A Quantum Computing Glossary
Originally published Jan. 24, 2022, revised, updated and reposted 12/6/24
For some readers, this list may server as a refresher for helpful reference. For others, this may all be very overwhelming and confusing so I’ve curated this list to provide a broad set of definitions that should help frame the Quantum Computing (QC) potential, and for ease of reference as you come across terms where a definitional reminder would be helpful. In my very first post, I introduced QC with the following word-cloud graphic:
While not every word in this cloud bears defining in this post, I hope many of these definitions help you in your efforts to understand and appreciate QC, and I have grouped them into silos to add context (although some may naturally apply to more than one silo). This is not intended to be a complete list, and it’s likely that more definitions will need to be added over time, but this should provide a good grounding in the general nomenclature and principles.
Quantum Concepts
Superposition: classical computers use a binary system, meaning each processing unit, or bit, is either a “1” or a ”0” (“on” or “off”) whereas Quantum Computers use qubits which can be either “1” or “0” (typically “spin up” or “spin down”) or both at the same time, a state referred to as being in a superposition.
Entanglement: Quantum entanglement is a physical phenomenon that occurs when a group of particles are created, interact, or share proximity in such a way that the particles are “connected,” even if they are subsequently separated by large distances. Qubits are made of things such as electrons (which spin in one of two directions) or photons (which are polarized in one of two directions), and when they become “entangled “, their spin or polarization becomes perfectly correlated.
Quantum Supremacy: Demonstrating that a programmable quantum device can solve a problem that no classical computing device can solve in a feasible amount of time, irrespective of the usefulness of the problem. Based on this definition, the threshold was passed by Google in October 2019.
Quantum Advantage: Refers to the demonstrated and measured success in processing a real-world problem faster on a Quantum Computer than on a classical computer. While it is generally accepted that we have achieved quantum supremacy, it is anticipated that quantum advantage is still some years away.
Collapse: The phenomenon that occurs upon measurement of a quantum system where the system reverts to a single observable state. Said another way, after a qubit is put into a superposition, upon measurement it collapses to either a 1 or a 0.
Observer Effect: Related to “Collapse,” this principle refers to the fact that the mere act of observing or measuring a quantum system can change its behavior. While one of the most profound quantum properties, it can easily be experimentally proven and in fact this was done in the famous double-slit experiment performed by Thomas Young in 1801.
Bloch Sphere: a geometrical representation of the state space of a qubit, named after the physicist Felix Bloch. The Bloch Sphere provides the following interpretation: the poles represent classical bits, and we use the notation |0⟩ and |1⟩. However, while these are the only possible states for the classical bit representation, quantum bits cover the whole sphere. Thus, there is much more information involved in the quantum bits, and the Bloch sphere helps depict this.
Schrodinger’s Cat: A quantum mechanics construct or thought experiment that illustrates the paradox of superposition wherein the cat may be considered both alive and dead (until the box is opened and its status is then known for certain). This “both alive and dead” concept often confuses early students of quantum mechanics.
Heisenberg Uncertainty: (also known as Heisenberg's uncertainty principle) is any of a variety of mathematical inequalities asserting a fundamental limit to the accuracy with which the position and momentum of a particle can be known. Generally, the more precise the position is, the less precise the momentum can be described, and vice versa. This also confuses early students of quantum mechanics who are used to classical physics where speed and position are usually well known by observation.
Quantum Tunneling: Quantum Tunnelling is the quantum mechanical effect in which particles have a probability of crossing a barrier or transitioning through an energy state normally forbidden by classical physics, due to the wave-like aspect of quantum particles.
Dirac Notation: Symbolic representation of quantum states via linear algebra, also called bra-ket notation. The bra portion represents a row vector and the ket portion represents a column vector. While a general understanding of QC does not necessarily require familiarity with linear algebra or these notations, it is fundamental to a deeper working knowledge.
Hardware/Physical Components
Qubit: Also known as a quantum bit, a qubit is the basic building block of a quantum computer. In addition to the conventional—binary—states of 0 or 1, it can also assume a superposition of the two values. There are several different ways that qubits can be created and each has various pros and cons, with no clear candidate emerging as the definitive method.
Physical Qubit: This is each physical quantum computing unit, so for superconducting QCs, it would be each Josephson Junction and for atom-based QC’s it would be each atom.
Logical Qubit: This is rapidly evolving QC construct where, because of the inherent noise still present in most QCs, multiple physical qubits are aggregated into one logical qubit, similar to repetition code in early classical computers. While some suggest as many as 1,000 physical qubits are needed for each logical qubit, recent machines have significantly lowered this ratio.
Auxiliary Qubit: Unfortunately, there is no such thing as quantum-RAM (rapid access memory), so it is difficult for QCs to store information for extended periods of time. An “Auxiliary Qubit” serves as a temporary memory for a quantum computer and is allocated and de-allocated as needed (also referred to as an ancilla qubit).
