Unveiling the Difference: Quantum Algorithms vs. Standard Algorithms

Before diving into the comparison between quantum and standard algorithms, let's first define what an algorithm is. An algorithm is a sequence of instructions that computes a function. It takes a mathematical object as input, performs a procedure starting at the first step, changes the object while the procedure is being performed, and then outputs the changed object. Each step of the algorithm specifies what operation is to be performed on the object in order to change it and what step to go to next based on an observation about the object.

Classical Algorithms and Their Operations

Classical algorithms and quantum algorithms are very similar in their mathematical objects, which both take as input and output are strings of bits. However, the key difference lies in the operations that can be attached to each step. Quantum algorithms also have access to quantum operations which puts bits into superposition, but they can't output this superposition and they don't have the power to observe the superpositions. In the end, a read operation must be used to convert the superposition back to a string of bits. While quantum operations are powerful, they enable operations that classical algorithms cannot perform efficiently.

General Procedure of Algorithms

Despite the differences, both classical and quantum algorithms share the same general procedure:

Take some input Perform operations Output the result

This procedure is the basis of what we call an algorithm. The most crucial part is the second step - manipulating the data/ states to solve the problem. This is where the differences between the two types of algorithms become apparent.

Classical Algorithms - The Turing Machine

Classical algorithms can be traced back to the concept of a Turing Machine, introduced by Alan Turing in the 1930s. While today's computers might be pocket-sized and incredibly powerful, they still operate on similar principles. This involves:

Many sequential steps, which are: A simple manipulation of 0s and 1s These 0s and 1s physically exist on a long tape

This basic design allows for complex computations, but the process is sequential and deterministic, meaning each operation is performed one after another without overlapping.

Quantum Algorithms - A Quantum Leap

On the other hand, quantum algorithms operate on entirely different principles. These principles allow for a much more complex manipulation of data. For instance, IBM’s 127 qubit Eagle is a testament to the power of quantum computing. Unlike standard computers, quantum devices use qubits:

While qubit states do not physically exist in reality until they are observed, they can hold multiple states simultaneously through superposition. One qubit can hold 2 binary states, 10 qubits can hold 1000 states, and 30 qubits can hold 1 billion states. Quantum steps move qubits from one quantum state to another.

This allows for the “searching” for a solution while being in a billion states at the same time. While this capability sounds exciting, it still requires significant ingenuity to come up with exact quantum operations that will solve the input problem. One of the most famous examples of such algorithms is Shor's algorithm.

Shor's Algorithm - A Quantum Breakthrough

Shor's Algorithm is a notable quantum algorithm that efficiently solves problems that are prohibitively difficult for classical algorithms. For example, Shor's algorithm can factorize large integers into their prime factors, a task that classical computers struggle with. This capability could revolutionize fields such as cryptography.

Conclusion

While both classical and quantum algorithms share a similar basic structure, the differences lie in the underlying principles and the operations they perform. Quantum algorithms, thanks to their unique principles of superposition and qubit states, can perform certain tasks more efficiently and with more complex data manipulation. Understanding these differences is crucial for anyone interested in the future of computing and its applications.