views, comments.

Representing Qubit States

rw-book-cover

Metadata

Highlights

  • classical variables
  • classical computers.
  • In quantum computers, our basic variable is the qubit: a quantum variant of the bit.
  • the same restrictions as normal bits do: they can store only a single binary piece of information, and can only ever give us an output of 0 or 1
  • Each element in the statevector contains the probability of finding the car in a certain place:
  • statevectors happen to be a very good way of keeping track of quantum systems, including quantum computers.
  • This restriction is lifted for quantum bits. Whether we get a 0 or a 1 from a qubit only needs to be well-defined when a measurement is made to extract an output
  • At that point, it must commit to one of these two options. At all other times, its state will be something more complex than can be captured by a simple binary value.
  • mutually exclusive
  • two orthogonal vectors. |0⟩=[10]|1⟩=[01].
  • the bra-ket notation, introduced by Dirac.
  • Since the states |0⟩|0⟩|0\rangle and |1⟩|1⟩|1\rangle form an orthonormal basis, we can represent any 2D vector with a combination of these two states.
  • the qubit’s statevector
  • In quantum mechanics, we typically describe linear combinations such as this using the word ‘superposition’.
  • In Qiskit, we use the QuantumCircuit object to store our circuits, this is essentially a list of the quantum operations on our circuit and the qubits they are applied to.