Comments on: Under the radar http://photicus.wordpress.com/2007/02/13/under-the-radar/ this doesn't exist until you read it. Sun, 06 Jul 2008 00:27:49 +0000 http://wordpress.org/?v=MU By: tramadol http://photicus.wordpress.com/2007/02/13/under-the-radar/#comment-13 tramadol Wed, 04 Apr 2007 14:00:55 +0000 http://photicus.wordpress.com/2007/02/13/under-the-radar/#comment-13 It is a very interesting story. Thanks! It is a very interesting story. Thanks!

]]> By: jon http://photicus.wordpress.com/2007/02/13/under-the-radar/#comment-12 jon Wed, 14 Feb 2007 15:04:57 +0000 http://photicus.wordpress.com/2007/02/13/under-the-radar/#comment-12 Dennis: I haven't heard anything about the demo, but I hope it went well. As for what we could do with a 16-qubit system, it probably isn't enough to crack an RSA code. But there are lots of interesting things we can do with only a few qubits. If we can truly tailor the interactions in this 16-qubit system, we could perform small-scale quantum simulations, in addition to investigating entanglement and probing the oddities of Quantum Mechnanics. Coming from a circuit model of Quantum Computing (which is the general practice with trapped ions) once we start getting 1000 qubits, we can start to implement quantum error correction and improving the fidelity of the computation. We could probably start doing something 'practical' too. Neil: Silly me, I forgot about the computing power it takes to find the largest eigenvalue. So, even though we have an analytic solution, it is quite useless in terms of actually calculating things. It seems from Geordie's comments that it will provide a quadratic speed-up. Is the solution to the Ising model equivalent to Grover's search algorithm? If it is, then I'm not sure that we <em>actually</em> have a quantum computer. I've seen papers in PRA & PRL that state that Grover's search only requires wave properties, and not entanglement. As such, it can be implemented using classical waves of light. [S. Lloyd, Phys. Rev. A 61, 010301(R) (2000)] [D. A. Meyer, Phys. Rev. Lett. 85, 2014 (2000)], [N. Bhattacharya, et. al., Phys. Rev. Lett. 88, 137901 (2002)]. Sure, entanglement could play a role, but it is not necessary to perform Grover's search. And yes, it probably is a bit premature to say that it won't work due to coherence. It seems to me that after reading: cond-mat/0609332 that the total time to run the system is on the order of the thermalization time. It seems like thermal decoherence does play a role after all. But it looks like it isn't detrimental, which is counter-intuitive. I guess the question then is whether or not the engineered homotopy from the initial Hamiltonian to the final one can be made adiabatic in the roughly 10-100ns timescale. I'd bet that that can be done. What about state detection and preparation? And entanglement? I haven't seen anything demonstrating that an entangled system had been created, and measured. Even a 6-qubit entangled state would make headlines. Dennis: I haven’t heard anything about the demo, but I hope it went well. As for what we could do with a 16-qubit system, it probably isn’t enough to crack an RSA code. But there are lots of interesting things we can do with only a few qubits. If we can truly tailor the interactions in this 16-qubit system, we could perform small-scale quantum simulations, in addition to investigating entanglement and probing the oddities of Quantum Mechnanics. Coming from a circuit model of Quantum Computing (which is the general practice with trapped ions) once we start getting 1000 qubits, we can start to implement quantum error correction and improving the fidelity of the computation. We could probably start doing something ‘practical’ too.

Neil: Silly me, I forgot about the computing power it takes to find the largest eigenvalue. So, even though we have an analytic solution, it is quite useless in terms of actually calculating things. It seems from Geordie’s comments that it will provide a quadratic speed-up. Is the solution to the Ising model equivalent to Grover’s search algorithm? If it is, then I’m not sure that we actually have a quantum computer. I’ve seen papers in PRA & PRL that state that Grover’s search only requires wave properties, and not entanglement. As such, it can be implemented using classical waves of light. [S. Lloyd, Phys. Rev. A 61, 010301(R) (2000)] [D. A. Meyer, Phys. Rev. Lett. 85, 2014 (2000)], [N. Bhattacharya, et. al., Phys. Rev. Lett. 88, 137901 (2002)]. Sure, entanglement could play a role, but it is not necessary to perform Grover’s search.

And yes, it probably is a bit premature to say that it won’t work due to coherence. It seems to me that after reading: cond-mat/0609332 that the total time to run the system is on the order of the thermalization time. It seems like thermal decoherence does play a role after all. But it looks like it isn’t detrimental, which is counter-intuitive. I guess the question then is whether or not the engineered homotopy from the initial Hamiltonian to the final one can be made adiabatic in the roughly 10-100ns timescale. I’d bet that that can be done. What about state detection and preparation? And entanglement? I haven’t seen anything demonstrating that an entangled system had been created, and measured. Even a 6-qubit entangled state would make headlines.

]]> By: Neil http://photicus.wordpress.com/2007/02/13/under-the-radar/#comment-11 Neil Wed, 14 Feb 2007 05:54:08 +0000 http://photicus.wordpress.com/2007/02/13/under-the-radar/#comment-11 If you've read that page about 2D Ising model that you linked to, you'll notice that one step in that "analytic solution" is to find the largest eigenvalue of a 2^n by 2^n matrix, which takes quite bad exponential time (2^(2n) time or worse?). The fastest worst-case scaling to solve the problem exactly with conventional software is about n(2^n) time, which is only slightly better than the brute-force solution, which takes (n^2)(2^n) time. Note that even the brute-force solution is much better than your "analytic solution". Also, since as you said, you don't know anything about adiabatic quantum computing, maybe it's a bit premature to be commenting that it won't work because of decoherence. If you had read much of the information Geordie has posted on AQC/TAQC, you would know that decoherence is quite unrelated to TAQC. That's not to say that there aren't other potential problems, but decoherence doesn't really apply, as Geordie has said several times. If you’ve read that page about 2D Ising model that you linked to, you’ll notice that one step in that “analytic solution” is to find the largest eigenvalue of a 2^n by 2^n matrix, which takes quite bad exponential time (2^(2n) time or worse?). The fastest worst-case scaling to solve the problem exactly with conventional software is about n(2^n) time, which is only slightly better than the brute-force solution, which takes (n^2)(2^n) time. Note that even the brute-force solution is much better than your “analytic solution”.

Also, since as you said, you don’t know anything about adiabatic quantum computing, maybe it’s a bit premature to be commenting that it won’t work because of decoherence. If you had read much of the information Geordie has posted on AQC/TAQC, you would know that decoherence is quite unrelated to TAQC. That’s not to say that there aren’t other potential problems, but decoherence doesn’t really apply, as Geordie has said several times.

]]> By: Dennis http://photicus.wordpress.com/2007/02/13/under-the-radar/#comment-10 Dennis Wed, 14 Feb 2007 00:21:38 +0000 http://photicus.wordpress.com/2007/02/13/under-the-radar/#comment-10 Hi! Have you heard how their demo went? I've been searching for info and finding nothing anywhere, even on the D-wave website! Also, as a lay person, what would be the capabilities of a 16 qubit system, anywey? Or of a 1,000 qubit system. Thanks for your reply! Hi! Have you heard how their demo went? I’ve been searching for info and finding nothing anywhere, even on the D-wave website! Also, as a lay person, what would be the capabilities of a 16 qubit system, anywey? Or of a 1,000 qubit system. Thanks for your reply!

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