Hi, this will be my first post here. I've been working on a class ab amplifier for my finals project in my electronics lab class. I attached the schematic:

It works perfectly fine on PSPICE simulation but once I build the circuit on my breadboard, the output and input signals both get a really high frequency and high amplitude signal. Even with no input signal.
I found that if I remove the 1000uf and 0.001uf capacitors, it works but my gain is ruined ]=
I also noticed if I just I touch (or hook up a wire) at the node between the 2 diodes (where the 0.001uf capacitor was), it reduces the high frequency oscillations by a bit.
I have also tried physically moving the output and input signals farther apart from each other but it didn't help.
Any idea what's going on and how to fix it? Much appreciated.

It works perfectly fine on PSPICE simulation but once I build the circuit on my breadboard, the output and input signals both get a really high frequency and high amplitude signal. Even with no input signal.
I found that if I remove the 1000uf and 0.001uf capacitors, it works but my gain is ruined ]=
I also noticed if I just I touch (or hook up a wire) at the node between the 2 diodes (where the 0.001uf capacitor was), it reduces the high frequency oscillations by a bit.
I have also tried physically moving the output and input signals farther apart from each other but it didn't help.
Any idea what's going on and how to fix it? Much appreciated.