Quantum Annealer: Annealing is used to harden iron, where the temperature is raised so the molecular speed increases and strong bonds are formed. The iron is then slowly cooled which reinforces these new bonds, a process called “annealing” in metallurgy. Quantum annealing works in a similar way, where the temperature is replaced by energy and the lowest energy state, the global minimum, is found via annealing. Quantum annealing is a quantum computing method used to find the optimal solution of problems involving many solutions, by taking advantage of properties specific to quantum physics. Since there are no “Gates”, the mechanics of annealing are less daunting than full blown QC, although the outputs are less refined and precise than they would be under a full gate-based QC.
Analog/Digital Quantum Computing: Analog is another non-gate form of quantum computing whereby the qubits are placed in specific geometries and then allowed to react with each other naturally, with their final arrangement being the solution. Digital quantum computing generally refers to using gates to run algorithms.
Quantum Dot: Quantum dots are effectively “artificial atoms.” They are nanocrystals of semiconductor trap and manipulate individual electrons. The dots can be confined in a photonic crystal cavity, where they can be probed with laser light.
Quantum Sensor: Quantum sensing has a broad variety of use cases including enhanced imaging, radar and for navigation where GPS is unavailable. Probes with highly precise measurements of time, acceleration, and changes in magnetic, electric or gravitational fields can provide precise tracking of movement. In this case, if a starting point is known, the exact future position is also known, without the need for external GPS signals, and without the ability for an adversary to jam or interfere with the signals, so this is of particular interest to the military. Another application of quantum sensing involves ghost imaging and quantum illumination. Ghost imaging uses quantum properties to detect distant objects using very weak illumination beams that are difficult for the target to detect, and which can penetrate smoke and clouds. Quantum illumination is similar and can be used in quantum radar.
Cryostat: A device that chills to cryogenic temperatures, generally meant to be less than -150 Celsius (equal to 123 Kelvin). Cryogenics are of particular interest for QC when applied to silicon-based semiconductors because at this temperature, such semiconductors operate with superconductivity (i.e., the electrons flow with no resistance).
Dilution Refrigerator: Often referred to as a “Dil-Fridge” it is an extreme cryostat that is used in superconducting qubits and often with quantum dots, whereby a series of physical levels (typically 7) are sequentially chilled to the lowest level, where the qubits operate. Dil-Fridges create the coldest environment possible, even colder than outer space. Some QCs require Dil-Fridge temperatures to reach millikelvin (i.e., just a tiny fraction above absolute zero).
High Performing Computer (HPC): Sometimes also referred to as a “supercomputer” is generally meant to represent any ultra-high performing classical computer. Powerful gaming PCs operate at 3 GHz (i.e., 3 billion calculations per second) while HPC’s operate at quadrillions of calculations per second. Despite this blazing speed, there are many problems that HPC’s cannot perform in a reasonable about of time, but theoretically can be solved with a QC in a very short amount of time.
Computing Operations
Gate: A basic operation on quantum bits and the quantum analogue to a conventional logic gate. Unlike conventional logic gates, quantum gates are reversible. Quantum algorithms are constructed from sequences of quantum gates.
Hadamard Gate: The Hadamard operation acts on a single qubit and puts it in a superposition (i.e., turns and spins the qubit so the poles face left and right instead of up and down). It is an important universal gate operation.
Clifford/Non-Clifford Gates: In addition to the Hadamard Gate, there are a variety of other gates. Clifford Gates generally refer to “full 180-degree rotations” of the qubit. For example, there are a series of Pauli gates that rotate the qubit on the X, Y or Z axis. There are also specialized non-Clifford Gates that apply only partial rotations, such the S, P and T gates and which are generally much more difficult to execute but which are essential for full quantum advantage.
Shot: Because quantum is probabilistic, in practice quantum algorithms are run or executed many (often thousands) of times and the results are averaged. Each execution is referred to as a “shot.”
Quantum Error Correction: The environment can disturb the computational state of qubits, thereby causing information loss. Quantum error correction combats this loss by taking the computational state of the system and spreading it out over an entangled state using many qubits. This entanglement allows observers to identify and remedy disturbances without observing the computational state itself, which would collapse it. Many error correcting qubits are required for each logical qubit.
Fault Tolerance: technical noise in electronics, lasers, and other components of quantum computers lead to small imperfections in every single computing operation. These small errors ultimately lead to erroneous computation results. Such errors can be countered by encoding one logical qubit redundantly into multiple physical qubits. The required number of redundant physical qubits depends on the amount of technical noise in the system. For superconducting qubits, experts expect that about 1,000 physical qubits are required to encode one logical qubit. For trapped ions, due to their lower noise levels, only a few dozens of physical qubits are required. Systems in which these errors are corrected are fault tolerant.
NISQ: Noisy intermediate-scale quantum, coined by John Preskill in 2017, meant to depict the current state of QC whereby qubits suffer from noise and rapid decoherence. It generally means the establishment of 50-100 logical qubits (the “intermediate-scale” portion of the definition, which would require 100,000 – 1,000,000 physical qubits with the balance of the qubits dedicated to noise reduction).
