The Ultimate Quantum Glossary

It can be hard to keep up with all the quantum jargon these days! This glossary serves as a little help. Refer back to it as many times as you need!

Edited by: Alexandra Herrtage

This is a glossary for all the technical terms that are mentioned in the blogs/podcast. Please refer back to it at any time when necessary! It shall be updated consistently so for the most up-to-date version please check the website under the section ‘Glossary’. Thankyou!

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All-To-All Connectivity: This is the ability to entangle any set of qubits to eachother within a quantum system as desired. This is an incredibly hard trait to manufacture and has many advantages.

Ancillary: Something on the side that supports the main part. For example, a qubit can be ancillary to the main qubits - meaning it has a supporting role.

Artificial Intelligence: The simulation of human intelligence in machines that are programmed to think, learn, and solve problems like humans do. By learning the complex relationship between words, they can be trained to almost fufill almost any purpose.

Beam Splitters: A type of optical device that divides an incident light beam into two or more separate beams. We can use this to develop superposition.

Bell's theorem: No theory of local realism, such as local hidden variables theory, can account for correlations between entangled particles predicted by quantum mechanics.

Bloch Sphere: An angular representation of the state of a qubit. It is mathematically valid and helpful for visualising how quantum operations affect a qubit. It also visually demonstrates phase.

CHSH inequality: A mathematical framework that has been purposefully violated in photon detector experiments to contradict local realism and thereby prove entanglement exists.

Classical Computing: This refers to normal computing where the devices compute using transistors. There is nothing quantum about these computers so we call them purely ‘classical’.

Coupling: Generally refers to the process where a system forms a transfer or interaction with another. If a quantum system couples to an external environment, energy and information can become lost to the environment as a result.

Cryogenic: Any super-cold setup, and I mean incredibly cold such as -272 °C, can be considered cryogenic. It is an important condition for certain types of quantum computing such as superconducting qubits.

Decoherence: The process in which a quantum state represented by qubits becomes less and less quantum. Factors such as the external environment or thermal fluctuations, to name a few, reduce the quantumness of a system over time. This can reduce how effective a quantum computer - essentially diminishing its advantageous properties such as entanglement and superposition.

Distributed Quantum Computing: An approach to quantum computing that enables multiple quantum processors, or quantum nodes, to work together in an entire system in order to solve problems with greater speed whilst mitigating errors. A single quantum computer cannot be scaled due to errors, multiple smaller quantum computers working together can achieve the same effect as one large quantum computer.

DiVincenzo Criteria: 5 essential requirements any quantum computer should adhere to in order to be considered a proper and useful quantum computer (technically there are two more extra criteria as well).

Electrical Resistance: A fundamental property of materials and circuits that opposes the flow of electric current. Caused by collisions between electrons and the atoms within the material, it converts electrical energy into wasted heat.

Energy Levels: In quantum systems and quantum particles, they can only exhibit certain energies. This can be thought of as the rungs of a ladder, there is no intermediate rung that a particle can stay on. The energy levels are discrete rather than continuous.

Entanglement: Refers to a quantum state in which two or more qubit states are correlated and indistinguishable. This means, essentially, that they are ‘mixed-up’ with each other and cannot be thought of as separate qubits anymore. When an operation is performed on one qubit, the other qubit experiences the same operation simultaneously.

Frequency: In physics, frequency refers to how often a wave repeats itself per second.

Gate Fidelity: Refers to how ‘faithful’ or reliable a quantum gate is. In other words, the probability that a quantum gate will correctly perform its operation as intended. A quantum system with low gate fidelity is unable to accurately calculate and solve problems.

Ground State: Refers to the lowest energy level of a qubit (state 0). This can be thought of as the most naturally ‘comfortable’ state for a qubit to be in - and generally quantum computation will begin with all qubits at this level. When we want to refresh and reset a quantum system we will put all qubits back to state 0.

Hardware: This refers to the physical devices that perform computation. Think, cables and wires and plugs.

Hilbert Space: Invented by Polymath John von Neumann and named after David Hilbert, the easiest way to describe a Hilbert Space is that it is a mathematical representation of all possible states that can occur. We use the term ‘Hilbert Space’ to describe all the mathematically possible states that qubits can be in.

Hybrid Quantum-Classical algorithm: An algorithm that utilises both a quantum computer and a classical computer. This can be advantageous as we can let the quantum computer handle what it is best at handling, and likewise allow the classical computer to do what it is best at.

Interference: Quantum interference is a phenomenon where quantum states, existing in superposition, interact with each other and either amplify or cancel out, significantly influencing the probability of specific measurement outcomes. This mechanic is the backbone function of almost all quantum algorithms.

