Arduino Nano v3.1, bottom side up, blue LED facing down
This is the smallest computer I have ever programmed so far. Not only the physically smallest, but having only 2 kilobytes of RAM and 32 kilobytes of flash memory makes it even smaller* in terms of storage capacity than my ancient IMSAI 8080** from 1976.
Preliminary speed measurements indicate that Arduino-friendly integer arithmetic in a simple C program is about 70 times slower than on the Raspberry Pi model B, and about 800 times slower than on a single core of an eight-core Opteron 4284 "Valencia" CPU from 2012.
(*) I did encounter some very early programmable calculators with less capacity, but they don't count as computers.
(**) My IMSAI initially had 4 kilobytes of RAM.