Comments on: Simulated Quantum Computers suck http://room408.wordpress.com/2008/03/13/simulated-quantum-computers-suck/ the two-hits Tony Gherghetta edition Tue, 22 Dec 2009 21:15:20 +0000 http://wordpress.com/ hourly 1 By: zevans http://room408.wordpress.com/2008/03/13/simulated-quantum-computers-suck/#comment-813 zevans Mon, 31 Mar 2008 02:50:48 +0000 http://room408.wordpress.com/?p=81#comment-813 That's some good information, Andrew. Thanks for that. I still haven't convinced myself that the Clifford group is indeed BPP-universal. I still have to think about it a bit more. That’s some good information, Andrew. Thanks for that.

I still haven’t convinced myself that the Clifford group is indeed BPP-universal. I still have to think about it a bit more.

]]> By: Andrew Landahl http://room408.wordpress.com/2008/03/13/simulated-quantum-computers-suck/#comment-812 Andrew Landahl Fri, 21 Mar 2008 23:04:42 +0000 http://room408.wordpress.com/?p=81#comment-812 Actually, X and CNOT are universal for classical computation by themselves if you allow "classical" magic states. Shor showed that one can simulate a Toffoli gate using the state (|000> + |001> + |010> + |100>)/2 and CNOT gates. This state has a natural classical "pbit" analogue (000 + 001 + 010 + 100)/4, which allows CNOT to simulate TOF in the same way. Of course, you have to distill such a state, which can only be done approximately using CNOT and X gates. In other words, the Clifford group is 'BPP-universal." I don't know the answer to the question of whether Clifford gates allow "P-universality." My guess is that they don't, but I don't have a proof. Actually, X and CNOT are universal for classical computation by themselves if you allow “classical” magic states. Shor showed that one can simulate a Toffoli gate using the state (|000> + |001> + |010> + |100>)/2 and CNOT gates. This state has a natural classical “pbit” analogue (000 + 001 + 010 + 100)/4, which allows CNOT to simulate TOF in the same way. Of course, you have to distill such a state, which can only be done approximately using CNOT and X gates. In other words, the Clifford group is ‘BPP-universal.” I don’t know the answer to the question of whether Clifford gates allow “P-universality.” My guess is that they don’t, but I don’t have a proof.

]]> By: astephens http://room408.wordpress.com/2008/03/13/simulated-quantum-computers-suck/#comment-806 astephens Mon, 17 Mar 2008 01:25:54 +0000 http://room408.wordpress.com/?p=81#comment-806 So maybe the Clifford group is not classical universal but if you could simulate a quantum computer that has just a Toffoli and a NOT then you could use that quantum computer to simulate a universal classical computer. Of course there isn't much quantum about a quantum computer with only those two gates and so it still sucks. So maybe the Clifford group is not classical universal but if you could simulate a quantum computer that has just a Toffoli and a NOT then you could use that quantum computer to simulate a universal classical computer. Of course there isn’t much quantum about a quantum computer with only those two gates and so it still sucks.

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