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DEFINITIONS

QUANTUM-COMPUTING

TERMS & DEFINITIONS

Please see below for some short definitions for some quantum-computing-related keywords you’ll be likely to come across and you traverse the world of quantum-computers:

BELL’S INEQUALITY

The original Bell’s Inequality was discovered by John Stewart Bell, an Irish physicist. Other inequalities were later discovered by other researchers. Together, all of Bell’s Inequalities combine to make Bell’s theorem.

Bell proved that that the world does not comply with local realism in the classical definition of the term. ‘Local’ means that an object can only be influenced by its immediate environment. ‘Realism’ - in the physics sense - means the property of an object exists in nature outside Man’s mind before and after - if it even is - measured by someone.

Classical mechanics says particles have real - definite -values taken before and after measurement. Take two particles which have collided and traveled far apart. Any influence that one has on the other must have been conveyed via a ‘field’ near-instantaneously (but never faster than the speed of light).

Bell’s Inequality is a series of measurements in a theoretical experiment involving photon spin. Measurements are made by detectors of varying orientation. The inequality refers to the fact that one set of photon measurements will be larger than the other set - if the world exhibits local realism. As this is not the case, it implies the physical world is governed by the theories of quantum mechanics. The revelation of quantum entanglements only corroborates this view.

COHERENCE

In the quantum sense the length of time a quantum state can exist without succumbing to environmental ‘noise’ and de-cohering. Put another way, it’s the survival time of a quantum state in superposition.

CORRELATION

A quantum correlation refers to the opposing properties of two quantum states in entanglement. Such a correlation could never occur in classical mechanics. Einstein implied correlation when he spoke of ‘spooky action at a distance.’

DENSITY MATRIX

Quantum systems can be in pure or mixed states. A quantum system in a pure state has a single state vector. For example, a qubit defined only as the spin of a photon would be said to be in a pure state. When a quantum state comprises many separate observable probabilities, then it’s said to be in a mixed state. Another way of expressing this mathematically is to refer to the quantum state as a density matrix.

ENSEMBLE

The ensemble interpretation views quantum mechanics as a collection of similarly prepared systems. This compares to viewing it as one physical system. It's a very minimalist interpretation. It applies a statistical quantity only to the ensemble, rather than over and over to individual vector states within one system. This removes any contradictory mathematical assumptions.

EPR PARADOX

The EPR Paradox was first expressed by Einstein in 1933 in defiance of Heisenberg’s Uncertainty Principle. The latter states that a particle’s precise momentum and position can never be known at a particular moment. This is because the instant the particle’s momentum is measured, its position becomes affected by the very measuring; and vice versa. No particle property can ever be pinned down.

Einstein countered by describing an experiment where two particles A and B split apart and travel far away. Their momentums and positions would be related, dependent on conditions, and both properties able to be deduced. This is despite the fact that there was no longer any physical connection between them. Einstein called this a paradox, and wondered if this was not brought about by some ‘spooky action at a distance.’

FIDELITY

Quantum fidelity is the measure or precision of how close two quantum states are to each other, of which the simplest example would be two qubits. It does not refer to the space contained within a density matrix. Channel fidelity is a measure of how well information is retained within the channel and is related to quantum fidelity.

POPULATION

In the quantum computing sense, refers to a group of quantum states identified by at least one common property or vector. Often used for the purposes of data collection and analysis.

QUANTUM ANNEALING

An algorithm used in adiabatic quantum computers for solving optimization and sampling problems. It works by allowing quantum systems to find their lowest energy states. Qubits home in on the lowest energy peaks amid a landscape of data fluctuations. These both control and lower the qubits towards zero, and eventually the solution.

QUANTUM ENTANGLEMENT

Entanglement was first described by Schrödinger as the characteristic trait of quantum mechanics. It’s the link between particles, where the quantum states cannot be defined independently, but rather must be defined for the whole system. The particles are said to be in entanglement. Any change to one particle is instantaneously applied to another, whatever the distance. The vector changes are always complementary. For example a positive change in spin for one particle will cause a negative spin in its entangled partner.

Quantum entanglement kills the idea of any of Einstein’s local, hidden variables affecting the system. It proves the Universe does not operate according to classical mechanics.

QUANTUM HARVESTING

In a vacuum, the electromagnetic field entangles particles that are in space-like separated regions (this is very complex physics combining relativity and quantum-mechanics). If you are interested in this, you might want to watch this video from Professor Martin-Martinez at the Institute for Quantum Computing.

QUANTUM FINGERPRINTS

Quantum fingerprinting is used in quantum cryptography. A long string of information is described by using a shorter string so that there is a high probability that any two distinct strings will remain distinguishable by comparing their fingerprints. This can be done without any correlation or entanglement in the fingerprint’s qubits.

QUANTUM MONEY

Proposed around 1970 by Stephen Wiesner, quantum money is an ingenious idea to thwart counterfeit currency fraud. Each bill in circulation is encoded with several photons stored in a sequence of complementary states, eg, up/down. The polarizations are known only to the issuing bank. Because of the no-cloning theorem of quantum mechanics, no-one else can ever copy them.

The main drawback with this idea is that only the issuing bank can verify the bill is genuine. For any popular currency to be accepted, it needs to be able to be verified by the bearers too.

QUANTUM PRIVATE CHANNELS

Quantum channels communicate information. This includes both the qubits and the classical bits that describe their relative arrangement.

A quantum private channel is the quantum equivalent of the one-time pad used in cryptography. This is a private key generated randomly, and shared between sender and recipient. It's used once only to encrypt the message and thus is unique. Provided the recipient receives the key safely, this form of encryption is virtually unbreakable.

QUBIT

A quantum unit of information that can have two different states (like 1/0 or on/off)

QUDIT

A quantum unit of information that can have ‘d’ states (with ‘d’ being greater than 2).

RANDOMIZED BENCHMARKING

An experimental technique used to determine the mean error rate of a set of quantum gates. It involves applying random circuits that would have zero effect if the gates work flawlessly. Benchmarking is a vital procedure for evaluating performance of multi-qubit quantum computers.

TOPOLOGICAL QUANTUM-COMPUTING

An elegant method of linking qubits in braided paths, making them sturdier like knots and able to better resist decoherence. Topological quantum systems are theoretically regarded as the most stable to date.