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Set of quantum operations
The Clifford group encompasses a set of quantum operations that map the set of n-fold Pauli group products into itself. It is most famously studied for
Clifford_group
Algebra based on a vector space with a quadratic form
In mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra with the additional
Clifford_algebra
Definition of quantum circuits
theory, the Clifford gates are the elements of the Clifford group, a set of mathematical transformations which normalize the n-qubit Pauli group, i.e., map
Clifford_gate
Quantum computing algorithm
theorem, it is known that some quantum operations (operations in the Clifford group) can be perfectly simulated in polynomial time on a classical computer
Magic_state_distillation
Theorem of quantum circuits
Pauli group, also called Clifford group—can be perfectly simulated in polynomial time on a probabilistic classical computer. The Clifford group can be
Gottesman–Knill_theorem
American animated children's television series
Clifford the Big Red Dog is an American animated educational children's television series, based upon Norman Bridwell's children's book series of the same
Clifford the Big Red Dog (2000 TV series)
Clifford_the_Big_Red_Dog_(2000_TV_series)
American musician (born 1945)
the group disbanded in late 1972, Clifford released a solo album and later joined CCR bassist Stu Cook in the Don Harrison Band. In 1995, Clifford and
Doug_Clifford
English actress (born 1982)
Sian Clifford (born 7 April 1982) is an English actress. She is best known for playing Claire, the older sister of the titular character in the BBC comedy-drama
Sian_Clifford
Double cover Lie group of the special orthogonal group
invertible elements in the Clifford algebra Cl(n). A distinct article discusses the spin representations. The spin group is used in physics when describing
Spin_group
American children's book series
Clifford the Big Red Dog is an American children's book series and media franchise focusing on the adventures of 8-year-old Emily Elizabeth and her titular
Clifford_the_Big_Red_Dog
Method of quantum computing
graph. The Clifford group C n {\displaystyle {\mathcal {C}}_{n}} is composed by elements which leave invariant the elements from the Pauli's group P n {\displaystyle
One-way_quantum_computer
Unit of quantum information
of qutrits the Clifford group is finite and therefore is not sufficient for universal quantum computation. Adding one single non-Clifford gate to a set
Qutrit
In mathematics, Clifford theory, introduced by Alfred H. Clifford (1937), describes the relation between representations of a group and those of a normal
Clifford_theory
American jazz trumpeter, pianist, and composer (1930–1956)
Clifford Benjamin Brown (October 30, 1930 – June 26, 1956) was an American jazz trumpeter, pianist, and composer. He died at the age of 25 in a car crash
Clifford_Brown
American football player (born 1998)
Sean Burke Clifford (born July 14, 1998) is an American professional football quarterback for the Cincinnati Bengals of the National Football League (NFL)
Sean_Clifford
Multinational law firm headquartered in London
Clifford Chance LLP is a British multinational law firm headquartered in London, England, and a member of the "Magic Circle", a group of leading London-based
Clifford_Chance
Clifford analysis, using Clifford algebras named after William Kingdon Clifford, is the study of Dirac operators, and Dirac type operators in analysis
Clifford_analysis
Method for assessing quantum computer hardware capabilities
independent sequence of twirls under that group, as conjectured in and later proven in. This Clifford-group approach to Randomized Benchmarking is the
Randomized_benchmarking
American rapper (born 1980)
Clifford Joseph Harris Jr. (born September 25, 1980), known professionally as T.I. or Tip, is an American rapper and actor. Born and raised in Atlanta
T.I.
American astronomer, author and teacher (born 1950)
Clifford Paul "Cliff" Stoll (born June 4, 1950) is an American astronomer, author and teacher. He is most notable for his investigation in 1986, while
Clifford_Stoll
Geometrical object in four-dimensional space
In differential geometry, the Clifford torus is the standard embedding of the 2-torus as a product of circles in Euclidean space R4 (equivalently C2).
