ISO/IEC 4879:2024

Information technology — Quantum computing — Vocabulary

This document defines terms commonly used in the field of quantum computing. This document is applicable to all types of organizations (e.g. commercial enterprises, government agencies, not-for-profit organizations) to exchange quantum computing concepts.

Technologies de l'information — Informatique quantique — Vocabulaire

General Information

• Status: Published
• Publication Date: 16-May-2024
• ICS: 01.040.35 - Information technology (Vocabularies)
• ICS: 35.020 - Information technology (IT) in general
• Technical Committee: ISO/IEC JTC 1 - Information technology
• Drafting Committee: ISO/IEC JTC 1 - Information technology
• Current Stage: 6060 - International Standard published
• Start Date: 17-May-2024
• Due Date: 08-Mar-2024
• Completion Date: 17-May-2024

Standards Content (Sample)

International
Standard
ISO/IEC 4879
First edition
Information technology — Quantum
2024-05
computing — Vocabulary
Technologies de l'information — Informatique quantique —
Vocabulaire
Reference number
© ISO/IEC 2024
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on
the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address below
or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: [phone]
Email: [e-mail]
Website: www.iso.org
Published in Switzerland
© ISO/IEC 2024 – All rights reserved
ii
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
3.1 Background .1
3.2 Quantum physics background .2
3.3 Quantum information .5
3.4 Quantum processing .7
3.5 Quantum technologies .11
3.6 Related quantum technologies . 13
Bibliography . 14
Index .15

© ISO/IEC 2024 – All rights reserved
iii
Foreword
ISO (the International Organization for Standardization) and IEC (the International Electrotechnical
Commission) form the specialized system for worldwide standardization. National bodies that are
members of ISO or IEC participate in the development of International Standards through technical
committees established by the respective organization to deal with particular fields of technical activity.
ISO and IEC technical committees collaborate in fields of mutual interest. Other international organizations,
governmental and non-governmental, in liaison with ISO and IEC, also take part in the work.
The procedures used to develop this document and those intended for its further maintenance are described
in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the different types
of document should be noted. This document was drafted in accordance with the editorial rules of the ISO/
IEC Directives, Part 2 (see www.iso.org/directives or www.iec.ch/members_experts/refdocs).
ISO and IEC draw attention to the possibility that the implementation of this document may involve the
use of (a) patent(s). ISO and IEC take no position concerning the evidence, validity or applicability of any
claimed patent rights in respect thereof. As of the date of publication of this document, ISO and IEC had not
received notice of (a) patent(s) which may be required to implement this document. However, implementers
are cautioned that this may not represent the latest information, which may be obtained from the patent
database available at www.iso.org/patents and https://patents.iec.ch. ISO and IEC shall not be held
responsible for identifying any or all such patent rights.
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and expressions
related to conformity assessment, as well as information about ISO's adherence to the World Trade
Organization (WTO) principles in the Technical Barriers to Trade (TBT) see www.iso.org/iso/foreword.html.
In the IEC, see www.iec.ch/understanding-standards.
This document was prepared by Joint Technical Committee ISO/IEC JTC 1, Information technology.
Any feedback or questions on this document should be directed to the user’s national standards
body. A complete listing of these bodies can be found at www.iso.org/members.html and
www.iec.ch/national-committees.

