Ever wondered how quantum computing is different from traditional also called classical computing? The article is for you.

Here, I will be sharing the difference between the two in more technical terms than layman's terms. The article is a long road so to get a firm grasp on the concepts make sure to read from starting till the end. I don't think you'll ever need an article again after this.

Quantum computing and traditional computing are two fundamentally different approaches to processing information.

Traditional computers have become so polished that we can use and even program them without understanding how they work at a fundamental level.

One day, quantum computing will get to this point of accessibility, where we can use and program them without worrying about their details. But we are not quite there, yet.

The following table lists how the concepts of computing differ between traditional

Fundamental Unit

Bits vs Qubits

A bit is the basic unit of information used in classical computing, and it can be either a 0 or a 1. It represents the state of a physical system that can be in one of two possible states, such as the presence or absence of an electric charge in a circuit.

A qubit, on the other hand, is the basic unit of information used in quantum computing, and it can be in a superposition of states. This means that a qubit can be a 0 and a 1 at the same time, with a probability associated with each state. The superposition of states is a key feature of quantum mechanics that allows quantum computers to perform certain types of calculations much faster than classical computers.

Gates

Logic Gates vs Unitary Gates

Logic gates are the basic building blocks of classical digital circuits and operate on classical bits to perform logical operations such as AND, OR, and NOT. These gates are represented using Boolean algebra and their outputs are always deterministic based on the inputs.

Unitary gates, on the other hand, are the basic building blocks of quantum circuits and operate on quantum bits (qubits) to perform quantum operations such as quantum entanglement and superposition. These gates are represented using linear algebra and their outputs are always reversible, meaning that the original input can be retrieved from the output by applying the inverse gate.

While both types of gates perform logical operations, logic gates are deterministic and irreversible, while unitary gates are probabilistic and reversible. This fundamental difference is due to the underlying principles of classical and quantum mechanics.

Gates reversible

In traditional (classical) computing, logic gates are irreversible, meaning that it is not possible to recover the original input from the output. For example, the AND gate will output a value of 1 only if both inputs are 1, but it is impossible to know which of the inputs was a 1 or a 0 from the output alone.

In quantum computing, however, all gates are reversible. This is because the laws of quantum mechanics require that information is not lost during a quantum computation. Therefore, all quantum gates must be reversible to ensure that the original quantum state can be recovered from the output state. This is one of the fundamental differences between classical and quantum computing.

Universal Gate set

In traditional (classical) computing, the universal gate set consists of NAND and NOR gates, which can be used to construct any other logical gate. That is, any classical logical function can be implemented using a combination of NAND or NOR gates.

In quantum computing, the universal gate set consists of single-qubit gates and a two-qubit gate. Single-qubit gates are used to manipulate the state of a single qubit, while the two-qubit gate is used to entangle two qubits. The single-qubit gates are usually chosen to be the Pauli gates (X, Y, and Z gates) and the Hadamard gate, while the two-qubit gate is usually the CNOT (controlled-NOT) gate.

Using these gates, any quantum computation can be implemented, and the quantum circuit can be expressed as a sequence of gate operations. The ability to implement any quantum computation using a universal gate set is known as the universality of quantum computation.

It is worth noting that the choice of the universal gate set can vary depending on the specific quantum computing architecture being used. For example, some quantum computing architectures may use different two-qubit gates or additional single-qubit gates to construct the universal gate set.

Programming Languages

In traditional (classical) computing, there are many programming languages available, including high-level languages such as Java, Python, C++, and many others. These languages are used to write software that runs on classical computers and perform tasks such as data analysis, web development, and machine learning.

In quantum computing, there are also several programming languages available, although they are still in their early stages of development. Some examples of quantum programming languages include Q#, Qiskit, and Cirq. These languages are used to write quantum algorithms and programs that can be executed on quantum computers

Algebra

In traditional computing, the algebra used is primarily boolean algebra, which deals with operations on true/false or 0/1 values. Boolean algebra is used extensively in the design of digital logic circuits and is used to build the logic gates and circuits used in classical computers.

In quantum computing, on the other hand, the algebra used is primarily linear algebra, which deals with operations on vectors and matrices of complex numbers. Linear algebra is used to describe the state of a quantum system, as well as the operations that can be performed on that system. Quantum gates are represented as matrices in linear algebra, and the evolution of a quantum system is described using matrix multiplication.

Error Correcting Code

An error-correcting code is a technique used in computing to detect and correct errors that may occur during the transmission or storage of data. The goal of error-correcting codes is to ensure that the transmitted or stored data remains as accurate as possible despite errors that may be introduced during the process.

In classical computing, error-correcting codes are based on redundancy, where extra bits are added to a message to allow errors to be detected and corrected. The most commonly used classical error-correcting codes are the Hamming code, the Reed-Solomon code, and the Bose-Chaudhuri-Hocquenghem (BCH) code.

In contrast, error-correcting codes in quantum computing are based on quantum error correction (QEC), which uses the principles of quantum mechanics to protect quantum information from errors. QEC uses quantum error-correcting codes that are designed to detect and correct errors that can occur due to noise and decoherence in a quantum system.

The basic idea behind QEC is to encode a quantum state into a larger quantum system, using quantum error-correcting codes that are designed to protect against specific types of errors. The encoded state is then manipulated using quantum gates, and the results are decoded to obtain the original state. The most commonly used quantum error-correcting codes are the surface code, the color code, and the toric code.

Complexity

In computer science, complexity theory is the study of the resources (time, memory, etc.) required to solve computational problems. The two most commonly used complexity classes are P and BQP, which represent the set of problems that can be solved efficiently by traditional (classical) computers, and the set of problems that can be solved efficiently by quantum computers, respectively.

P (Polynomial Time) is the set of decision problems that can be solved by a deterministic Turing machine in polynomial time, which means that the time required to solve the problem grows no faster than a polynomial function of the size of the input.

BQP (Bounded-error Quantum Polynomial Time) is the set of decision problems that can be solved by a quantum computer in polynomial time, with a bounded probability of error. In other words, a problem is in BQP if a quantum computer can solve it with high probability of success in polynomial time.

It is widely believed that BQP contains problems that are not in P, which means that quantum computers can solve some problems more efficiently than classical computers. However, it is not known for sure whether this is true, and it remains an active area of research in quantum computing.

Strong Church-Turing Thesis

The strong Church-Turing thesis is a hypothesis in computer science and mathematics that states that any problem that can be computed by an algorithm can be computed by a Turing machine. The Turing machine is a theoretical model of a general-purpose computer that was proposed by the mathematician Alan Turing in the 1930s.

The strong Church-Turing thesis is considered "strong" because it asserts that the Turing machine can compute any problem that can be computed by any algorithm, including those that have not yet been invented. It implies that the Turing machine is a complete and optimal model of computation, and that any other model of computation is equivalent to it in terms of computational power.

The strong Church-Turing thesis implies that quantum computers do not have any greater computational power than classical computers, and that any problem that can be solved efficiently by a quantum computer can also be solved efficiently by a classical computer, albeit possibly with different algorithms.

This does not mean that quantum computers are not useful or important, but rather that they do not violate the strong Church-Turing thesis. Quantum computers are particularly well-suited for certain types of problems, such as factoring large numbers and simulating quantum systems, where they can provide exponential speedup over classical computers. However, for many other types of problems, classical computers remain the most efficient and practical solution.

Conclusion

Quantum and traditional computing are two different paradigms of computation with some important differences in how information is processed, how computations are performed, and their ability to solve certain types of problems. While quantum computing has the potential to revolutionize computing in many ways, it is still a relatively new and developing field with many challenges to overcome.