4 ms·

This was pretty good, though I would still like to know 'how' the quantum computer gets all those amplitude (and how many are needed) to interfere with each oth

This was pretty good, though I would still like to know 'how' the quantum computer gets all those amplitude (and how many are needed) to interfere with each other to get the answer.

FartyMcFarter 4y ago
> and how many are needed According to this paper, one can use 2n+3 qubits to factor an integer with n bits: https://arxiv.org/abs/quant-ph/0205095 https://arxiv.org/abs/quant-ph/0205095 Those would be perfect qubits, if you use noisy qubits you'd need many more (maybe a factor of 1000x more), since quantum error correction imposes a lot of overhead.
semi-extrinsic 4y ago
If I understand your question on "how" correctly: all objects are interfering with each other at the quantum level all the time. But this effect is vanishingly tiny compared to e.g. thermal noise, we don't notice it at all. So the quantum computer isn't making the qubits interfere, that always happens, but it is working very hard to remove all other sources of noise such that only the quantum interactions remain.
Strilanc 4y ago
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/

This was pretty good, though I would still like to know 'how' the quantum computer gets all those amplitude (and how many are needed) to interfere with each other to get the answer.

FartyMcFarter 4y ago

> and how many are needed According to this paper, one can use 2n+3 qubits to factor an integer with n bits: https://arxiv.org/abs/quant-ph/0205095 https://arxiv.org/abs/quant-ph/0205095 Those would be perfect qubits, if you use noisy qubits you'd need many more (maybe a factor of 1000x more), since quantum error correction imposes a lot of overhead.

semi-extrinsic 4y ago

If I understand your question on "how" correctly: all objects are interfering with each other at the quantum level all the time. But this effect is vanishingly tiny compared to e.g. thermal noise, we don't notice it at all. So the quantum computer isn't making the qubits interfere, that always happens, but it is working very hard to remove all other sources of noise such that only the quantum interactions remain.

Strilanc 4y ago

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/