In speaking with some folks from HP at CES earlier this year, I was told that quad-core processors in 13.3-inch laptops aren't very far away. There were no specifics provided at the time, but according to some benchmarks that were spotted online, they could be coming later this year in Intel's eighth-generation 'Coffee Lake' processors.
Normally, Intel's U-series processors are dual-core with four threads, and if you wanted to go quad-core, you'd need something like an HQ-series chip, which is much more power-hungry and really only shows up in devices that are at least 15 inches.
The new models that are showing up are the Core i5-8250U and Core i7-8550U, both of which are listed as having four cores, and would therefore have eight threads. From the benchmarks, it looks like the i5 will be clocked at about 1.8GHz and the i7 will be 2GHz, and it looks like there are PCs planned with these chips from ASUS, Dell, HP, Acer, and Lenovo.
As far as scores go, the single-core benchmarks are all around 4,000 (around 4,500 for the i7), which is similar to Intel's seventh-generation 'Kaby Lake' chips, but the multi-core scores rock out at up to 14,265.
Intel continues generation after generation to make its processors more power-efficient. The ability to include quad-core chips in smaller devices is a huge leap for the firm.