Quantum Computing

A physical implementation of linear algebra, in a simplistic description.

wikpedia

• block sphere

• toffoli gate

topological quantum computer with notes

hamming code for adding parity bits for error correction is a classical version

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microsoft.Quantum.pdf

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Notes from Microsoft Research 2018

• built on logic gates just like traditional machines

Bit wise vectors

0

$$\left(\begin{array}{l} 1 \\ 0 \end{array}\right)$$

matrix multiplication

$$\left(\begin{array}{ll} a & b \\ c & d \end{array}\right)\left(\begin{array}{l} x \\ y \end{array}\right)=\left(\begin{array}{l} a x+b y \\ c x+d y \end{array}\right)$$

rank 3

$$\left(\begin{array}{lll} a & b & c \\ d & e & f \\ g & h & i \end{array}\right)\left(\begin{array}{l} x \\ y \\ z \end{array}\right)=\left(\begin{array}{l} a x+b y+c z \\ d x+e y+f z \\ g x+h y+i z \end{array}\right)$$

$$\left(\begin{array}{ll} a & b \\ c & d \end{array}\right)\left(\begin{array}{ll} w & x \\ y & z \end{array}\right)=\left(\begin{array}{ll} a w+b y & a x+b z \\ c w+d y & c x+d z \end{array}\right)$$

$$\left[ \begin{array}{llll} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]\left[\begin{array}{l} a \\ b \\ c \\ d \end{array}\right]=\left[\begin{array}{l} a \\ b \\ c \\ d \end{array}\right]$$

$$\left(\begin{array}{llll} 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right)\left(\begin{array}{l} 0 \\ 1 \\ 0 \\ 0 \end{array}\right)=\left(\begin{array}{l} 0 \\ 0 \\ 1 \\ 0 \end{array}\right)$$

The bit flipping is important. The four operations of a function are identity, negation, constant 0 and constant 1