Josephson-Junction: Developed by famous British physicist Brian Josephson, think of it simply as a small, looped circuit, capable of simulating properties akin to the quantum nature of atoms. Two superconductors are placed in close proximity and separated by a thin barrier - this allows for electrons to tunnel from side to side and generate supercurrent (current that flows indefinitely without any heat leakage via electrical resistance).

LLMs: These are Large Language Models, which are a type of Artificial Intelligence based on verbal communication and are trained on vast amounts of text data to understand and generate text-based responses.

Logical Qubit: A quasi-qubit that is made up of many. For example, we can use the state of three qubits to ‘represent’ overall qubit. This is useful for error-correction where we want qubit states to remain stable.

Many-body system: A complex system involving many interacting particles. As the size of this system grows it becomes harder to simulate on a classical computer. This is why we turn to quantum computers instead.

Matter-Wave Hypothesis: As coined by Louis de Broglie in his PhD Thesis in 1924, matter can behave like a wave when in motion. Therefore, even matter can have a frequency.

Measurement Backaction: A phenomena that causes uncertainty - the act of measurement has an innate uncertainty associated with it which can change the value of whatever property is being measured. This is because ultimately there is always a fluctuating uncertainty involved with every action in quantum mechanics.

Mixed State: A mixed state, unlike a pure state, has a degree of classical uncertainty about it. This means that the purely quantum description is not enough and it is being affected by the surrounding environment. It has a probability of being one pure state or perhaps another - there is a lack of knowledge about which quantum state it truly is.

Monte-Carlo Simulation: A mathematical technique that predicts possible outcomes of an uncertain event.

NISQ: Noisy-Intermediate-Scale-Quantum refers to the current era of quantum technology. Quantum devices suffer from noise and so therefore cannot be scaled beyond ‘intermediate’ size without suffering too much from errors.

Noise: Noise can be thought of as unwanted disruptions in the environment that affect quantum systems. Noise can arise from many sources such as thermal fluctuations, vibrations, charge and spin fluctuations or imperfections in the design of a quantum computer.

Parallelism: In the quantum computing context this refers to the ability for quantum computers to perform multiple calculations at the same time. This is one of the main advantages of using a quantum computer over a classical computer, the quantum computer can use superposition to its advantage.

Phase: When we think about a travelling wave, we can imagine looking at whether it is at the peak or the trough of such a wave. Equally, the quantum state of qubits can be described much like a wave. The phase refers to which point in the cycle the wave is currently at. Global phase is irrelevant in quantum computing as this describes a factor which shifts the phase of every single component equally. However, relative phase is CRUCIAL for quantum computing as this describes the difference in phase of different quantum states in superposition. Different phases can cancel each other out or combine in magnitude - thus this principle is the fundamental mechanism for prevalent quantum algorithms.

Photon: A particle of light. They are massless and behave as both a particle and a wave depending on how you observe them.

Polarisation: In the quantum-mechanical description, it is a property of any quantum state, say a photon, and can take on any direction. It can be thought of as the associated direction of it’s electric field / the spin of the photon.

Pure State: This is a type of quantum state where there is no classical uncertainty associated with it. This means that we have complete quantum knowledge of the state and it can be described in a completely quantum way (with a wavefunction).

QPU: Quantum Processing Unit, the heart of the computer made of qubits that powers all operations that take place within the quantum computer.

Quantum Advantage: Quantum advantage is a conceptual time period in which quantum computers generally outperform classical computers on most tasks. This is the direction all quantum computing physicists are trying to head towards.

Quantum Algorithm: This is a step by step procedure which runs on a quantum computer. This can involve one or many quantum circuits and can even make use of a classical computer on the side. We run quantum algorithms in order to achieve a purpose or answer to a problem. For example, Shor’s Algorithm can be used to factorise a large composite prime number - which takes a normal computer years and years to do otherwise.

Quantum Apocalypse: A conceptual era in which quantum computers are able to easily break current methods of digital encryption.

Quantum Circuit: A set of ordered instructions for a quantum computer to apply to a set of qubits. These instructions are generally in the form of quantum gates. A quantum circuit can be used to solve real-world problems and to give answers faster than classical computers.

Quantum Circuit Depth: Circuit depth is a measure of the amount of time and gates required to fully execute a quantum circuit. Larger depth circuits are harder to run on real quantum hardware as over time the qubits decohere.

Quantum Cryptography: This is the art of securely encoding data using a quantum computer or some quantum method. This allows for secure communication between two groups by leveraging properties such as superposition and entanglement.