Clifford_torus
Topics referred to by the same term
folk music group The Spinners. Robert Clifford Hall (1894–1972), American comedian Cliff Frederick Hall [Wikidata], English pianist Clifford Geoffrey Hall
Cliff_Hall
Type of group in mathematics
be defined for Clifford groups and pin groups in a similar way (in all dimensions). Over fields of characteristic 2 orthogonal groups often exhibit special
Orthogonal_group
2021 film by Walt Becker
Clifford the Big Red Dog is a 2021 live-action animated urban fantasy comedy film directed by Walt Becker from a screenplay by Blaise Hemingway and the
Clifford the Big Red Dog (film)
Clifford_the_Big_Red_Dog_(film)
Theater collective in New York City, US
ten years of its existence, the Group Theatre produced works by many important American playwrights, including Clifford Odets, Sidney Kingsley, Paul Green
Group_Theatre_(New_York_City)
American writer and actor (1906–1963)
Clifford Odets (July 18, 1906 – August 14, 1963) was an American playwright, screenwriter, and actor. In the mid-1930s, he was widely seen as the potential
Clifford_Odets
{\displaystyle xx^{-1}=x^{-1}x} . Examples of Clifford semigroups are groups and commutative inverse semigroups. In a Clifford semigroup, x y = y x ↔ x − 1 y = y
Clifford_semigroup
Flash-animated children's television series
Clifford the Big Red Dog is an animated children's television series adapted from the book series of the same name written by Norman Bridwell, and a reboot
Clifford the Big Red Dog (2019 TV series)
Clifford_the_Big_Red_Dog_(2019_TV_series)
Type of measurement in quantum mechanics
3390/axioms6030021. Appleby, D. M. (2005). "SIC-POVMs and the Extended Clifford Group". Journal of Mathematical Physics. 46 (5): 052107. arXiv:quant-ph/0412001
SIC-POVM
Concept in quantum computing
gates from the Clifford group, the two states are called locally Clifford equivalent. If and only if two graph states are locally Clifford equivalent, one
Graph_state
British flat racing jockey
Clifford Lee (born 1996) is a Group 1 winning British flat racing jockey. He is attached to the yard of trainer Karl Burke near Middleham, in North Yorkshire
Clifford_Lee
Subgroup of the Clifford algebra associated to a quadratic space
group is a certain subgroup of the Clifford algebra associated to a quadratic space. It maps 2-to-1 to the orthogonal group, just as the spin group maps
Pin_group
Computer scientist
degrees of freedom) parametrization of Clifford group elements by quantum circuits, and computational advantage by Clifford circuits over classical reversible
Dmitri_Maslov
Families of matrices in mathematics, physics, and quantum information
portal Heisenberg group § Heisenberg group modulo an odd prime p Hermitian matrix Bloch sphere Discrete Fourier transform Generalized Clifford algebra Weyl–Brauer
Generalizations of Pauli matrices
Generalizations_of_Pauli_matrices
American public official (1906–1998)
Clark McAdams Clifford (December 25, 1906 – October 10, 1998) was an American lawyer who served as an important political adviser to Democratic presidents
Clark_Clifford
American rock band (1959–1972)
brother, rhythm guitarist Tom Fogerty; bassist Stu Cook; and drummer Doug Clifford. These members had played together since 1959, first as the Blue Velvets
Creedence_Clearwater_Revival
Australian hard rock band
KOTS) are an Australian hard rock band, which were formed by brothers Clifford and Jeffrey Hoad in 1986. They released three studio albums, Kings of the
Kings_of_the_Sun_(band)
Kerry and Fossa Gaelic footballer (born 1999)
David Clifford (Irish: Daithí Ó Clúmháin) (born 22 January 1999) is a Gaelic footballer who plays corner-forward or full-forward for the Kerry county team
David_Clifford
1954 studio album by Clifford Brown & Max Roach Quintet
Clifford Brown & Max Roach is a 1954 album by jazz musicians Clifford Brown and Max Roach as part of the Clifford Brown and Max Roach Quintet, described
Clifford_Brown_&_Max_Roach
American rapper (born 1971)
Clifford Smith Jr. (born March 2, 1971), known professionally as Method Man, is an American rapper, record producer, and actor. He is a member of the East
Method_Man
1937 drama by Clifford Odets
Golden Boy is a drama by Clifford Odets. The play was initially produced on Broadway by The Group Theatre in 1937. Odets' biggest hit was made into a 1939
Golden_Boy_(play)
British peer (born 1966)
