Qubits

Qubits

1. |0>=(1,0) and |1>=(0,1)

   • Normalized a|0>+b|1> must have a^2+b^2=1
     • Complex numbers

2. |00>,|01>,|10>,|11> again must be normalized

   • Combine two independent 1-bit states by taking tensor product
   • Bell state: 1/\sqrt2 (|00>+|11>)
     • Measure one bit, know other bit, i.e., correlation
   • For n qubits, need 2^n complex number to specify state
     • Except we know they normalize to 1 and can wlog write first as real, i.e., 2^n-1 complex numbers

3. Bloch sphere

   • Wlog multiplying with |a|/a does not change probabilities.
     • So can assume first coordinate is real