I Have an old audio amplifier that has those switches to turn it on. I'm looking for the simplest motor/robotic arm (or any other relevant component) to control this switch - eventually via Raspberry Pi .
Are there any options ?
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If you just want to control the switches and not the knobs, some options are:
Dual acting solenoids or two simple acting solenoids.
Needs just a pulse of current in one direction to operate. In some dual acting solenoids, you need to reverse current to reverse the direction of force.
Image from http://www.magnetschultz.co.uk
RC servo-motor. (With that you can control the knobs too)
Normally more force for a given size/weight of solenoid. Slower than a solenoid but depending on the model still in the $ ms $ for a 60° rotation. Has more moving parts than a solenoid, so more wear. Major ones have a brushed DC motor so have the brushes wear too. Anyway, should last for maybe a decade without problem. It's a servo-mechanism, so has position feedback and precision positioning. Have the drive electronics, but you need to provide a PWM signal relative to the position you want it to rotate.
Car door lock actuator
Shares some of the properties from a RC Servo-motor, but has linear action like the solenoid, and don't have position feed-back (some have a open/closed feed-back). Needs a pulse of current to operate too, but needs reversing the current to reverse the direction of force.
Image from http://www.amazon.com/
Note: I presume by your question that you want to mechanical actuate the switch and electronic options are excluded.