What is the smallest manned aircraft with four engines? What is the smallest (by operating empty mass) quad-engine aircraft that satisfies these conditions?


Current or past airplane
aircraft with fixed wings, not a rotorcraft, not a lighter than air, etc
4 engines, pistons or turbines
fuel as a main source for propulsion
actual aircraft, not scaled model
piloted by a pilot or a crew
used for an actual military or scientific goal or business (not for design tests only).


Added to prevent flying suits to be proposed:


Need to takeoff and land under its own power.
Not a worn wing (flying suit), the aircraft must have a flight deck where the pilot can be.


If this one had been piston or turbine, it would be a good candidate:

  

... but it's an electric-powered aircraft.
I present you Yves Rossy's Jet wingpack, which satisfies your conditions (I know I'm pushing it, but couldn't resist).



Yves Rossy's Jet wingpack, By Rama - Own work, CC BY-SA 2.0 fr, Link

It is certified by FAA as an aircraft, powered by four Jetcat P400 turbojets, piloted by an individual, not a rotorcraft and used in show business.

According to the official site, it weighs 150 kg.



@ymb1's logic is correct. To get to lightweight four engined aircraft with, you have to go back when the engines were not powerful enough for large aircraft. So, I present you the Sikorsky Ilya Muromets, the World's first four engined bomber. 



Sikorsky Ilya Muromets, By www.cultinfo.ru, Public Domain, Link

The Ilya Muromets Type S-23 V is reported to have an OEW of around 3700 kg, powered by four Sunbeam Crusader engines. Its predecessor, the Sikorsky Russky Vityaz, was still lighter, though it never saw service in numbers, sadly.

Of course they are not autonomous as per your requirement. Why would you want a manned autonomous aircraft anyway?