There is a common misconception that the decoherence time is the time scale over which quantum mechanics is lost in a quantum system. This is not correct. Open quantum systems can have highly quantum mechanical equilibrium states, even when the decoherence time is very short. Under certain conditions, you can wait the lifetime of the universe and the entanglement in an open quantum system will never “go away”. These systems can have very short decoherence times.

Here is a presentation Mohammad Amin recently gave that explains why this is and how decoherence times affect AQC, and a technique we have implemented for measuring a key figure of merit for qubits used in AQC systems.

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Indeed anyone who thinks decoherence time = time to become classical certainly doesn’t know quantum error correction! Quantum error correction is essentially a manner for designing an effective Hamiltonian whose thermal equilibrium properties allow for the retention and manipulation of entanglement.

The real question, of course, is whether AQC has similar robust properties. Statements like “this is better in AQC than in the gate model” are kind of heavy handed until you can either experimentally or theoretically demonstrate the AQCs retain this robustness property, no?

Hi Dave,

Well for a single qubit you can easily show this both theoretically and experimentally (the latter by measuring the minimum gap using say Landau Zener measurements and then measuring the spectral broadening using MRT and comparing the two energy scales). The point Mohammad is making is that the metrics for what makes a qubit “good” differ in the two approaches. In AQC (or more specifically AQO) the spectral broadening of the energy eigenstates seems to be the right thing to focus on as it directly affects the ground state fidelity which is what matters. In gate model, T2 is the clear winner for what makes a good qubit as phase coherence between energy eigenstates is required.

Even in the gate model, though, their are variations where the energy eigenstate coherence doesn’t matter. For instance if you use geometric or holonomic gates.

For AQC with standard combinatorial adiabatic algorithms, I would think spectral broadening would be important. I would also guess that when you’re sweeping across a small gap that real excitations out of the ground state begin to matter. For universal AQC, it’s…more interesting… (I should probably write a paper on why🙂 )

Yes spectral broadening does matter, although how it affects performance is a tricky question. It seems to depend on the density of low-lying energy states. If there aren’t a lot of them then you might be able to get away with a statistical approach, ie run the computation many times and rank the results. I’m sure you can craft problems that have large numbers of low-lying states to break this approach, but it’s generally true that any particular algorithm for combinatorial optimization can be broken if you try hard enough, wouldn’t expect AQO to be different.

Are there any algorithms that are “natural” for geometric or holonomic versions?

LOL!

Based on Dave’s first point, and what I’ve seen of quantum computing commentary over the past several years, I would conclude that fewer than 1 out of every 100 Million people truly knows quantum error correction. At least to the degree that they could draw conclusions about the effects of decoherence on distinct quantum systems.

Geordie: Re: natural algorithms for geometric or holonomic quantum computing…I don’t know. That’s a good question.

hi glad to see your back, so are you going to have a nice demo for the SC09 show?

Hi JP, we’re working on something now that i think will be pretty cool, although we may demo it at a different venue than SC09.