Quantum Computing Series, Part 4: Superposition in Quantum Mechanics

Quantum superposition

Quantum computing studies theoretical computation systems that make direct use of quantum-mechanical phenomena, such as superposition and entanglement, to perform operations on data. Quantum computers are different from binary digital electronic computers, which are based on transistors.

Superposition and Entanglement

It’s only when you look at the tiniest quantum particles—atoms, electrons, photons, and the like—that you see intriguing phenomena like superposition and entanglement.

Superposition refers to the quantum phenomenon where a quantum system can exist in multiple states or places at the exact same time. In other words, something can be “here” and “there,” or “up” and “down” at the same time.

Entanglement is an extremely strong correlation that exists between two or more quantum particles. So strong, in fact, that the quantum particles are inextricably linked in perfect unison, even if separated by great distances. The particles are so intrinsically connected, they “dance” in instantaneous, perfect unison, even when placed at opposite ends of the universe. This might seem well nigh impossible, but is fundamental to quantum world. Einstein, intrigued by the mind-bending phenomenon, described entanglement as “spooky action at a distance.”

A composite system can be expressed as a sum or superposition of products of the individual states of the local constituents.

Superposition helps do away from binary constraints. The working of a quantum computer is based on using the particles in superposition. Rather than representing bits, such particles represent qubits, which can take on the value 0, 1, or both simultaneously.

Quantum computer can hold the information using a system that can exist in two states at the same time. This is possible due to the superposition principle of quantum mechanics. This “qubit” can simultaneously store a “0” and “1.” Similarly, two qubits can simultaneously hold four (22) values: 00, 01, 10, and 11.

Quantum Computers vs Digital Computers

Quantum computers differ from traditional digital computers, which are based on transistors. Common digital computing encodes data into binary digits (bits), each of which is always in one of two definite states (0 or 1). In contrast, quantum computation uses quantum bits, which can be in superposition of states. A quantum Turing machine, a theoretical model of such a computer, is also known as the universal quantum computer. The foundation of quantum computing was laid by the work of Paul Benioff and Yuri Manin in 1980, Richard Feynman in 1982, and David Deutsch in 1985. In 1968, a quantum computer that used spins as qubits was formulated for use as a quantum space–time.

A classical digital computer has a memory made up of bits, where each bit is represented by either 0 or 1. In a quantum computer, a sequence of qubits is maintained. A single qubit can represent 0, 1, or any quantum superposition of those two qubit states. Two qubits can be in any quantum superposition of four (22) states. Similarly, with three qubits, it can be any superposition of eight (23) states. Therefore, one can generalize that n qubits can simultaneously be in a superposition of up to 2n different states.

This is in contrast to a classical digital computer that can only be in one of these states at an instant.

How Does a Quantum Computer Work?

The working of a quantum computer involves setting the quantum bits (qubits) in a perfect drift, representing the problem it is solving and manipulating these qubits with a fixed sequence of quantum logic gates. The sequence of gates applied to solve a problem is called a quantum algorithm. Because making a measurement destroys the quantum system meaning collapse of the system of qubits into one of the states, the calculation ends with a measurement. A pure state is where each qubit is zero or one, decomposing into a classical state. This means that the outcome can include a maximum of n classical bits of information. In contrast with digital algorithms that are definite, quantum algorithms, in contrast, are mostly probabilistic. This means that quantum algorithms provide a solution to a problem with a certain probability.

An example of an implementation of qubits of a quantum computer could start with the use of particles with two spin states, “down” and “up.” However, any system possessing an observable quantity A, which is conserved under time evolution such that A has at least two discrete and sufficiently spaced consecutive eigenvalues, is a suitable candidate for implementing a qubit. This is true because any such system can be mapped onto an effective spin-1/2 system.

Qubits comprise controlled particles and the means of controlling these (more specifically, the states of) particles. Examples of such means are devices that trap particles and switch them from one state to another.

How Capable is a Quantum Computer?

Theoretically, large-scale quantum computers can solve certain problems much quicker than any available classical computer. Even the best currently known algorithms, such as integer factorization using Shor’s algorithm or the simulation of quantum many-body systems would be no match for quantum computers. There exist quantum algorithms, such as Simon’s algorithm, that run faster than any possible probabilistic classical algorithm. A digital computer could, in principle, simulate a quantum algorithm. This is because quantum computing does not violate the Church–Turing thesis. Such a simulation though requires an exponential rise in number of resources needed by the digital computer to do so. On the other hand, quantum computers may be able to efficiently solve problems not feasible on classical computers.

The Current State of Quantum Computing

As of 2017, the development of actual quantum computers is still in its infancy. Experiments have been carried out, however, wherein quantum computational operations were executed on a very small number of quantum bits. National governments, military agencies, and many others are funding both practical and theoretical research in quantum computing. Once realized, quantum computers will find extensive use in civilian, business, trade, environmental, and national security purposes, such as cryptanalysis.


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