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Qbits unstable: May Limit Quantum Computing
museumpeace writes "Netherlands Organiztion for Scientific Research provies a human-readable description of research into the stability of Qbits conducted at Leiden University. The bad news: " Much to their surprise they discovered that the coherence tends to spontaneously disappear, even without external influences." The whole story in physicist-readable form is in the June 17 Physical Review Letters by van Wezel, van den Brink, Zaanen [click abstract or huge PDF]. I am not buying any quantum computing startups 'til they nail this matter down...you can't build a computer if state information is going to evaportate in a second or less."
Qubits are not bits. If a bit is unstable then make lots of bits and use your favorite error correcting code to represent the data. Error correction is a hot topic for error-correcting codes too. But it's very much harder. In particular - the decay of a qubit to decoherence is exponentially rapid. By using error correcting codes you merely extend the decoherence time from something like picoseconds to dozens of picoseconds (those aren't exact numbers BTW, it might be femtoseconds or something else), but the exponential decay eventually wins. Classical systems can remain stable for millennia. (Egyptian hieroglyphs are encodings of classical bits.) Also, every paper I've ever read on quantum error-correcting codes makes assumptions about the form of the influences that causes decoherence. But real systems never fit these models exactly. Any deviation between reality and the model will again result in exponentially fast decay to decoherence. Many physicsts are totally sceptical about quantum computers, at least qubit based ones, for this reason. I personally think the decay of qubits is a showstopper.
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Classical ECC techniques won't work for quantum computing but they can be adapted. You can encode a single qubit across five qubits to protect against arbitrary errors (there are infinitely many possible errors) on any single qubit. You can get some protection against some errors that act symmetrically across a set of qubits by using decoherence free subspaces.
The trouble with just using ECC to refresh constantly is that you have to approximate some of the quantum gates needed to perform the refresh. It's possible to approximate them to an arbitrary accuracy, but you'll still have some error at each refresh and this error will accumulate like error in a classical analog system.
Decoherence free subspaces don't have this problem since there is no refresh phase for this technique. Basically you take advantage of the fixed points of the noise process and use a subspace spanned by these fixed points. The problem is, this technique only works in situations like sending a bunch of photons through a fiber optic cable that introduces the same error to all the photons.
Right now, I'm suspecting that we will never see any long term quantum storage. However, if you can perform operations on your qubits fast enough you may be able to get a lot done in a few seconds.
Research in QECC may still be able to provide us with some new tricks as well.
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The rules of boolean logic that generate Hamming codes do not apply to qubits.
There are quantum ECC techniques, but they're different and have their own issues.
But this "hey guys, it's easy!" snap judgement shows profound ignorance.
Ok, lots of people still don't know what this stuff is about and I can't say I blame them since I've studied it and still don't get all of it.
Ok, let's say you have a single qubit. Its state is described by a complex valued unit vector a|0>+b|1>. |0> and |1> is just shorthand for the vectors {1,0} and {0,1}. If you measure the qubit, the probability of getting a 0 is |a|^2 and a 1 is |b|^2.
You may be asking why it's necessary to have a complex valued vector space. This is because quantum gates are represented by complex valued matrices. This means that you can have a gate that acts differently on sqrt(2)/2(|0>+|1>) and sqrt(2)/2(|0>+i|1>) even though they both have the same chance of coming up as 0 and 1.
If you have a qubit in an unknown state you have no way of determining what a and b are. If you measure a qubit and it comes up as 0 then it's in the state |0> and if it's 1 then it's in the state |1>. You can also measure the qubit with respect to other bases. For example you can measure it with respect to |+>=sqrt(2)/2(|0>+|1>) and |->=sqrt(2)/2(|0>-|1>). The probability of getting |+> is equal to the absolute value of the square of the projection of the state vector onto |+>. If the result comes out as |+> then the qubit is in the state |+>.
You can't copy qubits without destroying the original. However, you can entangle qubits together so that their values are dependent on eachother. Understanding the entanglement between qubits in a quantum algorithm is of critical importance and it really makes quantum algorithms a lot harder to understand than classical algorithms.
Systems of two qubits are represented by vector spaces spanned by |00>,|01>,|10>, and |11>. Larger systems are represented similarly. Gates acting on multiple qubits are represented by unitary matrices (basically they map unit vectors to unit vectors). There are infinitely many quantum gates, but they can be approximated to infinite accuracy by using a handful of single qubit gates and CNOT gates. CNOT maps |00> to |00>, |01> to |01>, |10> to |11> and |11> to |10>.
I hope that at least some of you can follow all that.
My only political goal is to see to it that no political party achieves its goals.
Doesn't it make you feel good to know that our freedoms are protected by politicans, lawyers and journalists.
The number of operations per second depends on what sort of qubit you're using. Some methods have a potential to go into the terahertz range, but others don't. The thing is, this is talking about elementary operations. It takes a lot of elementary operations to approximate some quantum gates so the "clock speed" is misleading. Also dealing with error correction will also take up some operations.
The problem with this is that if we don't find a work around, there is an upper bound on how large a quantum computation can be. Traditional parallelism won't help either. Quantum algorithms already depend on massive parallelism, but in a different way. You can perform some operations simultaneously, but for the most part, the system will be tied up in operations on multiple qubits which aren't parallelizeable. Some important algorithms such as the quantum Fourier transform won't benefit at all from parallelization.
Error-correction in quantum algorithms is actually the key issue in future development of quantum computing. And, not only that, but you have to come up with a correction algorithm where the complexity scales polynomially with the size of the system. Also,
o s-ndd112904.php
It is a hard problem - even if we have years of theoretical research, the first succesful experiment that probed the real error correction was done only few months ago (see Nature - Dec 1 2004), or http://www.eurekalert.org/pub_releases/2004-12/ni
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