© ISO/IEC 2024 – All rights reserved
iv
Introduction
For most of computing history, the foundational hardware technology has been binary digital transistor
logic. In such digital systems, data and programs represented as binary classical digits (bits) are encoded
into physical transistors that have and can switch between two definite internal states: on and off. The field
of quantum computing introduces a new approach to the underlying computing hardware by shifting from
classical logic (“on” or “off”) to a quantum logic where the “quantum bits” or “qubits” (the simplest units
of quantum information) are encoded into physical registers that exhibit quantum-mechanical phenomena
such as superposition and entanglement.
This shift from the classical digital representation found in today’s conventional computers to a quantum
digital representation in tomorrow’s computers is expected to bring increases in computing power and new,
innovative software applications, allowing us to tackle more complex computational problems and carry
out powerful analysis of more complex data patterns that are already challenging or impossible for today’s
technology. Quantum computing holds the potential to revolutionize fields from chemistry and logistics to
finance and physics.
However, the increase in power and capability that quantum computing will provide, will also pose an
important security threat once quantum computers become large enough (or cryptographically relevant, as
it is sometimes described). As strong as today’s cryptographic mechanisms have been against conventional
computers, almost all cryptographic protocols used are vulnerable to quantum-computing-based attacks
with known algorithms. This widely known risk associated with the power of quantum computing is very
concerning for governments, institutions and individuals whose encrypted data are safe today, but may
become decryptable once quantum computers reach large enough size.
This document aims to assist in the understanding of quantum computing concepts and the exchange of
information.
© ISO/IEC 2024 – All rights reserved
v
International Standard ISO/IEC 4879:2024(en)
Information technology — Quantum computing — Vocabulary
1 Scope
This document defines terms commonly used in the field of quantum computing. This document is applicable
to all types of organizations (e.g. commercial enterprises, government agencies, not-for-profit organizations)
to exchange quantum computing concepts.
2 Normative references
There are no normative references in this document.
3 Terms and definitions
ISO and IEC maintain terminology databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
3.1 Background
3.1.1
model
physical, mathematical, or otherwise appropriate representation of a system, entity, phenomenon,
process or data
[SOURCE: ISO/IEC 22989:2022, 3.1.23, logical has been changed to appropriate]
3.1.2
model parameter
internal variable of a model (3.1.1) that affects how it computes its outputs
[SOURCE: ISO/IEC 22989:2022, 3.3.8]
3.1.3
machine learning
process of optimizing model parameters (3.1.2) through computational techniques, such that the model's
behaviour reflects the data or experience
[SOURCE: ISO/IEC 22989:2022, 3.3.5]
3.1.4
simulator
device, computer program, or system that behaves or operates like a given system when provided a set of
controlled inputs
[SOURCE: ISO/IEC/IEEE 24765:2017, 3.3750]

© ISO/IEC 2024 – All rights reserved
3.1.5
program
computer program
syntactic unit that conforms to the rules of a particular programming language (3.1.6) and that is composed
of declarations and statements or instructions needed to solve a certain function, task, or problem
[SOURCE: ISO/IEC 2382:2015, 2121374, modified — Notes to entry omitted]
3.1.6
programming language
artificial language for expressing programs (3.1.5)
[SOURCE: ISO/IEC 2382:2015, 2121374, modified — Notes to entry omitted]
3.1.7
programming
designing, writing, modifying, and testing of programs (3.1.5)
[SOURCE: ISO/IEC 2382:2015, 2121374, modified — Notes to entry and domain identifier terms> omitted]
3.1.8
coding
process of expressing a program (3.1.5) in a programming language (3.1.6)
[SOURCE: ISO/IEC 2382:2015, 2121374, modified — Notes to entry omitted]
3.1.9
algorithm
process for computation, defined by a set of rules, that will yield a corresponding output
[SOURCE: ISO/IEC 18031:2011, 3.1, modified — Definition was modified]
3.2 Quantum physics background
3.2.1
Hilbert space
vector space equipped with an inner product operation which allows distances, angles and vector norms to
be defined
Note 1 to entry: When used in the context of quantum physics (3.2.3), the space of quantum states (3.2.7) of a quantum
system (3.2.6) is described by a complex Hilbert space, referred to as the state space.
Note 2 to entry: All possible quantum states can be represented as operators (3.2.2) on the quantum system’s Hilbert space.
3.2.2
operator
mathematical entity that transforms the elements of an input space to the elements of an output space
Note 1 to entry: In quantum physics (3.2.3), simple operators can be mathematically represented by a matrix that acts
via matrix multiplication on vectors in a Hilbert space (3.2.1).
3.2.3
quantum physics
quantum mechanics
fundamental theory of physics, in which physical properties of systems are completely determined
by vectors in a complex Hilbert space (3.2.1) whose dynamics are determined by specific types of linear
transformations on that space
Note 1 to entry: There are many different formulations of quantum physics, but the specific linear transformations
allowed must all correctly describe stronger correlations than can arise in classical physics, such as those that are
probed by Bell and Kochen-Specker tests.

