4 ms·

Quantum/classical is orthogonal to the analog/digital distinction. There are analog quantum computers and digital quantum computers. Analog quantum computers (

Quantum/classical is orthogonal to the analog/digital distinction. There are analog quantum computers and digital quantum computers. Analog quantum computers (like annealers) are simpler to make, and they have a lot more play w.r.t. their building blocks when trying to make interesting effects... but ultimately they are limited by noise. Digital quantum computers restrict themselves to finite gate sets, often requiring expensive decompositions to do basic operations (e.g. [1]), but those gates are compatible with error correction so noise can be suppressed arbitrarily (e.g. [2]). It's very similar to how an analog classical computer can do addition with two resistors and a junction, but the accuracy is limited by the precision of the resistance. Whereas a digital classical computer will decompose the addition problem into bits and gain more precision by adding bits so that increasing precision becomes about increasing quantity instead of quality. [1]: https://www.mathstat.dal.ca/~selinger/newsynth/ https://www.mathstat.dal.ca/~selinger/newsynth/ [2]: https://arxiv.org/abs/1208.0928 https://arxiv.org/abs/1208.0928

HarHarVeryFunny 2y ago
Right, but even with the "digital quantum computer" (i.e. error-corrected quantum computer) aren't they still used in same fashion as an analog computer - one has to configure (cf patch panel) the computer into being an analog of the problem to be solved, then let the natural dynamics do it's thing, rather than being able to program it to perform some step-wise algorithm of the user's choosing?
- Strilanc 2y ago
  No, that's not true at all. For example, a chemistry simulation can be done in first quantization; where the state is a list of superposed 2s-complement integers indicating the positions of the electrons (as opposed to a more direct one-qubit=one-position mapping). And the list is initialized in a way that satisfies the Pauli exclusion principle by using a sorting network [1]. This is presumably not at all how Nature does it. Another example is factoring. Shor's factoring algorithm is not at all like behaving analogous to a physical system. It's about modular exponentiation and Fourier transforms; math things not physics things. Yet another example is Hamming weight phasing. If you need to rotate many qubits by a common angle around the Z axis, you can achieve that effect more cheaply by temporarily computing their Hamming weight (under superposition) and then rotating the first qubit of the Hamming weight register by the angle, the second by twice the angle, the third by four times the angle, etc. And actually that various-rotation-angles operation can then also be replaced by an addition into a special reusable phase gradient state; this achieves the desired effect by phase kickback [2]. Adding the Hamming weight of their spins into a helper state is probably not how Nature goes about precessing electrons in a uniform magnetic field. [1]: https://arxiv.org/abs/1711.10460 https://arxiv.org/abs/1711.10460 [2]: https://arxiv.org/abs/1709.06648 https://arxiv.org/abs/1709.06648

HarHarVeryFunny 2y ago

Right, but even with the "digital quantum computer" (i.e. error-corrected quantum computer) aren't they still used in same fashion as an analog computer - one has to configure (cf patch panel) the computer into being an analog of the problem to be solved, then let the natural dynamics do it's thing, rather than being able to program it to perform some step-wise algorithm of the user's choosing?

Strilanc 2y ago
No, that's not true at all. For example, a chemistry simulation can be done in first quantization; where the state is a list of superposed 2s-complement integers indicating the positions of the electrons (as opposed to a more direct one-qubit=one-position mapping). And the list is initialized in a way that satisfies the Pauli exclusion principle by using a sorting network [1]. This is presumably not at all how Nature does it. Another example is factoring. Shor's factoring algorithm is not at all like behaving analogous to a physical system. It's about modular exponentiation and Fourier transforms; math things not physics things. Yet another example is Hamming weight phasing. If you need to rotate many qubits by a common angle around the Z axis, you can achieve that effect more cheaply by temporarily computing their Hamming weight (under superposition) and then rotating the first qubit of the Hamming weight register by the angle, the second by twice the angle, the third by four times the angle, etc. And actually that various-rotation-angles operation can then also be replaced by an addition into a special reusable phase gradient state; this achieves the desired effect by phase kickback [2]. Adding the Hamming weight of their spins into a helper state is probably not how Nature goes about precessing electrons in a uniform magnetic field. [1]: https://arxiv.org/abs/1711.10460 https://arxiv.org/abs/1711.10460 [2]: https://arxiv.org/abs/1709.06648 https://arxiv.org/abs/1709.06648