This informal paper is a comprehensive dictionary of terms and phrases constituting the vocabulary of quantum computing. It is intended as more of a reference guide than a tutorial. It should assist the reader in decoding both general media articles on quantum computing and detailed technical and scientific papers as well. Although focused on quantum computing, it also covers quantum information science overall to some extent, and a modest amount of quantum mechanics, to the extent that it is relevant to quantum computing.
Beyond the vocabulary of terms which are strictly limited to quantum computing, subsets of terms from other domains, such as quantum mechanics, traditional digital computing, engineering, and mathematics, are included for convenient reference, context, and contrast with similar terms from other domains, and because quite a few of those terms will be used when discussing quantum computing.
This glossary presumes that the future of quantum computing will center on hybrid computing — a mix of quantum and classical computing. It is not the intention for this glossary to cover all aspects of classical computing, but certainly enough to cover the intersection, as well as to help to highlight aspects of classical computing that do not yet and may never carry over to quantum computing.
To be clear, the intent here is to be future-looking and to help lay the groundwork for future quantum computers, particularly hybrid modes of both quantum and classical computing, as well as current machines, so some significant fraction of the glossary will not apply to the quantum computers that exist today or even in the near future, but anything needed for today’s quantum computers should definitely be covered.
Marketing terms and phrases are included as well. Yeah, some hype terms and phrases too — mostly to frame them or debunk them.
The intent is to define and explain terms in as plain language as possible. Links are provided to greater detail, commonly from Wikipedia or arXiv.org, and other sites as well.
All definitions are tentative as quantum computing is such a new field, as is my own exposure to it since I am not an expert in the field of quantum computing, although I do have a deep technical background in traditional computing. Definitions will evolve as the field evolves and as my own knowledge and expertise evolve.
The glossary is too large for a single document (over 3,000 entries), so it is divided into six parts, plus this introduction:
- Quantum Computing Glossary — Introduction. This part.
- Quantum Computing Glossary — Part 1 — A-C. (705 entries)
- Quantum Computing Glossary — Part 2 — D-G. (632 entries)
- Quantum Computing Glossary — Part 3 — H-P. (945 entries)
- Quantum Computing Glossary — Part 4 — Q. (522 entries)
- Quantum Computing Glossary — Part 5 — R-S. (464 entries)
- Quantum Computing Glossary — Part 6 — T-Z. (296 entries)
Total of 2,446 entries, as of July 31, 2018.
Total of 2,812 entries, as of September 1, 2018.
Total of 2,927 entries, as of December 25, 2018.
Total of 2,955 entries, as of January 22, 2019.
Total of 2,993 entries, as of February 17, 2019.
Total of 3,030 entries, as of March 24, 2019.
Total of 3,033 entries, as of April 12, 2019.
Total of 3,047 entries, as of May 3, 2019.
Total of 3,130 entries, as of June 23, 2019.
Total of 3,136 entries, as of July 31, 2019.
Total of 3,140 entries, as of August 14, 2019.
Total of 3,145 entries, as of September 26, 2019.
Total of 3,164 entries, as of October 2, 2019.
Total of 3,290 entries, as of November 19, 2019.
Total of 3,293 entries, as of December 15, 2019.
Total of 3,308 entries, as of January 26, 2020.
Total of 3,385 entries, as of April 30, 2020.
Total of 3,481 entries, as of May 31, 2020.
Total of 3,549 entries, as of June 28, 2020.
Total of 3,553 entries, as of November 30, 2020.
Total of 3,554 entries, as of March 20, 2021.
Total of 3,555 entries, as of May 25, 2021.
Total of 3,556 entries, as of October 22, 2021.
Total of 3,560 entries, as of May 7, 2022.
Total of 3,564 entries, as of October 21, 2022.
