SpREM: Exploiting Hamming Sparsity for Fast Quantum Readout Error Mitigation

The current Noisy Intermediate-Scale Quantum (NISQ) era suffers from high quantum readout error that severely reduces the measurement fidelity. Matrix-based error mitigation has been demonstrated as a promising software-level technique, which performs matrix-vector multiplication to calibrate the probability distribution with noise. However, this approach shows poor scalability and limited fidelity improvement as the matrix size exponentially increases with the number of qubits. In this paper, we propose SpREM to exploit the inherent sparsity in the mitigation matrix. Inspired by the interaction mechanism between qubits, we identify structured sparsity patterns using Hamming distance. With this insight, we propose the Hamming-Distance Sparse Row (HDSR) compression method and its format, which can achieve higher sparsity than threshold-based pruning meanwhile exhibiting great fidelity improvement. Finally, we propose the computational dataflow of the HDSR format and implement it on hardware. Experiments demonstrate that SpREM achieves 98.9% sparsity and a 27.3× reduction in fidelity loss on the real-world quantum device, compared to threshold-based pruning. It achieves an average 11.2× 36.4× speedup compared to Xilinx Vitis SPARSE library and NVIDIA A100 GPU implementations.