Quantum Computing — What it requires?
Explores fields and concepts required for Quantum Computing
Contents
Explored major fields and topics. Starting with explaining a bit introduction of Classical Computers, Quantum Computing, Qubits — Basis state, State, Statevector, QC Works on, Advantage over Traditional Computing, Prerequisites, Fields or Subject Contributing, Quantum Properties, QC Serving Fields, QC Providers, Limitations of QC.
Starting with Classical Computers.
Classical Computers: Traditional Computers work both Theory (Turing Machines) and practice (PCs, laptops, tablets, smartphones, etc.,) on the basis of the laws of classical physics, specifically by utilizing the flow of electricity.
Bits: Traditional computing bits are in a state of either “0” or “1”.
Basis State: Consider a System with 2 basis states, call them 0 and 1 (only single-digit) in Classical Computers and vectors in Quantum Computing as |0> & |1> (vector)
Qubit: Any Quantum Bit or Qubit can take 0 or 1 or both 0–1 at the same time. All operations processing in the form of Qubits in Quantum Computing.
Qubit Representation: It can be in any superposition, it can take |0> or |1> or both |0>+ |1> with their amplitudes or probabilities and their norm must be 1. Well, The representation of |0> & |1> in Dirac Notation, which will see in this article.
Quantum State: A Quantum State can be held by a Qubit of any 2-Dimensional column vector of real or complex numbers with their norm is 1.
Quantum information is the information of the state of a quantum system.
Quantum State Vector: The State of a single Qubit can be represented by a 2-D column vector of the unit norm, and their magnitude or amplitudes or probabilities squared of its entries must sum to 1. This Vector is Quantum State Vector. Below picture shows
A Brief Introduction of QC over Traditional Computers:
What is Quantum Computing(QC)? Quantum Computing refers to the use of Quantum-mechanical phenomena (Quantum Properties: Superposition & Entanglement) to perform computation. The Quantum Volume (Interference) is a measurement that takes into account the number of Quantum bits (or Qubits) of a machine as well as their connectivity and error rates.
Quantum computers use these two properties to achieve speed and computational spaces that would defeat a classical machine, by encoding data into the Quantum States and performing Quantum Operations on it.
Quantum Computers are believed to be able to solve computational problems faster than classical computers and promise to outperform even the most capable of present and future supercomputers. Let us see how states of Classical Computers and Quantum Computers will compute.
Quantum Computer seeks to exploit the laws that govern the behavior of atoms and subatomic particles.
On What QC works? QC is a Computational Model, QC works on high-dimensional Vector Space.
Advantages Over Classical Computing? Space and Computational Power.
Prerequisites for Quantum Computing: Linear Algebra and Quantum Physics (which is optional).
Fields or Subjects contributing to Quantum Computing:
How each subject contributed to Quantum Computing? The above diagram helps to understand in a nutshell and its explanation is given in particular sections.
Quantum Mechanics: A Mathematical framework or set of rules for the construction of physical theories. The Physical Theory is Quantum Electrodynamics, which briefly explains with fantastic accuracy the interaction of atoms and light.
Quantum Electrodynamics is built up within the framework of quantum mechanics, but it has specific rules not determined by Quantum Mechanics.
The Relationship between Quantum Mechanics & Quantum Electrodynamics is rather the relationship of Computer OS to specific applications software.
Computer Science/ Maths / Probability: Where Algorithms can be written in the form of computer programs. Many other topics like Turing Machines, Finite Automata, etc., will be used in algorithms.
Stats / Probability: Stats and Probability used in Algorithms measurement of Quantum Properties.
Maths: Linear Algebra (LA) is essential to understand Quantum Computing, without LA unable to proceed.
Vectors:Vector Spaces, Norms of Vector, Unit Vector, Linear Combinations, Linear Independence/Dependence, Adjoint Vector, Inner product, outer product, Matrices: Matrix Multiplication and Tensor Products, Identity Matrices, Inverse, Unitary, Hermitian, Eigen Values, Eigen Vectors, Exponential Matrices, Diagonals, Spectral Theorem,etc.,
The following topics are minimally required in Linear Algebra. Topics described in Quantum Computing — required Linear Algebra.
Quantum Programming concepts explored in detail in the below article.
Information Theory: It is mostly concerned with the problem of sending classical information (alphabets, speech, string of bits) — over communications channels that operates on the basis of classical physics. Information Theory tends in Quantum Computing will become Quantum Information Theory. Quantum Information Theory is the study of communications channels and identifies 3 major fundamental goals to 1) identify elementary classes of static resources in quantum mechanics 2) identify elementary classes of dynamic processes in quantum mechanics 3) to qualify resource trade-offs.
Cryptography: It deals with the communication or computation involving two or more parties who may not trust each other. Well-known cryptographic problem is the transmission of secret messages. Two parties are Quantum Bits or Qubits.
Quantum Properties
To manipulate the state of a Qubit using ‘3’ properties, they are Superposition, Entanglement, and Interference.
Superposition: It refers to a linear combination of states we would ordinarily describe independently. For Example: If you play ‘2’ Musical Notes, what you will hear is a Superposition of 2 Notes. |St> = a |0> + b |1>.
Entanglement: Entangled particles (Bodies) behave together as a system in ways that cannot be possible in classical systems.
Interference: A Quantum System can exhibit interference effects during the course of evolution.
For Example, Quantum States undergo interference due to phenomenon as the phase when 2 waves are in phase their amplitudes are added, otherwise, amplitudes canceled.
Superposition deals with object exist at different points. Existence in multiple states is called Superposition and relationships among these states are called Entanglement.
In the above picture, Quantum Properties explained interacting Quantum bits. Superposition of 4 Qubits and Entanglement (relations, 1–2,2–3,3–4,4–1 (not drawn in the pic)) among 4 Qubits and only 2 bits were selected during Interference (Evaluation). Outside shows on Qubits but Internally it will get evaluated through amplitudes of its basis states.
How Internally will get work on amplitudes or probabilities in the Quantum Computing — Concepts of Quantum Programming.
Quantum Computing serves the following Industries: (Note: These industries supported by Honeywell’s Quantum Computing)
Data centers: For analysis of large data sets and Machine Learning, Aerospace & Defense, Oil & Gas, Manufacturing, Finance, Telecommunication, Pharmaceuticals, Chemicals.
Data Mining and Artificial Intelligence: Data Mining and AI would be major beneficiaries, along with sciences that deal in volumes of data, from astronomy to linguistics.
Quantum Computing Companies as of 2020: Accenture, Amazon Bracket, AT&T, Atos Quantum, Honeywell, Google Quantum AI Lab, IBM, Intel, Microsoft, and Baidu.
Limitation and Portability: As of now, we can execute our algorithms or programs in Quantum Computing as a service in Quantum Providers. Due to its size, configuration, the temperature it is not portable, once it is portable like Traditional Computer then really we can make wonders with machines.
Conclusion:
In 1981, the physicist Richard Feynman wrote: “Trying to find a computer simulation of physics seems to me to be an excellent program to follow out… Nature isn’t classical… and if you want to make a simulation of nature, you’d better make it quantum mechanical, and by golly, it’s a wonderful problem, because it doesn’t look so easy.”
If we start our journey by adopting a new computation model then definitely will achieve a more stable advanced technological life.
Thank you for reading my article, appreciated your feedback, comments, share, and mistakes if any.
References:
Quantum Computation and Quantum Information 10th Edition — Cambridge University Press — By Michael A.Nielsen & Issac L.Chuang
