I gathered a few of the comments made by participants of my lecture “Why quantum computers cannot work and how”, and a few of my answers. Here they are along with some of the lecture’s slides. Here is the link for the full presentation.
1) Getting started
Aram Harrow: Introduces me, mentions our Internet debate and that the day of the lecture was our first meeting in person, mentions that he (still :)) does not agree with me.
2) Special-purpose devices and the “trivial flaw”
(slides 4; 10/11).
3) Topological quantum computing
Why topological quantum computing cannot shortcut the need for ”traditional” quantum fault tolerance (slides 16-18).
Aaronson: Such an argument can be made against every yet unavailable technology.
Mary Beth Ruskai: Agree(?) regarding topological quantum computers, but not that the argument has anything to do with cluster state computation. Several other people expressed the belief that cluster-state computation is not in conflict with my conjectural view of noisy quantum systems.
Shor: Do you disbelieve in the fractional quantum hall effect, then?
(Answer: No, just not in the possibility to create highly stable qubits based on anyons. Mixture of different codewords representing a topological state is OK.)
4) My conjectures 1-4
AM1 (audience member 1): Conjectures 1-3 (but perhaps not 4) are not in conflict with quantum fault-tolerance and the threshold theorem. (Answer: I dont think so; this was discussed in the debate.)
Ruskai: The two-qubit conjecture is too weak to cause QFT to fail. (Answer: indeed I strengthen the conjecture two slides ahead, but I am not sure that we meant the same thing.)
5) Sure/Shor separator
Aaronson: Constant depth quantum computing still allows certain quantum advantages over classical computing.
Aram: also Shor’s algorithm can be implemented with rapid classical control.
(Answer: we will attend to it in due time 🙂 )
6) Smoothed Lindblad evolutions
And my conjecture that realistic quantum systems are well approximated by smoothed Lindblad evolutions (briefly: SLE). (Slides 36-39.)
Shor: You get something different (by smoothing) when you take time intervals [0,1/2] and [1/2,1]; It makes no sense that the conjecture applies in all scales; You need scales and you need units (I did not get the last point.)
Ruskai: What do you mean by “approximate?” (Answer: excellent question.)
Shor: What about spin echo (NMR)?
(A comment I made in response: actually, Aram raised NMR among several other points “against” SLEs a few days before the lecture; we will have to look at them. Since my smoothing just reorganizes the noise, I expect that it will have little effect for quantum systems that do not enact quantum fault-tolerance.)
AM2: Can you prove that SLE do not support FTQC? (Answer: no) AM2: So what are we talking about here?
Why smoothed Lindblad evolutions are still Lindblad. (Thanks to Robert Alicki.)
AM3: My explanation resembles something in classical mechanics which naively appears to contradict causality (the principle of least action, perhaps); Aaronson: Ironically, this causality paradox from classical physics is explained using quantum mechanics. (AM3 made other good comments that I don’t remember.)
8) Simulating physics
Ruskai : But what does “simulate” mean? (Answer: Excellent question! But if I get to that it will not be a short answer, and probably the “yes” will be modified.)
9) A few additional remarks and questions
Alex Arkhipov: Do my conjectures forbid certain states or only some evolutions (Answer: States are also restricted but this requires the setting of noisy quantum computers: local operations on a Hilbert space with tensor product structure.)
Seth Lloyd: Are there experimentalists in the room? (Apparently not.) The lecture seems remote from what experimentalists care about. Lloyd does not expect mathematical proofs for impossibility of quantum fault-tolerance (answer: neither do I). He is a theoretician much involved with experimental work. In reality, there is all sort of crazy noise (non Lindbladian, even non-completely-positive,) and one should pay attention also to 1/f noise. Overall, he disagrees with me.
AM4: Nature does not understand ‘conjectures,’ it just does what it does.
10) Reasons to disbelieve
(Slide 57; based on this post.)
Update (July 2013): The comment thread contains a long interesting discussion with Peter Shor, and Aram Harrow mainly on smoothed Lindblad evolutions, with contributions also by Klas Markström and John Sidles. I added also a couple remarks on further comments I heard while giving a similar lecture at HUJI, and from participants in QStart, and a comment with my 5-minute talk at the rump session in QStart.