Timing Constraints Imposed by Classical Digital Control Systems on Photonic Implementations of Measurement-Based Quantum Computing

Most of the architectural research on photonic implementations of measurement-based quantum computing (MBQC) has focused on the quantum resources involved in the problem with the implicit assumption that these will provide the main constraints on system scaling. However, the "flying-qubit" architecture of photonic MBQC requires specific timing constraints that need to be met by the classical control system. This classical control includes, for example, the amplification of the signals from single-photon detectors to voltage levels compatible with digital systems; the implementation of a control system which converts measurement outcomes into basis settings for measuring subsequent cluster qubits, in accordance with the quantum algorithm being implemented; and the digital-to-analog converter and amplifier systems required to set these measurement bases using a fast phase modulator. In this article, we analyze the digital system needed to implement arbitrary one-qubit rotations and controlled- not gates in discrete-variable photonic MBQC, in the presence of an ideal cluster state generator, with the main aim of understanding the timing constraints imposed by the digital logic on the analog system and quantum hardware. We have verified the design using functional simulations and have used static timing analysis of a Xilinx field-programmable gate array (7 series) to provide a practical upper bound on the speed at which the adaptive measurement processing can be performed, in turn constraining the photonic clock rate of the system. The design and testing system is freely available for use as the basis of analysis of more complex designs, incorporating more recent proposals for photonic quantum computing. Our work points to the importance of codesigning the classical control system in tandem with the quantum system in order to meet the challenging specifications of a photonic quantum computer.