Brainstorm Tech 2018: One-on-One With Jerry Yang I Fortune

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@annamariahultquist8445 5 жыл бұрын

Explenation to the fortune journalist about Quantum computing as is :To better understand this point, consider a classical computer that operates on a three-bit register. If the exact state of the register at a given time is not known, it can be described as a probability distribution over the {\displaystyle 2^{3}=8} 2^{3}=8 different three-bit strings 000, 001, 010, 011, 100, 101, 110, and 111. If there is no uncertainty over its state, then it is in exactly one of these states with probability 1. However, if it is a probabilistic computer, then there is a possibility of it being in any one of a number of different states. The state of a three-qubit quantum computer is similarly described by an eight-dimensional vector {\displaystyle (a_{0},a_{1},a_{2},a_{3},a_{4},a_{5},a_{6},a_{7})} {\displaystyle (a_{0},a_{1},a_{2},a_{3},a_{4},a_{5},a_{6},a_{7})} (or a one-dimensional vector with each vector node holding the amplitude and the state as the bit string of qubits). Here, however, the coefficients {\displaystyle a_{i}} a_{i} are complex numbers, and it is the sum of the squares of the coefficients' absolute values, {\displaystyle \sum _{i}|a_{i}|^{2}} {\displaystyle \sum _{i}|a_{i}|^{2}}, that must equal 1. For each {\displaystyle i} i, the absolute value squared {\displaystyle \left|a_{i} ight|^{2}} {\displaystyle \left|a_{i} ight|^{2}} gives the probability of the system being found in the {\displaystyle i} i-th state after a measurement. However, because a complex number encodes not just a magnitude but also a direction in the complex plane, the phase difference between any two coefficients (states) represents a meaningful parameter. This is a fundamental difference between quantum computing and probabilistic classical computing.[11] If you measure the three qubits, you will observe a three-bit string. The probability of measuring a given string is the squared magnitude of that string's coefficient (i.e., the probability of measuring 000 = {\displaystyle |a_{0}|^{2}} {\displaystyle |a_{0}|^{2}}, the probability of measuring 001 = {\displaystyle |a_{1}|^{2}} {\displaystyle |a_{1}|^{2}}, etc.). Thus, measuring a quantum state described by complex coefficients {\displaystyle (a_{0},a_{1},a_{2},a_{3},a_{4},a_{5},a_{6},a_{7})} {\displaystyle (a_{0},a_{1},a_{2},a_{3},a_{4},a_{5},a_{6},a_{7})} gives the classical probability distribution {\displaystyle (|a_{0}|^{2},|a_{1}|^{2},|a_{2}|^{2},|a_{3}|^{2},|a_{4}|^{2},|a_{5}|^{2},|a_{6}|^{2},|a_{7}|^{2})} {\displaystyle (|a_{0}|^{2},|a_{1}|^{2},|a_{2}|^{2},|a_{3}|^{2},|a_{4}|^{2},|a_{5}|^{2},|a_{6}|^{2},|a_{7}|^{2})} and we say that the quantum state "collapses" to a classical state as a result of making the measurement. An eight-dimensional vector can be specified in many different ways depending on what basis is chosen for the space. The basis of bit strings (e.g., 000, 001, …, 111) is known as the computational basis. Other possible bases are unit-length, orthogonal vectors and the eigenvectors of the Pauli-x operator. Ket notation is often used to make the choice of basis explicit. For example, the state {\displaystyle (a_{0},a_{1},a_{2},a_{3},a_{4},a_{5},a_{6},a_{7})} {\displaystyle (a_{0},a_{1},a_{2},a_{3},a_{4},a_{5},a_{6},a_{7})} in the computational basis can be written as: {\displaystyle a_{0}\,|000 angle +a_{1}\,|001 angle +a_{2}\,|010 angle +a_{3}\,|011 angle +a_{4}\,|100 angle +a_{5}\,|101 angle +a_{6}\,|110 angle +a_{7}\,|111 angle } {\displaystyle a_{0}\,|000 angle +a_{1}\,|001 angle +a_{2}\,|010 angle +a_{3}\,|011 angle +a_{4}\,|100 angle +a_{5}\,|101 angle +a_{6}\,|110 angle +a_{7}\,|111 angle } where, e.g., {\displaystyle |010 angle =\left(0,0,1,0,0,0,0,0 ight)} {\displaystyle |010 angle =\left(0,0,1,0,0,0,0,0 ight)} The computational basis for a single qubit (two dimensions) is {\displaystyle |0 angle =\left(1,0 ight)} |0 angle =\left(1,0 ight) and {\displaystyle |1 angle =\left(0,1 ight)} |1 angle =\left(0,1 ight). Using the eigenvectors of the Pauli-x operator, a single qubit is {\displaystyle |+ angle ={\tfrac {1}{\sqrt {2}}}\left(1,1 ight)} |+ angle ={\tfrac {1}{\sqrt {2}}}\left(1,1 ight) and {\displaystyle |- angle ={\tfrac {1}{\sqrt {2}}}\left(1,-1 ight)} |- angle ={\tfrac {1}{\sqrt {2}}}\left(1,-1 ight).