Counting the number of amplitudes isn't really the right way to approach it. Individual amplitudes are basically irrelevant to a large quantum computation. It's

Counting the number of amplitudes isn't really the right way to approach it. Individual amplitudes are basically irrelevant to a large quantum computation. It's all about large scale patterns in the amplitudes. Little exceptions to these patterns don't matter much. Suppose I gave you the power to negate a billion amplitudes of your choosing in the middle of a 2000 bit quantum factoring computation. You might think this could destroy the computation, but a billion is way way way less than 2^2000 so the computation would for all intents and purposes be completely unaffected. The things the quantum computers operate on are the qubits, not the amplitudes. Noise processes also operate on qubits, not amplitudes. It's the quantity and quality of the qubits that matter. You can factor 2048 bit RSA integers if you have 20 million qubits each having a 0.1% gate error rate [1]. 1: https://quantum-journal.org/papers/q-2021-04-15-433/ https://quantum-journal.org/papers/q-2021-04-15-433/