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Euromicro Conference on Digital System Design (DSD)

FPGA-Based Real-Time Laser Beam Profiling and Stabilization System for Quantum Simulation Applications

Stefano Marti, Enis Mustafa, Giacomo Bisson, Pratyush Anand, Philipp Fabritius, Tilman Esslinger, Abdulkadir Akın

Published Sep 6, 2023• 1 citation
Publisher

Abstract

Lasers are imperative in quantum simulation experiments to trap and cool atoms. With the growing complexity of experimental setups, precise control and stability of the position and exotic shape of lasers have become essential for high-fidelity operations. However, disturbances such as temperature fluctuations, mechanical vibrations, deformation of materials, and acoustic noise pose challenges to fulfill these requirements. In this paper, we propose and evaluate the first system for stabilizing the laser's beam position using two high-resolution cameras with high frame-rates, and image processing in a field-programmable gate array (FPGA) with low latency and subsequent in-loop feedback to the laser control. The proposed image processing hardware extracts the Gaussian beam distribution from two 5 MP cameras at 47 fps and 435 ns latency. These are fed to four proportional-integral-derivative (PID) controllers implemented on the FPGA. The PID modules provide feedback through parallel digital-to-analog converter (DAC) channels for steering mirrors to stabilize the beam within 5 µm accuracy. Using two cameras at distinct sample distances on the optical axis allows for controlling the incidence angle of the laser beam onto the image planes. The current system is a building block for future extensions allowing real-time phase-feedback on optical lattices, stabilization of independent optical tweezers in an array, and focus position stabilization of transverse electromagnetic (e.g. TEM01) modes enabling large-scale quantum simulations.

