A quiet fan is a large fan.
(This should be understood in relation to either mechanical power or lift. Of course, a multi kilowatt industrial turbine is way noisier than the fan cooling your computer.)
A single large and slower propeller (or two coaxial) instead of 4 or 6 small ones will do wonders, provided one can get good enough automatic pitch control. A better energy efficiency will be a bonus.
We just invented the helicopter.
There is a fundamental difference in how rotors of quadcopters and helicopters work.
The quadcopter has fixed blades and variable speed. To vary the speed of an electric motor is easy, the whole thing is simple. But: we need at least 3 rotors (and things get easy with at least 4) in order to control the vector of the lift. Rotors are small, they rotate at high speed. Results:
- blades have some compromise form, they are not optimal at any speed
- blades have some compromise angle of attack, again not optimal in any condition
- blades are small for the load they lift (no place for bigger ones).
These three things mean a constant partial stall for some part of the blade. A lot of energy is lost to sound and vortices.
On the other hand, on a heli we have:
- single rotor with big blades, running at more or less constant speed, optimized for lift, drag and noise at that speed
- the angle of attack (pitch) of the blades is precisely controlled at every revolution. That's how both the lift amount and the lift vector are controlled (keywords: group and cyclic control).
The reason why small UAV are not usually made as helicopters is the pitch control. The mechanism is complex and maintenance-heavy, its control algorithm is complex as well.
On the other hand, the technology constantly improves and we COULD get something workable in the near future.
On the good side, helicopters powered by internal combustion have the limitation of the engine speed not being able to change much and not being able to change quick. A variable pitch AND a variable speed of the electric motor may offer additional means of control and efficiency improvements.
In regard to comments that helicopters are noisy as well:
The lightest one is probably ~500kg, there are ones that are tens of tons. This is the main reason why they are noisier than a quadcopter.
I don't want to even imagine the sound of a 4-rotor 1000kg copter.