On Fri, Apr 24, 2015 at 11:27:26AM +1000, Bruce Kellett wrote: > LizR wrote: > > > >But there's no-cloning to consider - plus whether a simulated > >quantum state is the same as a real one... > > No-cloning of an unknown quantum state is simply the statement that > there is no unitary operator that will enable you to transfer the > properties of one unknown quantum state to another. > > Simulating a quantum state might be another matter. Quantum states > are generally described in terms of some basis in Hilbert space. The > coefficients of the expansion in that basis are arbitrary complex > numbers, subject to the usual normalization conventions for the > state. If you want to simulate this state, you have to simulate > these coefficients to arbitrary precision. This is not possible in > finite time with a digital computer.
Not sure I follow you here. Arbitrary precision does not mean infinite precision. If I want my calculation to be accurate to 300 digits, then it can be calculated to 300 digits precision within finite time. If I then want it to 600 digits, I can do that also, but very likely it will 10^300 times as long. > However, if an infinite number > of calculations are routinely possible for a Turing machine in > Platonia, then who knows? > > I will give my proof that these coefficients are indeed dense in the > complex plane at a later time, if required. > The set Q x Qi is dense in the complex plane, and each point in that set can be specified precisely to infinite precision. > Bruce > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/d/optout. -- ---------------------------------------------------------------------------- Prof Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Professor of Mathematics [email protected] University of New South Wales http://www.hpcoders.com.au ---------------------------------------------------------------------------- -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
