The main argument it makes is based on counting amplitudes, and noting there are far too many to ever control:
> The hypothetical quantum computer is a system with an unimaginable number of
continuous degrees of freedom - the values of the 2^N quantum amplitudes with N ~ 10^3–10^5 . [...] Now, imagine a bike having 1000 (or 2^1000 !) joints that allow free rotations of their parts with respect to each other. Will anybody be capable of riding this machine? [...] Thus, the answer to the question in title is: As soon as the physicists and the engineers will learn to control this number of degrees of freedom, which means - NEVER.
The reason this is a joke is because it fundamentally misunderstands what is required for a quantum computation to succeed. Yes, if you needed fine control over every individual amplitude, you would be hosed. But you don't need that.
For example, consider a quantum state that appears while factoring a 2048 bit number. This state has 2^2048 amplitudes with sorta-kinda-uniform magnitudes. Suppose I let you pick a million billion trillion of those amplitudes, and give you complete control over them. You can apply any arbitrary operation you want to those amplitudes, as long it's allowed by the postulates of quantum mechanics. You can negate them, merge them, couple them to an external system, whatever. If you do your absolute worst... it will be completely irrelevant.
Errors in quantum mechanics are linear, so changing X% of the state can only perturb the output by X%. The million billion trillion amplitudes you picked will amount to at most 10^-580 % of the state, so you can reduce the success of the algorithm by at most 10^-580 %. You are damaging the state, but it's such an irrelevantly negligible damage that it doesn't matter. (In fact, it's very strange to even talk about affecting 1 amplitude, or a fraction of the amplitudes, because rotating any one qubit affects all the amplitudes.)
To consistently stop me from factoring, you'd need to change well more than 10% of the amplitudes by rotations of well more than 10 degrees. That's a completely expected amount of error to accumulate over a billion operations if I'm not using error correction. That's why I need error correction. But Dyakonov argues like you'd only need to change 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001% of the amplitudes to stop me from factoring. He's simply wrong.
And your rebuttal amounts to "if I let you mess with a trivial number of amplitudes then the error will be trivial". Well duh. Another way of phrasing what you said is that you need to control 90% of 2^2048 amplitudes. Which is Dyakanov's point, that nobody knows how to do this.
Strilanc|2 years ago
The main argument it makes is based on counting amplitudes, and noting there are far too many to ever control:
> The hypothetical quantum computer is a system with an unimaginable number of continuous degrees of freedom - the values of the 2^N quantum amplitudes with N ~ 10^3–10^5 . [...] Now, imagine a bike having 1000 (or 2^1000 !) joints that allow free rotations of their parts with respect to each other. Will anybody be capable of riding this machine? [...] Thus, the answer to the question in title is: As soon as the physicists and the engineers will learn to control this number of degrees of freedom, which means - NEVER.
The reason this is a joke is because it fundamentally misunderstands what is required for a quantum computation to succeed. Yes, if you needed fine control over every individual amplitude, you would be hosed. But you don't need that.
For example, consider a quantum state that appears while factoring a 2048 bit number. This state has 2^2048 amplitudes with sorta-kinda-uniform magnitudes. Suppose I let you pick a million billion trillion of those amplitudes, and give you complete control over them. You can apply any arbitrary operation you want to those amplitudes, as long it's allowed by the postulates of quantum mechanics. You can negate them, merge them, couple them to an external system, whatever. If you do your absolute worst... it will be completely irrelevant.
Errors in quantum mechanics are linear, so changing X% of the state can only perturb the output by X%. The million billion trillion amplitudes you picked will amount to at most 10^-580 % of the state, so you can reduce the success of the algorithm by at most 10^-580 %. You are damaging the state, but it's such an irrelevantly negligible damage that it doesn't matter. (In fact, it's very strange to even talk about affecting 1 amplitude, or a fraction of the amplitudes, because rotating any one qubit affects all the amplitudes.)
To consistently stop me from factoring, you'd need to change well more than 10% of the amplitudes by rotations of well more than 10 degrees. That's a completely expected amount of error to accumulate over a billion operations if I'm not using error correction. That's why I need error correction. But Dyakonov argues like you'd only need to change 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001% of the amplitudes to stop me from factoring. He's simply wrong.
[1]: https://ebooks.iospress.nl/pdf/doi/10.3233/APC200019
squabbles|2 years ago
And your rebuttal amounts to "if I let you mess with a trivial number of amplitudes then the error will be trivial". Well duh. Another way of phrasing what you said is that you need to control 90% of 2^2048 amplitudes. Which is Dyakanov's point, that nobody knows how to do this.