SDC-based Resource Constrained Scheduling for Quantum Control Architectures

Instruction scheduling is a key transformation in backend compilers that take an untimed description of an algorithm and assigns time slots to the algorithm's instructions so that they can be executed as efficiently as possible while taking into account the target processor limitations, such as the amount of computational units available. For example, for a superconducting quantum processor these restrictions include the amount of analogue instruments available to play the waveforms to drive the qubit rotations or on-chip connectivity between qubits. Current small-scale quantum processors contain only a few qubits; therefore, it is feasible to drive qubits individually albeit not scalable. Consequently, for NISQ and beyond NISQ devices, it is expected that classical instrument sharing to be designed in the future quantum control architectures where several qubits are connected to an instrument and multiplexing is used to activate only the qubits performing the same quantum operation at a time. Existing quantum scheduling algorithms either rely on ILP formulations, which do not scale well, or use heuristic based algorithms such as list scheduling which are not versatile enough to deal with quantum requirements such as scheduling with exact relative timing constraints between instructions, situation that might occur when decomposing complex instructions into native ones and requiring to keep a fixed timing between the primitive ones to guarantee correctness. In this paper, we propose a novel resource constrained scheduling algorithm that is based on the SDC formulation, which is the state-of-the-art algorithm used in the reconfigurable computing. We evaluate it against a list scheduler and describe the benefits of the proposed approach. We find that the SDC-based scheduling is not only able to find better schedules but also model flexible relative timing constraints.