From my(admittedly relatively light) reading on this subject, it seems that some philosophers of consciousness really like to take certain things they can imagine as proof of such statements. The only proof I've read about for this idea that qualia are non-computational are thought experiments
One is "what if in some future where we understand the workings of the brain and physics perfectly, Alice grows up all her life in a green room, while learning every possible thing about the color red, except for any picture of it; when she then walks out of the room and sees red with her own eyes for the first time, she will still learn something knew, the subjective experience of the color red, the qualia for it - so this must be a non-physical phenomenon".
Or "imagine an intelligent being that has exactly our ability for reasoning, but doesn't experience qualia. It would behave exactly like us, and can talk about seeing red or feeling warmth, but it doesn't actually experience them; so, since the external behavior is indistinguishable form us, but the internal experience is different, this proves qualia are non-physical".
They all remind me of a similar proof of God's existence, which has mysteriously also been taken seriously by some philosophers - "let's imagine something which has all possible good qualities, it is perfect in every way. Since things that exist are better than things that don't, this perfect thing must exist, and we call it God".
One is "what if in some future where we understand the workings of the brain and physics perfectly, Alice grows up all her life in a green room, while learning every possible thing about the color red, except for any picture of it; when she then walks out of the room and sees red with her own eyes for the first time, she will still learn something knew, the subjective experience of the color red, the qualia for it - so this must be a non-physical phenomenon".
Or "imagine an intelligent being that has exactly our ability for reasoning, but doesn't experience qualia. It would behave exactly like us, and can talk about seeing red or feeling warmth, but it doesn't actually experience them; so, since the external behavior is indistinguishable form us, but the internal experience is different, this proves qualia are non-physical".
They all remind me of a similar proof of God's existence, which has mysteriously also been taken seriously by some philosophers - "let's imagine something which has all possible good qualities, it is perfect in every way. Since things that exist are better than things that don't, this perfect thing must exist, and we call it God".