Levels of terminology
There are a number of levels at which quantum computing can be considered. This glossary attempts to cover them all, not all details of all levels, but anything even loosely connected to quantum computing. The levels are:
- Physics — basic, elementary particles, electromagnetism, solid state
- Quantum mechanics
- Theory of quantum computing
- Hardware — Superconductor fabrication and operation
- Hardware — Chip fabrication
- Hardware — chip design and interconnection on chips
- Hardware — Use of chips
- Hardware — system architecture
- Electrical engineering
- Mechanical engineering
- Operating software, quantum logic gate control, gate execution flow
- Instruction set architecture
- Software — quantum circuits and programs
- Algorithms — utilizing and optimized for features of qubits and quantum logic gates
- Application software
- Classical software
- Hybrid mode of operation
- Business models
Here’s a list of the most significant terms needed to get started with quantum computing, not in any particular order:
- quantum computing
- classical computing
- quantum computer
- universal quantum computer
- general-purpose quantum computer
- quantum ready
- quantum mechanics
- qubit or quantum bit
- qubit count
- classical bit
- Bloch sphere
- quantum system
- quantum state
- cat state
- quantum information
- hybrid mode of operation
- quantum computation
- quantum logic gate
- classical logic gate
- reversible logic gate
- quantum circuit
- classical circuit
- quantum circuit depth
- quantum algorithm
- quantum preparation
- quantum execution
- quantum measurement
- wave function
- collapse of wave function
- millikelvin or mK and absolute zero
- coherence and decoherence
- bra, ket, and bra-ket notation
- basis state
- probability and probabilistic
- amplitude or probability amplitude
- quantum error correction
More advanced terms
Once you’ve mastered the basic concepts of quantum computing, some of the deeper concepts include:
- vector and vector space
- linear algebra
- linear combination
- basis vector
- eigenvalue and eigenvector
- Hilbert space
- Hermitian operator
- complex number
- matrix and matrix operation
- cavity and resonator
- microwave pulse
- Faraday cage and shielding
- Josephson junction
- superconducting loop
- trapped ion qubit
- spin qubit
- transmon qubit
- connectivity map
- electromagnetic radiation (EMR)
- post-quantum cryptography
- Grover’s algorithm
- Shor’s algorithm
- quantum annealing
- fixed-function quantum computer
- noisy intermediate-stage quantum (NISQ)
- Bell’s inequality, Bell’s theorem, and Bell state
And many, many more. That’s simply a small sample.
Technically, I consider this glossary to still be at the draft stage. I expect it to take me some number of months to fill in gaps, add more terms, and refine definitions.
That said, it should be quite usable even in its current, initial state.
Suggestions for improvement are welcome.
The vast majority of terms have complete definitions, but quite a few remain undefined or incomplete — they are marked as TBD — To Be Determined.
There are some issues that may take me some time to sort out since even with a fair amount of reading I still have not identified reasonably cogent and crisp definitions, including:
[Update: The issues and questions on the list below have been move to a newer paper, Questions About Quantum Computing. There will be no further updates to the TBD list here. It is provided strictly for historical reference, reflecting the list at the time this paper was originally written.]
- Pure vs. mixed states — is the latter superposition or not?
- Whether coupling and entanglement are exact synonyms or whether there are differences.
- Crispness and distinction of overlap between quantum noise and decoherence.
- Whether |0> is necessarily the ground state for a qubit, or whether that is merely a convention or whether it is a choice of the designer of a particular quantum computer.
- Whether measurement is guaranteed to collapse the wave function of a qubit, or just generally or only in some cases — the IBM Q documentation suggests that their readout resonator can in fact read the quantum state of a qubit without disturbing its state.
- Whether more than two qubits can be entangled together.
- How many independent pairs of qubits can be simultaneously entangled.
- Nuances of behavior which may exist on a simulator but not on a real quantum computer, and vice versa.
- Whether a wave function across all qubits makes sense, or just for individual and entangled qubits.
- Whether decoherence time is driven by dissipation of trapped microwave photon in resonator, at least on current IBM Q machines vs. environmental EMR noise.
- What “state of matter” does a single particle have, such as a free electron, single atom, trapped ion, or single molecule.
- Are probability amplitudes real or complex?
- What constitutes fully entangled, since not all qubits can be entangled on a particular quantum computer? Is it simply all pairs, or all permitted pairs, or… what?
- Specific meaning of each type of logic gate, including Pauli gates, and how to express how they can be used for real-world applications and algorithms.
- What precisely constitutes a Clifford gate and Clifford group, in plain English?
- Are rotation angles quantized or not?
- Are phase shift angles quantized or not?
- How precise a value of pi, pi/2, and pi/4 (number of digits) are needed to achieve correct results for logic gates?
- Is superposition represented in a Bloch sphere with a single vector, or two shorter vectors?
- Does a Bloch sphere represent only a single qubit, or can it be used to represent the state vectors of all qubits of a quantum computer in one sphere?
- How does a Bloch sphere represent the state of a pair of entangled qubits, or since their state is identical, do they share the same sphere, or have two separate but identical spheres?
- Is there a Planck-type limit to the amplitude of a state in the wave function of a quantum system, such that there is a maximum number of states in a quantum system?
- How isolated do two particles, waves, or quantum systems have to be to constitute isolated quantum systems, or how close can two qubits be placed and still be considered isolated?
- What does the T of T-gate stand for?
- Do the controlled logic gates require that the control qubit be in a pure |1> state, or some threshold of amplitude, or is control strictly probabilistic, such as equal probability of control if, for example, a Hadamard gate was just executed on the control qubit?
- Is there an actual MEASURE logic gate, or is there some other method for measuring the state of a qubit?
- Is there an actual RESET logic gate, or is there some other method for preparing the state of a qubit to be |0>?
- What does the S gate do (phase shift by 90 degrees — twice the rotation of a T gate, and half the rotation of a Z gate)?
- What constitutes a computational basis?
- Are the |0> and |1> basis states supposed to be orthonormal — in the Bloch sphere they are opposing vectors, |0> pointing to the north pole, and 1> pointing to the south pole, but NOT at right angles to each other, so are they really an “orthonormal basis”?