Miles Edward Southwell Russell, 28th Baron de Clifford (born 7 August 1966) is a British hereditary peer, and a former crossbench member of the House of
Miles Russell, 28th Baron de Clifford
Miles_Russell,_28th_Baron_de_Clifford
Non-tensorial representation of the spin group
representations of the spin group or of the associated Clifford algebra. After choosing a matrix realization of the Clifford algebra, spinors may be represented
Spinor
ring to the Brauer–Wall group obtained by sending a quadratic space to its Clifford algebra. The map factors through the Witt group, which has kernel I3
Brauer–Wall_group
1998 studio album by Benny Golson Group
Remembering Clifford is an album by the saxophonist/composer Benny Golson, recorded in 1997 and released on the Milestone label the following year. The
Remembering_Clifford
In mathematics, a Clifford bundle is an algebra bundle whose fibers have the structure of a Clifford algebra and whose local trivializations respect the
Clifford_bundle
English noble (1558–1605)
George Clifford, 3rd Earl of Cumberland, 13th Baron de Clifford, 13th Lord of Skipton (8 August 1558 – 30 October 1605), was an English peer, naval commander
George Clifford, 3rd Earl of Cumberland
George_Clifford,_3rd_Earl_of_Cumberland
American musician (1941–2018)
Reese Francis Clifford III (October 8, 1941 – January 26, 2018), known professionally as Buzz Clifford, was an American pop singer and songwriter. His
Buzz_Clifford
Name list
cliff". Clifford Andrews (1912–1973), English athlete in cricket Clifford Antone (1949–2006), American musical producer and club owner Clifford Warren
Clifford_(name)
Classification in abstract algebra
finite-dimensional Clifford algebras for a nondegenerate quadratic form are completely classified as rings. In general, the Clifford algebra is either
Classification of Clifford algebras
Classification_of_Clifford_algebras
Element of an algebra using quaternions and split-complex numbers
space, and this structure by Clifford in 1873 is an instance. Split-biquaternions form an algebra over a ring, but not a group ring. The direct sum of the
Split-biquaternion
Underwater archaeologist, discovered pirate ship Whydah
Barry Clifford is an American underwater archaeological explorer. Around 1982, Clifford began discovering the remains of the Whydah Gally, a former slave
Barry_Clifford
American metal supergroup
band Isis: bassist Jeff Caxide, drummer Aaron Harris and guitarist Bryant Clifford Meyer. After the demise of Isis in 2010, Caxide, Harris and Meyer decided
Palms_(band)
1955 studio album by Clifford Brown
Clifford Brown with Strings is a 1955 studio album by trumpeter Clifford Brown, with string arrangements by Neal Hefti, recorded on January 18–20, 1955
Clifford_Brown_with_Strings
1973 studio album by Clifford T. Ward
Irish music-hall artistes. In 1962, Clifford became the singer with Cliff Ward and the Cruisers, a proficient beat group that won the 1963 Midland Band of
Home_Thoughts
American racing driver
Robert Clifford Allison (October 20, 1964 – August 13, 1992) was an American stock car racing driver. Son of NASCAR champion Bobby Allison, he was a member
Clifford_Allison
Topics referred to by the same term
PIN Group was a German courier and postal services company. "Pin group" may also refer to: Pin group, subgroup of the Clifford algebra associated to a
PIN_Group_(disambiguation)
2009 studio album by You Say Party
the band's original longer name and the last album with drummer Devon Clifford (who died in April 2010). The album was recorded between January and August
XXXX_(album)
In mathematics, a Clifford–Klein form is a double coset space Γ\G/H, where G is a reductive Lie group, H a closed subgroup of G, and Γ a discrete subgroup
Clifford–Klein_form
Hoax concocted by Alan Abel
Abel persuaded the actor Buck Henry to assume the role of the group president, G. Clifford Prout, Jr., in U.S. television news and talk show appearances
Society for Indecency to Naked Animals
Society_for_Indecency_to_Naked_Animals
Season of a Philippine television reality show
2025. Retrieved December 23, 2025. "Housemates form new groups under leaders Princess, Clifford, Joaquin". GMA Integrated News. January 5, 2026. Retrieved
Pinoy Big Brother: Celebrity Collab Edition 2.0
Pinoy_Big_Brother:_Celebrity_Collab_Edition_2.0
Drama by American playwright Clifford Odets
a drama play written by American playwright Clifford Odets. The play was initially produced by The Group Theatre in 1935. The play is set in The Bronx
Awake_and_Sing!
