Introduction to Quantum Gates : Implementation of Single and Multiple Qubit Gates

A quantum gate or quantum logic gate is an elementary quantum circuit working on a small number of qubits. It means that quantum gates can grasp two primary feature of quantum mechanics that are entirely out of reach for classical gates : superposition and entanglement. In simpler words quantum gates are reversible. In classical computing sets of logic gates are connected to construct digital circuits. Similarly, quantum logic gates operates on input states that are generally in superposition states to compute the output. In this paper the authors will discuss in detail what is single and multiple qubit gates and scope and challenges in quantum gates.

So, denoting +1/2 as binary 1 and -1/2 as binary 0 in electron spin which acts as our qubit (which were simply bit in classical computers made up of whole atom instead of electron).
At a particular instant qubit can have either 0 or 1 or both at the same time. In quantum mechanics we cannot determine exact spin of electron, we can only determine it's probability of having +1/2 or -1/2 at a particular instant. So, particle have to spin at same time also termed as Entanglement. Now 1 qubit is equivalent to 2 classical bits and 2 qubit is equivalent to 4 classical bits.
And, N qubit is equivalent to 2n classical bits.

It rises exponentially.
For example-if there are 300 quibts in fully entangled state. So, the resultant will be 2 to the power 300 classical bits which are many particles are in our universe.
Classical computer does 'n' operations at one time using n-bits where as quantum computer does 2 n operations in n-qubits in the same time. So, quantum computers can do more work and it increases exponentially in the same time.

A. Qubit
A Qubit by definition is quantum bit.
A qubit bit can hold both 1 and 0 simultaneously and is named a superposition state.
A bit on the other hand can hold either 0 or 1 at the same time. So, in theory it can be said that a qubit can simultaneously participate in numerous processes.
Thus, quantum computers are super fast. Example: There is a maze with only one way out and a million other ways leading to dead ends. Now, imagine you are at the center of the maze. If we have millions of clones of one person, then that person and his clones will start finding the way out simultaneously and thus, one of the clone will find the way out in the first go itself. Thus, one can find the way out in the first try.
These clones working simultaneously to explore and find out the correct way out at once are the superposition states same as qubits.
Theoretically, the more complicated the problem the faster the solution attained with the help of quantum computer.

B. Superposition and Entanglement
A qubit can be denoted in an exceedingly linear combination of states : The numbers α and β are complex numbers. The property of having the ability to exist in multiple states is termed superposition. Quantum mechanics does not allow the view of amplitudes, ie. α and β, of the two base vectors are. Instead, when we measure a qubit, we get the state |0>with probability | | 2 and the state |1> with probability |β| 2 . The addition of these probabilities must be up to 1. If a quantum operation is performed on a qubit in multiple states, then the operation is performed on all states at the same time.
Once the qubit ascertained, it will collapse back into a single state stochastically, according to the squares of the probabilities.
The famous physicist R. Feynmann advised that a qubit α|0>+β|1> occupies all the states between 0 and 1 at the same time, however collapses into 0 or 1 once ascertained physically. Therefore an infinite amount of information can be encoded in a qubit, but as it can never be observed most of the information is useless. This raises various fascinating philosophical questions about what information actually is. As expressed previously, when observed, a qubit collapses into one of it's basis states. Nobody is aware why this happens, it is one of the essential tenets of quantum mechanics. The reason that a quantum state collapses upon physical observation is understood because of the Kobenhavn Interpretation, and is that the standard(though not the only) means of explaining the collapse upon measurement.
Superposition is one of the properties that enables the Quantum Computing paradigm to supersede classical computing and the other is Entanglement. A two qubit system has four computational basis states, which are |00>, |01>, |10> and |11>. The two qubit system may be in any superposition of these states.
There are four very fascinating states that such a system can be prepared in. These states are referred to as the Bell States or EPR states. An example of Bell State : When one measures the first qubit in this state, there are two possible results; 0 with probability 1/2 leaving the other qubit in the state |00>, and |11> with probability 1/2, leaving the other qubit in the state |11>. This suggests that once the second qubit is measured it will forever be in the same state as the first qubit! This correlation between the qubits is understood as entanglement. The measurement correlations between the two qubits are stronger than could ever exist between classical systems is proved by Bell. For example, entanglement between two qubits can persist even though they are spatially separated.
The properties of entanglement and superposition mean that certain speedups can be employed in quantum algorithms that will never be attainable on classical computers. The two most famed quantum algorithms are Shor's algorithm, which can find out the factor a number which is the product of two large primes in exponential time, and Grover's algorithm which searches a random database in quadratic time.

Introduction to BOSCH SPHERE :
We'll begin by considering the action of a quantum gate on a single quantum bit. A single classical bit (cbit) is relatively boring; either it's in a zero state, or a one state. [4] In contrast a quantum bit is a much richer object that can exist in a quantum superposition of zero and one. This state can be conveniently visualized as a point on the surface of a 3-dimensional ball, generally called the Bloch sphere [2, 0]. The sphere is rotated around some axis due to the the action of a 1-qubit gate.  The Y-gate can be considered a combination of X and Z gates, Y = −iZX. With respect to the computational basis, we interchange the zero and one states and apply a relative phase flip.    The Fredkin gate (also CSWAP or CS gate), named after Edward Fredkin, is a 3-bit gate that performs a controlled swap.
Truth Table Matrix  The research for this problem is still continuing the effort applied to identify a solution for this problem that has no positive progress.

1.
Qubits are not digital bits of the day thus they cannot use as conventional error correction.

2.
The main disadvantage of Quantum computing is the technology required to implement a quantum computer is not available at present days.

3.
The minimum energy requirement for quantum logical operations is five times that of classical computers.

4.
Quantum CPU will have efficiency and heating problems of its own.

5.
When a measurement of any type is made to a