On Wed, Jan 29, 2020, 1:25 PM <[email protected]> wrote: > what if a quantum computer isnt a finite amount of qbits, its actually an > exponential amount. >
Lloyd calculated the computing capacity of the universe to be 10^120 quantum operations and 10^90 bits. https://arxiv.org/abs/quant-ph/0110141 A qubit flip in time t requires borrowing h/2t energy, where h is Planck's constant (6.626 x 10^-34 J-s). If you converted all the 1.5 x 10^53 kg of mass in the universe to energy (E = mc^2 = 1.3 x 10^70 J) then you get about 10^120 operations over the age of the universe, 4 x 10^17 s. Memory can be encoded in the positions and momentums of the universe's 10^80 particles with resolution h (by Heisenberg's uncertainty principle) and bounded by available energy. This gives you 10^90 bits. I get similar numbers using a different calculation. The Bekenstein bound ( https://en.m.wikipedia.org/wiki/Bekenstein_bound ) of the entropy contained in the Hubble radius (13.8 billion light years) is 1/ln 16 bits per Planck unit area of the enclosing sphere. This is 2.95 x 10^122 bits. (Coincidentally this gives you roughly the size of a proton as the volume of a bit, independent of the properties of any particles). This is the upper bound for a black hole, which would be a little more than the actual mass of the universe, so the actual information content is smaller. But most of these bits are not usable. Reading and writing memory, including reading the output of a quantum computer, are not time reversible operations, and therefore not quantum. These operations require by the Landauer principle kT/ln 2 free energy, where k is Boltzmann's constant, 1.38 x 10^-23 J/K, and T is the cosmic background radiation temperature of the universe = 3 K. This gives you about 10^92 memory bit operations. In either case, the numbers are finite, so there will be no singularity. ------------------------------------------ Artificial General Intelligence List: AGI Permalink: https://agi.topicbox.com/groups/agi/T65747f0622d5047f-Mfbc2c5ef279e93cb0d6d9a51 Delivery options: https://agi.topicbox.com/groups/agi/subscription
