We have talked about quantum concepts and its applications in our previous post. Here we will be talking about applications enablement through quantum procedures, also known as quantum algorithms. We are going to write here about the workings of quantum. In computer programming, an algorithm is a set of well-defined instructions to solve a particular problem. It takes a set of input and produces a desired output. Quantum algorithms are a specific procedure for solving computational problems. These are different from protocols because they are a set of standard rules that allow multiple devices to communicate. The advantages of an effective quantum algorithm are as follows:

- Accuracy – solve a problem correctly
- Efficiency – solve a problem as fast as possible

Clearly the primary concern for quantum algorithms is its speed of execution. While it is important to solve every problem correctly, the long pole for the quantum algorithm is its efficiency. There is a well defined metric to measure the efficiency of the particular algorithm and it’s called Big-O-Notation. Big-O-Notation is a mathematical notation of the worst case performance of the algorithm relative to the input size (n). It is fundamentally different from runtime complexities because that later is inherently tied to hardware performance.

Using the above criteria, algorithm efficiency is represented in Big-O-Notation in the form of O(f(n)). Here O stands for Order and f(n) is a function of “n” to determine the number of operations that can be done as the input size fluctuates. Figure 1 lists some common functions of input size represented in Big-O Notation.

The main goal of quantum algorithms designers is to create algorithms that can perform any computation exponentially more efficiently on quantum computers than on conventional computers. This can be done by exploiting quantum properties such as superposition, quantum entanglement and many more. Unsurprisingly, some of the quantum algorithms have already achieved this goal. Some of the example of quantum algorithms is as follows:

- The Deutsch Jozsa algorithm is a good example. It is the first algorithm that shows the separation between the quantum and classical difficulty of a problem. This algorithm demonstrates the significance of allowing quantum amplitudes to take both positive and negative values, as opposed to classical probabilities that are always non-negative
- Shor’s algorithm is used for factoring integers in polynomial time. The computing ability of quantum computers could factor complex RSA encryption thereby undermining the global financial system. Shor’s Algorithm gave credence to the fact that quantum computers could have unforeseen economic impact
- Grover’s algorithm is another complex implementation that enables searching of an unordered list in a square root n time. Every element is scanned in an unordered list and a quantum computer could achieve this in a function order of square root

Many algorithms have been developed using quantum concepts, but not all can comply with the requirements of accuracy and efficiency – the two pillars of quantum algorithms. Therefore, not every quantum algorithm is better than classical algorithms. So, a novel approach is to devise hybrid algorithms to take advantage of the best of both worlds of classical and quantum computing. Hybrid algorithms apply concepts of both quantum and classical computing to perform higher computations and obtain better results than on one or the other. It is assumed that hybrid algorithms will become more prevalent in future as they prudently employ both quantum and classical computational power.

We will write on hybrid algorithms soon.

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