Australian businessman and executive
Tinto Group, starting as a mining engineer and retiring as chief executive, spanned 37 years and included time both in Australia and overseas. Clifford was
Leigh_Clifford
British singer-songwriter (1944–2001)
Clifford Thomas Ward (10 February 1944 – 18 December 2001) was an English singer-songwriter, best known for his career as a solo artist. Ward's 1973 album
Clifford_T._Ward
1999 film by Roger Kumble
Kathryn notices romantic tension between Cecile and her music teacher Ronald Clifford, and reveals this to Cecile's mother, who fires Ronald. Sebastian and Kathryn
Cruel_Intentions
1977 studio album by Linda Clifford
Linda is the debut studio album recorded by American singer Linda Clifford, released in 1977 on the Curtom Records label. The album features the single
Linda_(Linda_Clifford_album)
Algebraic structure
often called "Clifford semigroups". In the English literature, the name "Clifford semigroup" is used synonymously to "inverse Clifford semigroup", and
Completely_regular_semigroup
1956 studio album by Clifford Brown
Clifford Brown All Stars (also released as Caravan) is an album by American jazz trumpeter Clifford Brown featuring tracks recorded in 1954 but released
Clifford_Brown_All_Stars
American computer scientist (1954–2025)
Clifford Alan Lynch (December 31, 1954 – April 10, 2025) was an American computer scientist and director of the Coalition for Networked Information (CNI)
Clifford_Lynch
English sculptor
Clifford Frank Last OBE (13 December 1918 – 20 October 1991) was an Australian modernist sculptor. Born in Barrow in Furness, England, he was the son of
Clifford_Last
1992 studio album by Arturo Sandoval
Remember Clifford is a 1992 album by Arturo Sandoval, the second album he made after leaving his native Cuba. The entire album is a tribute to Clifford Brown
I_Remember_Clifford_(album)
American soul group
Crossroads," written by group member James Stroud. The original members were Clifford Curry, Lasalle Matthews, and Stroud. The group stayed with Twilight
The_Notations
Social group defined by shared traits
Groups and Boundaries: The Social Organization of Cultural Difference; Eric Wolf 1982 Europe and the People Without History p. 381 Geertz, Clifford,
Ethnicity
Trinidad", The Geologist, 6: 363–364, retrieved 2019-02-07 Porter, Henry Clifford (1974), The geology of the western part of the Northern range of Trinidad
Older_Parian_Group
American singer (born 1948)
Linda Clifford (born June 14, 1948) is an American R&B, disco and house music singer who scored hits from the 1970s to the 1980s, most notably "If My Friends
Linda_Clifford
In mathematics, a generalized Clifford algebra (GCA) is a unital associative algebra that generalizes the Clifford algebra, and goes back to the work of
Generalized_Clifford_algebra
2004 American film
Clifford's Really Big Movie is a 2004 American animated adventure comedy film based on the PBS Kids TV series Clifford the Big Red Dog, itself an adaptation
Clifford's_Really_Big_Movie
1996 sectarian murder, during The Troubles
National Liberation Army in Long Kesh prison, and the group disbanded in August 1998. Clifford George McKeown was found guilty of McGoldrick's murder
Murder_of_Michael_McGoldrick
1956 studio album by Clifford Brown, Max Roach
Clifford Brown and Max Roach at Basin Street (also known as At Basin Street) is a 1956 album by the Clifford Brown and Max Roach Quintet, the last album
Clifford Brown and Max Roach at Basin Street
