On the accelerator front, the primary advancement has been the massive increase in core count, now reaching thousands -nearly two orders of magnitude more than CPUs. The number of cores and peak performance depend on the floating-point (FP) format; typically, double-precision (DP) cores are half as numerous as single-precision (SP) cores. The shift toward narrower FP formats has been driven by AI, which tolerates reduced precision (16-bit, 8-bit, and even 4-bit formats are in use). Modern GPUs achieve remarkable performance using smaller FP formats and Tensor Cores, which are optimized for dense matrix multiplications. To illustrate these differences, Table compares the computational performance of a high-performance CPU and a GPU released within the same time frame. Peak performance reflects execution speed only when computation is the bottleneck, not memory transfers or inter-node communications, which are too slow to keep up with the execution units. With standard DP operations (FP64), GPU peak performance is about five times that of a high-end CPU. When Tensor Cores are used, this increases to a factor of ten. For SP (FP32) Table : Comparison of the peak performance with different precision modes, the amount of memory, the memory bandwidth and the thermal design power (TDP) of an Nvidia H100 GPU and an AMD EPYC (Bergamo) CPU . operations, both CPU and GPU performance doubles, but with Tensor Cores, the GPU reaches 989 TFlop/s, over 70 times that of the CPU. Reducing precision to 8 bits (FP8) adds another factor of four. While smaller FP formats can sometimes be used for standard FP32 and FP64 tasks, Tensor Cores mainly benefit computations reliant on dense matrix multiplication. Achieving GPU peak performance is harder than on CPUs, as it requires high levels of parallelism. Consequently, matrices on the GPU must be much larger , or numerous, requiring batching algorithms. Furthermore, GPUs have less memory than CPUs and large workloads necessitate memory transfers from the host to the accelerator, which must be managed in parallel with computations to prevent communication bottlenecks. We further elaborate below on the implications of these CPU and GPU performance differences for quantum simulations.