alquimiayciencias: Basic concepts in quantum computation.

Thomas, responding to your question.

A qubit is a quantum system in which the Boolean states

0

and

1

are represented by a prescribed pair of normalised and mutually orthogonal quantum states labeled as $\{|0\rangle ,|1\rangle \}$

The two states form a `computational basis' and any other (pure) state of the qubit can be written as a superposition $\alpha |0\rangle +\beta |1\rangle$ for some $α$ and $β$ such that $| α | 2 + | β | 2 = 1.$ A qubit is typically a microscopic system, such as an atom, a nuclear spin, or a polarised photon. A collection of $n$ qubits is called a quantum register of size $n$ .

We shall assume that information is stored in the registers in binary form. For example, the number $6$ is represented by a register in state $|1\rangle \otimes |1\rangle \otimes |0\rangle$ . In more compact notation: $|a\rangle$ stands for the tensor product $|a_{n-1}\rangle \otimes |a_{n-2}\rangle \ldots |a_{1}\rangle \otimes |a_{0}\rangle$ , where $a_i\in\{0,1\}$ , and it represents a quantum register prepared with the value $a=2^{0}a_{0}+2^{1}a_{1}+\ldots2^{n-1}a_{n-1}$ . There are $2 n$ states of this kind, representing all binary strings of length $n$ or numbers from $0$ to $2 n - 1$ , and they form a convenient computational basis. In the following $a\in \{0,1\}^n$ ( $a$ is a binary string of length $n$ ) implies that $\left| a \right\rangle$ belongs to the computational basis.

(La mecánica cuántica es la rama de la física que considera que la trasmisión de la energía ano es continua; esta especialidad nos ha aportado soluciones tecnológicas tan importantes como lo es el láser.)

adolfocanals@educ.ar

alquimiayciencias

jueves, 10 de julio de 2008

Basic concepts in quantum computation.

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