Can quantum computers design quantum computers autonomously better than other methods?

Question

We've seen people use computers to design computers, AI to write computer programs, robots teach themselves, and even robots build themselves. I understand that conventional computers can be used to emulate quantum computers.

Robotic arm builds more robotic arms.

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My question is: Will quantum computers be inherently able to design better quantum computers (which presumably robots could then build) or is that task better suited to Deep Learning / AI and conventional computers (with human intervention)?

Perhaps another way to ask the question, though I'm fairly certain that this won't make it clearer: "Do conventional computers limit us to quantum Darwinism while quantum computers might enable universal Darwinism with respect to the evolution of quantum computer design?".

Oversimplified (not the question): Could they understand (design) themselves better than classical computers, Deep Learning / AI, or mankind - IE: they do not suffer from what Zurek calls “pointer states”.

Answer 1

Sort of, quite possibly, if by degrees

This is a speculative, but plausible, answer

First of all, how do qubits interact and states evolve with time?

The description of how individual qubits evolve (i.e. a single qubit gate operation) is given by some Hamiltonian¹. Multiple, non-interacting qubits (that are exactly the same) therefore evolve using multiples of that same Hamiltonian. However, as soon as you include some form of interaction, simulating the exact evolution of a large number of interacting qubits quickly becomes intractable (which is exactly why quantum computers should be useful, in theory).

Now, how are quantum processors designed?

Designing the microarchitecture of a processor (such as the connectivity, layout of the chip etc.) is one thing, but engineering sizes of qubits, waveguides etc. requires going on a computer and running detailed simulations a lot of the time. If there was a way to simulate large Hamiltonians for a long time, it's reasonable to assume that this would help improve knowledge of how the qubits interact with each other and the environment, such as in a more detailed version of this and extensions thereof, as well as generally being able to look at how multiple qubits interact at once. This would in turn allow for improved design of the details of chip, which would lead to effects such as reduction of decoherence.

Finally, what are quantum computers good at?

As mentioned above, quantum computers are potentially useful because of what makes them hard to simulate - a quantum computer is a system that quickly becomes intractable it simulate with increasing numbers of qubits. However, something that quantum computers offer a speedup of is... Hamiltonian simulation.

In other words, by iteratively running a quantum Hamiltonian simulation, using a classical computer to (tell the quantum computer to) vary certain parameters, it's not unreasonable to assume that a quantum computer could help for optimising certain aspects of the chip to e.g. reduce decoherence times, improve fidelities etc. In turn offering better simulations and allowing for yet more qubits, which potentially offers better simulations and the continual improvement would (hopefully) begin.

As for whether it does, or if classically simulating a few qubits and extrapolating from this would give a just-as-good design is something that only time will tell.

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^{1 Having said that, in linear optical quantum computers (at least), unitaries are implemented directly using physical components such as beam splitters and phase shifters directly describing the unitary, as opposed to, say, superconducting, where applying microwaves is described in terms of a Hamiltonian, which is then used to give a unitary. OK, all this is maybe simplifying a bit, but that gets the gist across. What does matter is that, in linear optical quantum computers, generating the photons on say, a ring resonator, is described by a Hamiltonian}

Answer 2

We don't yet know if quantum computers are actually better than classical computers, as @heather mentions here. As for now there are just some theoretical algorithms which we know of, specifically for quantum-computers, which have much better time complexities than equivalent classical algorithms. For example - prime factorization and discrete logarithms.

Wiki also says:

Besides factorization and discrete logarithms, quantum algorithms offering a more than polynomial speedup over the best known classical algorithm have been found for several problems, including the simulation of quantum physical processes from chemistry and solid state physics, the approximation of Jones polynomials, and solving Pell's equation. No mathematical proof has been found that shows that an equally fast classical algorithm cannot be discovered, although this is considered unlikely. For some problems, quantum computers offer a polynomial speedup. The most well-known example of this is quantum database search, which can be solved by Grover's algorithm using quadratically fewer queries to the database than are required by classical algorithms. In this case the advantage is provable. Several other examples of provable quantum speedups for query problems have subsequently been discovered, such as for finding collisions in two-to-one functions and evaluating NAND trees.

Whether you can use these speedups to design better quantum computers, depends. I can imagine that you could of course simulate a quantum computer using another quantum computer, which could help in making new designs or rather testing-before-building. But I don't think polynomial speedups, faster prime factorizations, etc. will directly help in designing a quantum computer, unless you actually make use of it somehow.

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P.S: This is a very short and perhaps incomplete answer, I know. I just wanted to give the OP a basic idea. I'd request others to write alternate answers to this question.