© ISO/IEC 2024 – All rights reserved
Note 2 to entry: Measurement outcome probabilities are determined from the complex vectors, typically via the Born rule.
Note 3 to entry: Importantly, quantum physics is able to successfully describe the behaviour of light and matter in
operating regimes where classical theories of physics can break down, like ultrasmall sizes or energies or at low
temperatures.
Note 4 to entry: In the context of quantum computing (3.4.3), it is normally sufficient to consider quantum state
(3.2.7) evolution as being governed by the non-relativistic Schrödinger equation through the Hamiltonian (3.2.12), for
particles with mass, or the quantum electrodynamics formulation of Maxwell’s equations, for light. However, quantum
dynamics also includes broader contexts, such as the dynamics of relativistic systems, which are governed by the
Dirac equation.
3.2.4
quantum, adjective
making use of or arising from the laws of quantum physics (3.2.3) in an essential way
3.2.5
quantum, noun
discrete, finite, indivisible, and measurable unit of a physical property such as energy
3.2.6
quantum system
system whose properties are determined by the laws of quantum physics (3.2.3), and cannot be completely
described by just the laws of classical physics
3.2.7
quantum state
description of the state of a quantum system (3.2.6) defining the probability distribution of possible outcomes
of any measurement upon it
Note 1 to entry: A quantum state can be mathematically represented by a vector or, more generally, a density operator
(3.2.2) in the complex Hilbert space (3.2.1). (See Note 1 to entry in quantum operator (3.2.11) for discussion of density
operators.)
Note 2 to entry: A quantum (3.2.4) wave-function is the mathematical representation of a quantum state in a particular
basis of the Hilbert space. Wave-functions are often defined over continuous parameters, such as position, momentum
and phase.
3.2.8
quantum superposition
complex linear combination of two or more different quantum states (3.2.7)
3.2.9
basis states
members of a set of quantum states (3.2.7) which span the Hilbert space (3.2.1) of a quantum system (3.2.6)
Note 1 to entry: Any quantum state in the Hilbert space can be written as a linear combination, or quantum
superposition (3.2.8), of basis states.
Note 2 to entry: A set of basis states is often chosen to be complete and orthonormal. That is, the set spans the entire
Hilbert space, and individual elements are orthogonal and normalised to length 1.
3.2.10
quantum entanglement
property of a quantum state (3.2.7) within a joint quantum system (3.2.6), consisting of at least two
subsystems, for which the quantum state cannot be described in terms of independent characteristics of its
individual constituents
© ISO/IEC 2024 – All rights reserved
3.2.11
quantum operator
operator (3.2.2) that acts on quantum states (3.2.7) in Hilbert space (3.2.1)
Note 1 to entry: In quantum physics (3.2.3), non-pure (or mixed) states, which are classical statistical mixtures of
distinct pure quantum states, are represented by Hermitian density operators instead of complex vectors. Density
operators contain information about both coherences between the basis states (3.2.9) used to represent the quantum
state, and about the statistical distribution of those states.
3.2.12
Hamiltonian
quantum operator (3.2.11) which determines the coherent evolution of a quantum
system (3.2.6)
Note 1 to entry: The Hamiltonian operator usually corresponds to the total energy of a quantum system.
Note 2 to entry: The expectation value of the Hamiltonian gives the total energy for a particular quantum state.
3.2.13
eigenstate
quantum state (3.2.7) left unchanged by the action of a quantum operator (3.2.11), except
for a complex scaling factor
3.2.14
eigenvalue
complex scaling factor corresponding to the eigenstate (3.2.13) of a quantum operator
(3.2.11)
Note 1 to entry: Eigenvalues are real for Hermitian operators (3.2.2) and complex roots of unity for unitary operators.
3.2.15
eigenspace
Hilbert space (3.2.1) spanned by a set of eigenstates (3.2.13) that share the same
eigenvalue (3.2.14)
3.2.16
quantum measurement
process that outputs a physical property of a quantum state (3.2.7)
Note 1 to entry: Quantum measurement usually involves interaction with a meter system which encodes the output of
the physical property.
Note 2 to entry: In quantum computing, quantum measurement is often modelled as a projective measurement (3.2.17).
3.2.17
projective measurement
quantum measurement (3.2.16) for which instantaneously repeated measurements do not change the
quantum state (3.2.7) achieved after an initial measurement
3.2.18
quantum coherence
existence or extent of unambiguous phase relationships between possible states of a quantum system (3.2.6)
Note 1 to entry: Quantum coherence in a quantum system is often defined between populations of different basis
states (3.2.9) in an individual quantum state (3.2.7) of that quantum system.
3.2.19
decoherence
loss or degradation of quantum coherence (3.2.18)
Note 1 to entry: Decoherence requires interaction between a quantum system (3.2.6) and environmental degrees of
freedom.
© ISO/IEC 2024 – All rights reserved
3.2.20
coherence time
characteristic time scale for decoherence (3.2.19)
Note 1 to entry: Different measurement protocols can be designed to probe different types of decoherence (3.2.19), and
give rise to different complementary coherence times. Important examples of commonly used protocols are Ramsey,
Hahn echo and CMPG.
3.2.21
relaxation time
characteristic time scale for decay from a non-equilibrium state to the steady state of a
quantum system (3.2.6)
Note 1 to entry: Relaxation commonly refers to decay from an excited state to a lower energy state as a result of
energy decay.
Note 2 to entry: The relaxation time constant is usually denoted by T .
3.3 Quantum information
3.3.1
quantum information
information contained or encoded in a quantum state (3.2.7).
Note 1 to entry: Quantum information may be transformed via quantum (3.2.4) operations and processes.
3.3.2
quantum encoding
representation of information in states of a quantum system (3.2.6)
3.3.3
qubit
quantum system (3.2.6) with two basis states (3.2.9)
Note 1 to entry: Qubit stands for quantum (3.2.4) bit.
Note 2 to entry: Qubit is the smallest unit of quantum information (3.3.1).
Note 3 to entry: The Hilbert space (3.2.1) of a qubit is the space spanned by its two basis states. The quantum state
(3.2.7) of a qubit can therefore be any quantum superposition (3.2.8) of these states.
Note 4 to entry: In practice, qubits are often realised as physical qubits (3.3.5) in many-state quantum systems where
the computational information is stored in only two basis states (3.2.9).
Note 5 to entry: See also logical qubit (3.3.7) and qudit (3.3.4).
Note 6 to entry: By default, this document generally defines terms in relation to qubits, but these definitions can
usually also be straightforwardly applied or generalised to the case of qudits (3.3.4).
3.3.4
qudit
quantum system (3.2.6) with basis states (3.2.9) where is an integer greater than or equal to two
Note 1 to entry: Qudit stands for quantum (3.2.4) dit or quantum -level system.
Note 2 to entry: Qudit is a -fold unit of quantum information (3.3.1).
Note 3 to entry: The Hilbert space (3.2.1) of a qudit is the space spanned by its basis states (3.2.9). The quantum state
(3.2.7) of a qudit can therefore be any quantum superposition (3.2.8) of these states.
Note 4 to entry: In practice, qudits are often realised as physical qudits (3.3.6) in many-state quantum systems where
the computational information is stored in only basis states.
Note 5 to entry: Qubit (3.3.3) is a special case of qudit in which “d” is equal to 2.

