# Quantum Computing

I am writing this section only to satisfy your curiosity concerning qubits and quantum computing which we alluded to in another page. There we discussed boolean and quantum logic systems. Think boolean unless of course your going to major in a science; then you may need all of these pages.

Boolean matches our everyday common sense. Our beliefs frequently appear to us as true or false but never both! Qubits on the other hand have the ability to exist in a state of the superposition of the basic two component column vector states. A qubit is represented by a vector, denoted by |0> or |1>. The basic two-qubit system has four possible such states. We will consider the superposition of each pair of such states to be another single state. |S>= a|0> + b|1>. Think of the two superposition states as pointing to and parallel to the two binary pairs. Imagine two coins (qubits) spinning on their edges; the edge is the superposition of two states, true or false, heads or tails. A slight disturbance or measurement of one coin would cause it to collapse into heads (|1>) or tails (|0>). So?

These 2 superposition states each composed of two vector states can act simultaneously. This is a capability that classical computers lack. A Quantum computer with only 30 qubits can keep pace with a ten teraflops conventional machine. IBM is selling a 20 qubit device commercially, and has a 50 qubit computer in its lab. Google has a 53 qubit machine in the laboratory.

All boolean logic gates can be constructed with either NOT OR gates or NOT AND gates.A boolean gate is an electronic device which accepts scalar bits (0 or 3.5 volts each) as inputs and outputs a bit. In the process, a boolean operation is performed. Quantum computers can make use of these too in qubit form. However, a quantum computer has the Hadamard gate, which can take a qubit and place it in a state of superposition of both |1> and |0> states. Remember Algebra 2 and matrix algebra; the symbol |0> denotes a 2×1 matrix called a state vector. The state S is described as |S>= a|0> + b|1> where a b are complex numbers. A quantum procedure known as a quantum algorithm can be written to alter the weightings a and b. An n-qubit system can be in 2^n states simultaneously. The algorithm manipulates |S> by changing a and b such that values corresponding to answers that are closer to right are increased and wrong values decreased.The optimal solution in the form of the final superposition state of all n qubits is found.Optimization problems are solved rapidly.

Algorithms and applications are being developed for the quantum machine. Code breaking is one.The genetic algorithm another.That is a system optimization routine.

A digital supercomputer can do 200 quadrillion calculations (Stefanie Condon June 8, 2018 for Between the Lines) or 200 petaflops per second. Still, the gap between the quantum computer and our fastest conventional one is closing.