DOI
10.1109/dsd60849.2023.00012

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Lasers are imperative in quantum simulation experiments to trap and cool atoms. With the growing complexity of experimental setups, precise control and stability of the position and exotic shape of lasers have become essential for high-fidelity operations. However, disturbances such as temperature fluctuations, mechanical vibrations, deformation of materials, and acoustic noise pose challenges to fulfill these requirements. In this paper, we propose and evaluate the first system for stabilizing the laser's beam position using two high-resolution cameras with high frame-rates, and image processing in a field-programmable gate array (FPGA) with low latency and subsequent in-loop feedback to the laser control. The proposed image processing hardware extracts the Gaussian beam distribution from two 5 MP cameras at 47 fps and 435 ns latency. These are fed to four proportional-integral-derivative (PID) controllers implemented on the FPGA. The PID modules provide feedback through parallel digital-to-analog converter (DAC) channels for steering mirrors to stabilize the beam within 5 µm accuracy. Using two cameras at distinct sample distances on the optical axis allows for controlling the incidence angle of the laser beam onto the image planes. The current system is a building block for future extensions allowing real-time phase-feedback on optical lattices, stabilization of independent optical tweezers in an array, and focus position stabilization of transverse electromagnetic (e.g. TEM01) modes enabling large-scale quantum simulations.
A highly digital optical phase-locked loop (OPLL) is designed and implemented to generate phase-coherent lasers in quantum optics. All the controlling circuit in this OPLL are implemented in a single field programmable gate array (FPGA) chip. Pipeline and parallelism technology have been adapted in PID controller. Especially, an equivalent 3.5 GHz high speed clock and twisted ring counter have been integrated in the most crucial part. This OPLL has the narrow beat note line width below 1 Hz, residual mean-square phase error of 0.05 rad2and transition time of 100 μs under 10 MHz frequency step.
Electronic systems for qubit control and measurement serve as a bridge between quantum programming language and quantum information processors. With the rapid development of superconducting quantum circuit technology, synchronization in a large-scale system, low-latency execution, and low noise are required for electronic systems. Here, we present a field-programmable gate array (FPGA)-based electronic system with a distributed synchronous clock and trigger architecture. The system supports synchronous control of qubits with jitters of ∼5 ps. We implement a real-time digital signal processing system in the FPGA, enabling precise timing control, arbitrary waveform generation, in-phase and quadrature demodulation for qubit state discrimination, and the generation of real-time qubit-state-dependent trigger signals for feedback/feedforward control. The hardware and firmware low-latency design reduces the feedback/feedforward latency of the electronic system to 125 ns, significantly less than the decoherence times of the qubit. Finally, we demonstrate the functionalities and low-noise performance of this system using a fluxonium quantum processor.
This paper reports the development of a low-latency arbitrary waveform generator (AWG), which is suitable for the control and measurement of superconducting quantum computers. It can generate qubit control signals and measurement signals in real time. Compared with commercial AWG, our AWG has less latency and higher analog bandwidth. Compressing latency can reduce system feedback time, and higher analog bandwidth improves the system's integration by mounting more qubits on the readout line. The AWG integrates four high-speed digital-to-analog converters (DACs), phase-locked loop (PLL) circuits, field-programmable gate arrays (FPGAs), and related circuits into a standard PXI 3U board. The waveform generator module, communication interface module, clock module, and configuration module are realized utilizing the FPGA. The FPGA-based hardware architecture enables AWG to be flexibly configured to meet the various needs of quantum experiments. The four-channel AWG has a 2-GSa/s sampling rate, a 14-bit resolution, and 500 MHz bandwidth. The jitter in the AWG output waveform is approximately 3 ps; the latency of the AWG (the time from the feedback trigger received until a feedback pulse is generated) is approximately 55 ns. These designs form the basis of realizing control system for large-scale quantum computing.
Digital micromirror devices (DMDs) have seen recent popularity as spatial light modulators (SLMs) for arbitrary and dynamic potential generation in the manipulation of neutral atom systems for quantum simulation and quantum computing platforms. In enabling the use of a DMD for this purpose, its latency, frame rate, and micromirror movement dynamics must be well characterized for various settings. In this paper, we present our FPGA-based system to control the DMD and the optical setup developed for its verification. Image information and control parameters are generated and configured using a Python user interface and sent to the FPGA using a C++ wrapper and the Cypress FX2 USB protocol. The FPGA design enables the leveraging of the high frame rate capabilities of the DMD as well as ensuring deterministic operation by first storing this USB data on an external DDR memory and updating the micromirror states upon receiving an external trigger pulse. The DMD is imaged onto a scientific camera and two photodiodes as a means of verifying the system behavior and investigating the metrics of interest. Using this framework, the DLP7000 consisting of 768x1024 micromirrors has been shown to refresh at 22 kHz with 45.4 μs latency. Furthermore, a single block consisting of 48x1024 micromirrors is able to refresh at 140 kHz with 7.1 μs latency. The loading and clearing behavior of micromirrors has also been characterized for varying refresh rates.
The implementation of a classical control infrastructure for large-scale quantum computers is challenging due to the need for integration and processing time, which is constrained by coherence time. We propose a cryogenic reconfigurable platform as the heart of the control infrastructure implementing the digital error-correction control loop. The platform is implemented on a field-programmable gate array (FPGA) that supports the functionality required by several qubit technologies and that can operate close to the physical qubits over a temperature range from 4 K to 300 K. This work focuses on the extensive characterization of the electronic platform over this temperature range. All major FPGA building blocks (such as look-up tables (LUTs), carry chains (CARRY4), mixed-mode clock manager (MMCM), phase-locked loop (PLL), block random access memory, and IDELAY2 (programmable delay element)) operate correctly and the logic speed is very stable. The logic speed of LUTs and CARRY4 changes less then 5%, whereas the jitter of MMCM and PLL clock managers is reduced by 20%. The stability is finally demonstrated by operating an integrated 1.2 GSa/s analog-to-digital converter (ADC) with a relatively stable performance over temperature. The ADCs effective number of bits drops from 6 to 4.5 bits when operating at 15 K.
We report a design and implementation of a field-programmable-gate-arrays (FPGA) based hardware platform, which is used to realize control and signal readout of trapped-ion-based multi-level quantum systems. This platform integrates a four-channel 2.8 Gsps@14 bits arbitrary waveform generator, a 16-channel 1 Gsps@14 bits direct-digital-synthesis-based radio-frequency generator, a 16-channel 8 ns resolution pulse generator, a 10-channel 16 bits digital-to-analog-converter module, and a 2-channel proportion integration differentiation controller. The hardware platform can be applied in the trapped-ion-based multi-level quantum systems, enabling quantum control of multi-level quantum system and high-dimensional quantum simulation. The platform is scalable and more channels for control and signal readout can be implemented by utilizing more parallel duplications of the hardware. The hardware platform also has a bright future to be applied in scaled trapped-ion-based quantum systems.