Quantum Dot: A tiny crystal that can absorb energy and spit out single photons at a time. Moreover, these photons can sometimes come out entangled with each other.

Quantum Electrodynamics: A Quantum Field Theory describing how matter and light interact with each other. It is the first theory that allows for special relativity and quantum mechanics to agree with each other.

Quantum Error Correction: This a field of quantum computing that is dedicated to reducing and mitigating errors that occur in quantum devices. Quantum errors can be mitigated in many ways, for example, through ‘surface codes’ or ‘dynamical decoupling’. These methods are very advanced so it is left for the reader to read further.

Quantum Gate: An instruction given to a quantum computer to execute. A quantum gate can manipulate the state of 1 or more qubits at a time. A quantum circuit is a set of ordered quantum gates (instructions), therefore. A ‘native gate set’ is the arsenal of quantum gates that a particular quantum computer has - these can be combined in certain sequences to create other gates which it does not inherently have (see universal set).

Quantum Mechanics: This is the study of all things quantum, and the processes that define them. It is a field that has existed since the 1900’s, with pioneers such as Max Planck or Erwin Schrödinger or indeed Albert Einstein (to name a few). Quantum mechanics helps us to understand the smallest things, atomic processes that ultimately govern our world at the largest of scales.

Quantum Sensing: Quantum sensing is the field in which quantum devices leveraging quantum properties can be used to detect and measure physical properties with much greater accuracy than traditional sensing methods.

Quantum Stack: The quantum stack is the entire quantum machine, all the way from the innate qubit system to the classical computer that interprets the results, and everything inbetween.

Qubit: The fundamental building block and unit of information of a quantum computer. Qubits can come in many different physical forms but all qubits can inherently utilise superposition and entanglement. Some notable types:

• Photonic Qubits are qubits which are made from particles of light, i.e: photons. They rarely decohere.

• Topological qubits are a complicated type of qubit in which its state can be represented by the properties of anyons that braid with eachother. (nuff’ said)

• Superconducting qubits are qubits made from a superconducting circuit that have properties such as zero-resistance at very cold temperatures.

• Trapped-ion qubits are spatially confined charged particles which can be used as a qubit.

Simple Harmonic Oscillator: It is a type of system in which a body in motion moves cyclically between a point of equilibrium. This type of oscillation can be found in nature and is mathematically used to describe phenomena, for example, heated atoms.

Software: The computer code that runs on hardware, that peforms calculations and solves problems. Some software can run using the fundamental syntax of the computer and others are more ‘high-level’ and use fancy commands and words to effect complex operations with ease. Think, coding and hacking.

Spin: It is an inherent and intrinsic form of angular momentum. It does not mean it is literally spinning. It is a quantum property which particles have, they just do. We have verified this experimentally.

Subroutine: In the context of quantum algorithms, a subroutine is a self-contained quantum circuit or process that is contained within a larger algorithm.

Superconductivity: At incredibly cold temperatures, certain materials can exhibit strange and wonderful properties - such as zero resistance or expelling magnetic fields. This is known as superconductivity.

Superposition: Refers to a quantum state that cannot be defined to be 0 or 1, rather it is its own independent state which is a combination of both. Any operation performed on a superposition state affects both the 0 and the 1 at the same time.

The Theory of Relativity: Primarily developed by Albert Einstein, this comprehensive theory combines special relativity and general relativity. Special relativity deals with the relationship between space and time, stating that time is relative. General relativity incorporates gravity, describing gravity as a curvature of spacetime.

The Transistor: The fundamental building block of the classical computer. It is much like a light switch that can be put in the ‘off’ or ‘on’ state. We use this transistor to perform computation and to store information.

Uncertainty Principle: As developed by Werner Heisenberg, the principle states that the position and the momentum of an electron (or indeed any quantum particle) cannot be simultaneously known to full precision. In trying to measure one of these properties to 100% accuracy, you end up losing information about the other as a trade-off.

Universal Set: Referring to quantum gates, a universal set is a set of gates that can perform any type of transformation on a quantum computer to create any type of algorithm or desired circuit.

Wavefunction: A mathematical description of the quantum state of a system. From the wavefunction, we can determine the probability of measuring each component of the state.

Wavefunction Collapse: This is a phenomena whereby the act of observing or measuring a quantum state causes the wavefunction to collapse into only one constituent. This is because the act of measuring is classical and so the quantum state can no longer exist upon observation - much like Schrödinger’s cat.

Weak measurements: A type of quantum measurement that doesn’t disturb the quantum state - yet whether it provides accurate information is still up for debate.

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