at IF frequencies. In this sense, the AOM behaves as a mixer with an IF frequency of order 100 MHz and an “LO” frequency in the hundreds of terahertz. One key difference between an AOM and a mixer however is that the modulation spatially deflects the output beam. An important consequence of this is that the LO leakage and other undesired spectral components can be easily removed by using a pinhole at the desired location as a spatial filter. This simplifies the signal requirements and makes the AOM a highly effective optical switch.
Cooling, Pumping, and Readout
Quantum computing is characterized by a phase coherence between qubit states, and this coherence requirement is often reflected in control electronics. Nonetheless, there are several operations such as doppler cooling, optical pumping, and state readout that are dissipative, removing the phase dependence and significantly relaxing the requirements for coherence and modulation complexity.
There are many methods for laser cooling trapped ions, and the simplest is doppler cooling. This method involves the application of near-resonant laser light to the ions. Typically, there is more than one possible photon emission path so additional lasers are used, and sidebands must be applied to the lasers using an electro-optic modulator (EOM) to continuously repump the ions. State initialization in trapped ions can also be performed by a dissipative process using near-resonant lasers. By removing a specific repump line from a cooling laser, the population quickly becomes trapped in the desired state. Finally, state readout in trapped ions can be performed via state-dependent fluorescence, again by application of resonant laser fields.
The resonant lasers used to apply these rotations are typically controlled by switching the RF drive signal to either an EOM to switch sidebands on and off or more commonly to an AOM to switch the entire beam on and off. This drive signal may be generated by a CW frequency source such as a Direct Digital Synthesizer (DDS) whose output signal passes through an RF switch controlled by a digital signal. Although this is a very simple modulation scheme, it is important that the digital control signal has a precise timing relationship with the rest of the experiment, and it is therefore often generated from an FPGA-based controller.
Microwave Control
In trapped-ion experiments that use microwave qubits, researchers can manipulate the qubit state by directing microwave radiation through an antenna towards the ions. Because inter-ion spacing is very small, it is not possible to individually address ions within a chain with this free-space radiation, and the result is typically a global rotation of the qubits. Despite this drawback, microwave rotations of trapped ion qubits have produced some of the highest fidelity quantum operations ever demonstrated. Two-qubit interactions can also be realized with microwave fields using magnetic-field gradients or near-field radiation. Finally, even for laser-driven gates, a microwave source is often required as a part of the laser-locking circuit.