© ISO/IEC 2024 – All rights reserved
Note 6 to entry: Qutrit is a special case of qudit in which “d” is equal to 3.
Note 7 to entry: See also logical qudit (3.3.4) and qubit (3.3.3).
3.3.5
physical qubit
individual tangible quantum system (3.2.6) that is used to encode the two basis states (3.2.9) of a qubit (3.3.3),
or one qubit of quantum information (3.3.1)
Note 1 to entry: Unlike a logical qubit (3.3.13), a physical qubit is usually “irreducible” in that it cannot be broken down
into multiple independent information-carrying components.
Note 2 to entry: A physical qubit is often realized (brought about in practice) by storing computational information
in a two-state subspace of a larger full Hilbert space (3.2.1), engineered to minimize interactions between the qubit
computational quantum states and other non-computational quantum states.
Note 3 to entry: In the scientific literature, a physical qubit is often just called a qubit, even though its state space may
not be strictly two-dimensional.
3.3.6
physical qudit
individual tangible quantum system (3.2.6) that is used to encode the multiple (d) basis states (3.2.9) of a
qudit (3.3.4) or one qudit of quantum information (3.3.1)
Note 1 to entry: Unlike a logical qudit (3.3.4), a physical qudit is usually “irreducible” in that it cannot be broken down
into multiple independent information-carrying components.
Note 2 to entry: A physical qudit is sometimes realised (brought about in practice) by storing computational
information in a -state subspace of a larger full Hilbert space (3.2.1), engineered to minimize interactions between the
qudit computational quantum states and other non-computational quantum states.
Note 3 to entry: In the scientific literature, a physical qudit is often just called a qudit, even though its state space may
not be strictly -dimensional.
3.3.7
logical qubit
qubit (3.3.3) encoded in a joint two-dimensional eigenspace (3.2.15) of one or more symmetry operators
(3.2.2) defined with a larger physical Hilbert space (3.2.1)
Note 1 to entry: The two basis states (3.2.9) of the logical qubit Hilbert space are used to specify its logical, or canonical,
quantum operators (3.2.11).
Note 2 to entry: Symmetry operators must have support across the entire Hilbert space (3.2.1). Mathematically, this
requires that the symmetry operators do not have a zero-eigenvalue (3.2.14) eigenspace (3.2.15).
3.3.8
logical qudit
qudit (3.3.4) encoded in a joint d-dimensional eigenspace (3.2.15) of one or more symmetry operators (3.2.2)
defined within a larger physical Hilbert space (3.2.1)
Note 1 to entry: The d basis states (3.2.9) of the logical qudit Hilbert space (3.2.1) are used to specify its logical, or
canonical, quantum operators (3.2.11).
Note 2 to entry: Symme
...