# What’s a Quantum Bit ?

Computational Science

A bit is the most fundamental unit of storage in classical computation. When it comes to quantum computation we have an analogues namely quantum bit or qubit in short. Scientists relate states of a single classical bit with real life binaries like state of Light Bulb, Truth-False, voltage levels, open-close, etc. It tells us that a single classical bit can only be in one of the two states, i.e either 0 or 1. Thats something typical of a classical bit.

So, what is a qubit? A qubit just like a classical bit has two possible states  $|0>$and $|1>$(denoted in dirac notation ). But unlike classical bit a qubit can be in more than two possible states. That is, it can be in a superposition of states $|0>$and $|1>$. Mathematically, a superposition state looks like,

$|\psi> = \alpha |0> + \beta |1>$

In the above expression $\alpha$is the probability amplitude for state $|0>$and $\beta$is the probability amplitude for state $|0>$. $\alpha$and $\beta$both can be complex numbers. Since $\alpha$and $\beta$are probabilities amplitudes, they must be normalized. Mathematically,

$|\alpha|^2 + |\beta|^2 = 1$

Qubits can be respresented in terms of polarization of a photon where vertical and horizontal polarization are the two states. It can also be represented in terms of spin of an electron. A qubit can also be visualized geometrically as a unit vector on a plane.

A qubit remains in the superposition until and unless the state of the qubit is measured. If we try to perform a measurement on a qubit the superposition state breaks down and what we get is either a $|0>$or $|1>$state.

Just like classical bits we can pass qubits through different quantum gates to produce new sets of qubits.

Implications of superposition

Let us suppose that we have a solution that is encoded with $n$bits. Then total number of possible solution is $2^n$. With $n$classical bits we can check all possible strings with $\O(2^n)$checkups. Thats a lot of checkups to perform.

However, with $n$qubits we can put all the bits in a superposition state such that all the possible solutions (states) exists simultaneously. If we measure the qubits in superposition then we will get a random $n$bit state which may or may not be the solution. We need to have a circuit which can verify if the measured state is solution or not. Consequently this will reduce the required checkups to $\O(\sqrt{2^n})$.

Superposition is the phenomena that sets quantum computation apart from classical line of thoughts. It is superposition that gives qubits unprecedented advantage over classical bits. Quantum computation carries huge potential in the field of cryptography and scientific calculations where number of steps to a solution are exponentially high.

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