- Are there any current quantum computers which support multipartite entanglement — 3 or more qubits in a single entanglement? How common is it?
- Are there any current quantum computer simulators which support multipartite entanglement — 3 or more qubits in a single entanglement? How common is it?
- Are the eigenvalues (probability amplitudes) for the eigenvectors (basis states) of the quantum state of a qubit in a quantum computer ever complex, with an imaginary component, or always real? Where are some examples, and when does this occur?
- What is the effect, if any, of executing another Hadamard gate after a Hadamard gate — is it essentially an identity operation (no-op), or is there some effect?
- What is the effect, if any, of executing another CNOT gate after a CNOT gate — does it simply flip the target qubit back, or what? Does it retain entanglement? Doe it maintain the same Bell state, or does it flip to the complementary (?) Bell state?
- What does the Ising logic gate really do, in plain language? Is it supported by any transmon qubit machines, or does it apply only to trapped-ion machines?
- Are the probabilities for superposition states always identical (symmetric), 0.5, or can they be asymmetric, like 0.75 and 0.25? What logic gates would have such an effect?
- Are the initial quantum states of qubits always |0> by definition, forced by the hardware, or are they unpredictable or undefined, by definition, or does this vary depending on the whim of the designer of the machine, and is there a recommended best practice for initializing qubit state? Or is it up the the operating/control software or control firmware to artificially force the initial state before beginning execution of a new quantum program or circuit, and is there a standard convention and predictable expectation of initial state for a new program, especially for a quantum cloud service?
- Is there a logic gate which dis-entangles two qubits? Do they start with the same exact same state, or each take part of the state or does the state collapse into two distinct states, or what? Is there a different answer for each of the four Bell states?
- If the target qubit of CNOT is already entangled which a different qubit, what exactly happens, both with the target qubit and the other qubit it was already entangled with? Such as the sequence H(2), CNOT (2, 3), H(1), CNOT(1, 2).
- What are the standard, recommended logic gates for setting (preparing) a qubit for |0> and |1>?
- Is CNOT the only gate which creates an entanglement, or do all controlled gates create an entanglement, or any other gates? CCNOT?
- If all three qubits of a CCNOT (controlled-controlled-NOT) logic gate are entangled, but not with each other, what can be expected of the quantum state of the target qubit after the gate has been executed? And what state will the other qubits which had been entangled with the two control qubits be in after the CCNOT has been executed?
- Can you measure both states of a qubit using temporary entanglement — entangle to capture state, then disentangle to permit measurement without disrupting the original qubit? Even if that is so, can that work if the target qubit is already entangled and if only bipartite entanglement is supported?
Existing quantum computing glossaries
For reference, here’s the best I could do at locating existing glossaries on quantum computing.
Hopefully the glossary in this paper is superior, but sometimes historical use and niche uses offer additional perspective.
- Glossary of elementary quantum mechanics — https://ipfs.io/ipfs/QmXoypizjW3WknFiJnKLwHCnL72vedxjQkDDP1mXWo6uco/wiki/Glossary_of_elementary_quantum_mechanics.html
- Quantum Computing and Shor’s Algorithm — https://pdfs.semanticscholar.org/8072/dc7247460849b18abbb463429a09cfb2e3e6.pdf
- Quantum phenomena in nanotechnology — https://www.iso.org/obp/ui/#iso:std:iso:ts:80004:-12:ed-1:v1:en
- Glossary for Computational Chemistry — https://www.shodor.org/chemviz/glossary.html
- Wikipedia Glossary of elementary quantum mechanics — https://en.wikipedia.org/wiki/Glossary_of_elementary_quantum_mechanics
- Quantiki — social portal for quantum information science — https://www.quantiki.org/
- Continue adding terms and phrases as I continue my reading.
- Flesh out TBD’s incrementally as I figure out what those terms really mean.
- Refine existing terms as I uncover nuances and come up with crisper ways to articulate definitions.
- Consider publishing the glossary, at least as an e-book. Including full hyperlinking of terms within definitions to facilitate navigation between terms.
- Consider one or more stripped down glossaries, including a basic introduction for beginners, one for non-technical policymakers, one for non-technical managers, and separate glossaries for niches — not everyone needs to know or care about the fine-grained details of how to construct a qubit.
- Add the glossary to Wikipedia? Possible, although I’m not inclined to take on that task, but if somebody else wants to do the work, maybe.
For now, my main effort will be to incrementally update this glossary as I become aware of new terms or if I discover mistakes or opportunities for greater clarity.
Continue on to the main body of the glossary
- Quantum Computing Glossary — Introduction. This part.
- Quantum Computing Glossary — Part 1 — A-C. Start here.
- Quantum Computing Glossary — Part 2 — D-G.
- Quantum Computing Glossary — Part 3 — H-P.
- Quantum Computing Glossary — Part 4 — Q.
- Quantum Computing Glossary — Part 5 — R-S.
- Quantum Computing Glossary — Part 6 — T-Z.