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picture1_Evolution Ppt 78457 | Qc Ch2 P80 97


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File: Evolution Ppt 78457 | Qc Ch2 P80 97
2 2 postulates of quantum mechanics quantum mechanics is the math framework for the development of physical theories the basic postulates below were derived after a long process of trial ...

icon picture PPT Filetype Power Point PPT | Posted on 05 Sep 2022 | 3 years ago
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        2.2 Postulates of Quantum 
                   Mechanics
  Quantum mechanics is the math 
   framework for the development of 
   physical theories
  The basic postulates below were derived 
   after a long process of trial and (mostly) 
   error
  The motivation for the postulates is not 
   always clear and appear surprising even 
   to experts
         2.2.1 Postulate 1: State 
                    Space
  Associated to any isolated physical 
   system is a Hilbert space (complex vector 
   space with inner product) known as the 
   system state space
  The system is completely described by its 
   state vector, a unit vector in the system 
   state space
            2.2.1 Postulate 1: State 
                          Space
  The simplest quantum mechanical 
   system, our fundamental system, is the 
   qubit
     2D state space with orthonormal basis     
     With arbitrary state vector                                
           as the superposition of the basis states
     For example, the state                  
            is a superposition of the states 
             2.2.2 Postulate 2: 
                   Evolution
  The evolution of a closed quantum 
   system is described by a unitary 
   transformation U
     Operator U changes the state from t  to t
                                          1    2
  For single qubits, any unitary operator 
   can be realized in realistic systems
            2.2.2 Postulate 2: 
                 Evolution
  Examples: Pauli unitary matrices X, Y, Z
  Hadamard gate H matrix representation
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...Postulates of quantum mechanics is the math framework for development physical theories basic below were derived after a long process trial and mostly error motivation not always clear appear surprising even to experts postulate state space associated any isolated system hilbert complex vector with inner product known as completely described by its unit in simplest mechanical our fundamental qubit d orthonormal basis arbitrary superposition states example evolution closed unitary transformation u operator changes from t single qubits can be realized realistic systems examples pauli matrices x y z hadamard gate h matrix representation...

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