Coherence/Decoherence: Coherence is the ability of a qubit to maintain its state over time. Decoherence generally occurs when the quantum system exchanges energy with its environment, typically from gravity, electromagnetism, temperature fluctuation or other physical inputs (see “Noise”). Longer coherence times generally enable more computations and therefore more computational power for QCs.
Speedup: The improvement in speed for a problem solved by a quantum algorithm compared to running the same problem through a conventional algorithm on conventional hardware.
Measurement: the act of observing a quantum state. This observation will yield classical information, but the measurement process will change the quantum state. For instance, if the state is in superposition, this measurement will ‘collapse’ it into a classical state of 1 or 0. Before a measurement is done, there is no way of knowing what the outcome will be.
Noise: In QC, noise is anything which impacts a qubit in an undesirable way, namely electromagnetic charges, gravity or temperature fluctuations, mechanical vibrations, voltage changes, scattered photons, etc. Because of the precise nature of qubits, such noise is nearly impossible to prevent and requires substantial error-correction (to correct for the noise) in order to allow the qubits to perform desired calculations.
No Cloning Theorem: The no-cloning principle is a fundamental property of quantum mechanics which states that, given a quantum state, there is no reliable way of producing extra copies of that state. This means that information encoded in quantum states is unique. This is sometimes annoying, such as when we want to protect quantum information from outside influences, but it is also sometimes especially useful, such as when we want to communicate securely with someone else.
Applications
Quantum Algorithm: An algorithm is a collection of instructions that allows you to compute a function, for instance the square of a number. A quantum algorithm is exactly the same thing, but the instructions also allow superpositions to be made and entanglement to be created. This allows quantum algorithms to do things that cannot be done with classical algorithms.
Shor’s Algorithm: An integer factorization algorithm written in 1994 by American mathematician Peter Shor. It is open-sourced and currently available to anyone to use to break encryption protocols relying on the difficulty of factoring large numbers. No QCs are yet powerful enough to use this algorithm to circumvent RSA or related encryption, but that will change at some point in the coming years and many cite this as the primary catalyst for the massive investment currently underway in QC, notably by large governments. “Post-Quantum” encryption is generally meant as a protocol that would not be vulnerable to Shor’s Algorithm.
Grover’s Algorithm: Another open-source algorithm already written, intended for search optimization. For most current computer searches, the target samples must either be processed one at a time until the desired result is found, or the data must be organized (i.e., put in numerical or alphabetical order) to be searched more efficiently. Grover’s algorithm can simultaneously search much of the entire field (depending on the power of the QC) and therefore find results much faster. Shor’s and Grover’s algorithms are often the first two algorithms cited when discussing quantum supremacy and are elegant examples of the speedup that QC’s can provide.
Quantum Development Kit (QDK): A number of providers offer different types of QDK’s including some that are proprietary and others that are open source. It generally contains the programming language for quantum computing along with various libraries, samples and tutorials. QDK’s are available from the following companies (with their QDK name in parentheses): D-Wave (Ocean), Rigetti (Forest), IBM (Qiskit), Google (Cirq), Microsoft (Q#), Zapata (Orquestra), 1Qbit (1Qbit SDK), Amazon (Braket), ETH Zurich (ProjectQ), Xanadu (Strawberry Fields) and Riverlane (Anian).
Oracle: A subroutine that provides data-dependent information to a quantum algorithm at runtime. It is often used in the context of “how many questions must be asked before an answer can be given” in order to confirm or establish quantum advantage.
Quantum Cloud: Access to Quantum Computers via a cloud-based provider. Some prominent firms currently offering such access includes IBM, Amazon, Google, and Microsoft, among others. Two benefits of such QC access include lower up-front costs (users do not need to buy any hardware) and futureproofing (i.e., as the QC makers create more powerful machines, cloud access can be directed to the newer machines without any added investment required by the users).
Quantum Communication: A method of communication that leverages certain features of quantum mechanics to ensure security. Specifically, once a given qubit is “observed” or measured, it collapses to either a “1” or a “0”. Therefore, if anyone intercepts or reads a secure quantum message, the code will have changed such that the sender and receiver can see the impact of the breach. QKD or quantum key distribution is an existing technology that is already in use over fiber optics, certain line-of-sight transmissions, and recently by China via a special satellite, between Beijing and Austria.
I hope this glossary is a useful companion for your journey in understanding and appreciating Quantum Computing. Feedback is always invited.
Disclosure: I have no beneficial positions in stocks discussed in this review, nor do I have any business relationship with any company mentioned in this post. I wrote this article myself and express it as my own opinion.
References:
Quantum Computing: Progress and Prospects, The National Academies Press, 2019
Azure Quantum Glossary, Microsoft.com, accessed January 22, 2022
The Rise of Quantum Computing, McKinsey & Company, December 14, 2021
Glossary, Dotquantum.io, accessed January 22, 2022
Dilmegani, Cem, Quantum Computing Programming Languages, AI Multiple, published April 11, 2021, updated January 4, 2022.
Parker, Edward, “Commercial and Military Applications and Timelines for Quantum Technology” Rand Corporation, July 2020.
This is extremely helpful!