For about 20 years there have been articles relating to quantum computers, which seem to have great theoretical potential. All the articles I have read are highly optimistic. I am wondering if they will ever be useful. About 5-10 years ago there was an article with a headline about a great break though in Quantum Computer technology. It started with a description of the problem of factoring large numbers & explained how a quantum computer would solve this problem in a jiffy compared to a classical computer. After a lot of hullabaloo, the break through was described in detail. Some Quantum computer successfully factored 15, determining that 3 & 5 were the prime factors. I might have missed further developments, but have not noticed any more recent articles on the subject of factoring large numbers using a Quantum Computer. The January 2010 issue of Scientific American has an article titled: “Warp Speed Algebra” The sub-title is: “New Quantum algorithm can solve monster-size equations.” At the end of the article is mention of the existence of only experimental Quantum Computers with a few bits . The article then states that it will be many years before a Quantum computer will actually out perform a classical computer. “Publish or Perish” is an apt description of the working of the academic community. I wonder if articles relating to Quantum Computers are due to a desire not to perish, rather than being descriptions of a technology actually viewed as practical. A useful Quantum Computer requires a large number of quantum entities, which must be shielded from environmental effects which can cause unwanted changes of their state. The practical problem of assuring accuracy might be insurmountable & is seldom mentioned. There is a big difference between theory & practice. For example, I remember a theoretical method advocated for solving simultaneous linear equations. The description is simple: Divide each cofactor (not sure this term is correct) by the determinant. When computers became capable of actually solving 50 to 100 equations in 50 to 100 unknowns, no sensible programmer ever tried to implement that theoretically sound algorithm, which was a horror in practice. I wonder if there will ever be a useful Quantum Computer.
I dunno, things seem to be going ok: http://www.newscientist.com/article/dn18272-google-demonstrates-quantum-computer-image-search.html Might not be exactly a true quantum computer, but we're getting there.
I think the answer to your questions depends on your point of view. Quantum computing, as an intellectual idea, has already proven enormously fruitful in many areas of physics. The developments this idea is helping to promote will in some cases end up being technologically relevant despite having nothing directly to do with quantum computing. Still, I think you want more. I do too, in fact. My personal feeling is that a large scale programmable quantum computer is still many years away, but the program is far from hopeless. You are quite right that it is hard to protect quantum systems from decoherence, but nature offers many subtle paths: topological quantum computing, clean optical lattice systems, or robust josephson junction arrays to name a few. My attitude is to forgive the scientists their hype (innocent or not) and focus on the amazing progress being made as we struggle towards the grand goal of realistic quantum computing. And trust me when I tell you that the workers in this field are deeply concerned about the issues you raised, even if their "propaganda" doesn't show it.
There's two different approaches to qquantum computing; the hardware and the software. A great deal of work, which is what a lot of the stuff in the media is about, has been done on the software. Mathematicians and physicists have done a lot of work on what algorithms a quantum computer could run better than a classical one or vice versa. The issue of building a quantum computer is an entirely different one because you need very precise and delicate systems which don't fall out of quantum coherence when you use them to compute something. I've seen a quantum algorithm which can factorise numbers less than 30 into primes implemented on a classical computer, so the work of people coming up with algorithms to run on a quantum computer isn't a waste. Mind you, the computer I saw was one which had the algorithm hardwired into it and it was the size and mass of a paving slab, illustrating how large a job a quantum algorithm is for classical computers.
I too have doubts regarding the viability of quantum computing. One of the reasons for the switch from analog to digital computers way back in the 1950s was partly because analog computers were difficult to program. Solving a different problem meant, at a minimum, physically reconfiguring the computer. Some problems required creating new analog devices, while even others required the creation of a new analog computer. The lack of a good model of analog computation was another key problem. These quantum computers are in a very real sense, analog computers reborn. The same underlying problems that motivated the switch to digital computers still exist.
With current technology, quantum computers need to be run at nearly absolute zero temperature, that's another serious technical difficulty.
I went to a seminar a little while back presented by a group working on optical quantum computing. They had developed little silicon chips with optical waveguides embedded in them through which they would shoot single photons. The waveguides would move close together at stages to enable entanglement of the photons. It was really very cool. It's probably not the most viable approach out there, but it's certainly my favourite from a romantic point of view Please Register or Log in to view the hidden image!.
I guess that's one reason for the heavy focus on software theory. Has there been any ongoing research into models of analog computation in the last 50 years?
I guess I have seen a different side of quantum computing to AN because I haven't noticed any of the progress regarding algorithms, but I have heard a whole lot of things about the technologies being developed in the quest for some viable quantum computing hardware. There are a lot of research groups, experimentalists, working on this stuff, both at the pure research level and at the commercial level. I'm not sure that quantum computers with ever replace conventional computers for our everyday needs, but they will be incredibly useful for the specific applications at which they excel.
I personally feel that the digital/analog comparison doesn't represent a very useful analogy. In the case of the switch to digital, I would argue that the analog computer was not really more powerful than the digital computer, so there was no reason to stick with analog. On the other hand, quantum computers, even if they are similar in some respects to analog classical computers, offer quite different computational capabilities compared to classical digital computers. For example, there exist problems for which a quantum computer is vastly more powerful than its digital counterpart. Even with all the potentials issues of reconfiguration, etc., the quantum computer might still represent a worthwhile tool. In particular, the simulation of quantum systems is a problem the quantum computer was born to solve, and no classical computer can even come close.
This is patently untrue. Fault tolerance and quantum error correction were among the first areas to see vigorous research efforts following the discovery of generally interesting quantum algorithms (i.e., Grover's and Shor's algorithms), precisely because people do realize that coherence (which I'm assuming is what you mean by accuracy) is a problem. And that is strictly from the "software" side. A spectacular result, known as the "fault tolerance" or "threshold" theorem shows that the fidelity of qubit gates can be fairly low if we use error correction. It works out to something like 99.9% IIRC (which would be ridiculously poor fidelity if we were working classically), using the best quantum error correction codes. I'm not entirely sure, but I also seem to recall that with the latest major result in hardware (2 qubits implemented by superpositions of currents in ring superconductors, I think) reported in Nature a week or two back, there was considerable discussion of the fidelity problem.
