Over at Fact and Fiction there is an interesting post about an article in New Scientist called Attack of the Quantum Worms.
Having not read the article, I thought I’d be an idiot and comment on what one could possibly mean by the statement that quantum computers are more susceptible to malicious attacks. I’m an even bigger idiot because I know very little about computer software security. But life’s about saying silly things and then getting chewed out by all you smart people, know?
The first thing one might mean is that quantum data cannot be backed up due to the no cloning theorem. OK, suppose I’m a hacker who wants to attack your quantum computer. Surely if I write some code which is executed by the computer and it damages the quantum state of the system, then, because I can’t back up the state of the quantum computer, I’m in big trouble. So it seems that one cannot prevent crashing a quantum computation by backing the state of the system up. But this isn’t quite right, is it? I mean suppose we have a classical computation and we make two backups of the state of the computation at any time. Then we can use this to test whether one of these states has been corrupted by majority voting. But we’ve learned that we can do exactly the same thing for quantum computers: we can detect if the quantum state of one of our copies has been corrupted by encoding into a quantum computer. Now we need to use more than three qubits per bit, but still, this doesn’t seem like such a big deal (from a theorist perspective 😉 ) Now I’d also like to say that I don’t think this is even the way classical computers protect themselves versus malicious software.
So what about attacking the “quantum software?” Well in a standard circuit model of quantum computation, the software is just a list of classical expressions. There is nothing quantum about the data describing a quantum computing program. So it seems that there can’t be any difference here between the quantum and classical world.
Oh well, I really should get a copy of the New Scientist and figure out if any of this rambling has anything to do with the article (on a similar note, I don’t understand the second part of the post at Fact and Fiction. I just don’t see the relevance of copying in a fixed basis: this is something which we almost always avoid in quantum computing because it destroys the coherence properties of the subsystem being so copied.)
O brave new quantum world!
Here’s my take, without reading the article:
But think about it, what really is meant by a “safe copy”? Classically, this means that we copy all the information off the hard drive and put the duplicate copy in a bank. Or we make several copies and put them in various different locations. Then later, if we want to detect that data has been modified, we bring together two copies and see if they are still equal.
Quantumly we can do the same thing. We encode each qubit we want to store into a quantum error-correcting code and put each qubit in a different location. When we want to detect if the data has been modified, we bring together the copies and check for detected errors. So far everything is nearly the same.
The difference is that classically, we can continue to compute even with just one copy. We can apply a series of classical gates to that copy and get a result. (If we want to check that result against a virus, we’d have to apply the same sequence of gates to the duplicates, and then bring them together to check for errors.) Quantumly, it is not possible to compute universally on just one copy; we need to apply operations to all the copies with non-local operations. (For say just stabilizer operations, which can be prepared transversally, this isn’t true.) Perhaps the idea of the article is that these non-local operations are susceptible to a virus (localized attack)? (It seems like you can perhaps cache a set of encoded Toffoli states at the very beginning, but then you’ll be limited in the number of steps you can run..) Of course they can be carried out fault-tolerantly, but the model is somehow different so that is probably not enough.
The article in question has been published in Quantum Information Processing and a link is available here. The New Scientist piece, which was published several months before the article, is available here.