Clifford_Brown_and_Max_Roach_at_Basin_Street
American army officer and astronaut (1952–2021)
Michael Richard Clifford (October 13, 1952 – December 28, 2021) was a United States Army officer and NASA astronaut. Clifford was a Master Army Aviator
Michael_R._Clifford
1973 compilation album by Clifford Brown
End (Columbia Records, 1973) is a Clifford Brown compilation album. The album opens with two tracks that Clifford Brown recorded with Chris Powell's
The Beginning and the End (Clifford Brown album)
The_Beginning_and_the_End_(Clifford_Brown_album)
Irish activist
United Ireland against their wishes. Clifford soon became a prolific publisher of material advocating the group's viewpoint. The ICO later changed its
Brendan_Clifford
American mathematician (1908–1992)
Mackie (1976), Theory of Unitary Group Representations, Chicago Mathematics Lecture, ISBN 0-226-50051-9 Clifford, Alfred Hoblitzelle; Preston, Gordon
Alfred_H._Clifford
England international rugby union player
as they defeated Exeter Chiefs with a score of 43–21. Clifford represented England at age-group levels during her teenage years. In 2019, she captained
Kelsey_Clifford
1956 album by Clifford Brown
Memorial Album is an album by American jazz trumpeter Clifford Brown recorded on June 9, 1953 and August 28, 1953 and released on Blue Note in September
Memorial Album (Clifford Brown album)
Memorial_Album_(Clifford_Brown_album)
British mathematician and philosopher (1845–1879)
William Kingdon Clifford (4 May 1845 – 3 March 1879) was a British mathematician and philosopher. Building on the work of Hermann Grassmann, he introduced
William_Kingdon_Clifford
Country in Southeast Asia
Archived from the original on 8 February 2019. Retrieved 13 January 2021. Clifford, Hugh Charles (1911). "Malays" . In Chisholm, Hugh (ed.). Encyclopædia
Malaysia
British psychologist and academic
Clifford John Thornton Stott MBE (born July 1965) is professor of social psychology at Keele University. He is a specialist in the psychology of crowds
Clifford_Stott
Japanese mathematician (1930–2019)
March 2004). Arithmetic and Analytic Theories of Quadratic Forms and Clifford Groups. Mathematical Surveys and Monographs (Hardcover ed.). American Mathematical
Goro_Shimura
American businessman and politician (born 1941)
Clifford Bundy Stearns Sr. (born April 16, 1941) is an American businessman and politician who was the U.S. representative for Florida's 6th congressional
Cliff_Stearns
American rock band
Year's Day festival in downtown Winston-Salem. The group was performing Irish music, and Clifford, Bivins, and Pollen traveled to Ireland to learn their
Jump,_Little_Children
Method in quantum communication
manipulating columns of the above matrix are Clifford operations. Clifford operations preserve the Pauli group Π n {\displaystyle \Pi ^{n}} under conjugation
Entanglement-assisted stabilizer formalism
Entanglement-assisted_stabilizer_formalism
1993 studio album by Seefeel
receive praise on its re-issue. Mark Clifford formed Seefeel in 1992 after posting advertisements for potential group members. After performing a few shows
Quique_(album)
1956 studio album by Clifford Brown
Memorial is a 1956 jazz album by trumpeter Clifford Brown, issued posthumously. It was originally released on the Prestige label as PRLP 7055. The album
Memorial (Clifford Brown album)
Memorial_(Clifford_Brown_album)
Scottish footballer (born 2001)
Billy Clifford Gilmour (born 11 June 2001) is a Scottish professional footballer who plays as a defensive midfielder for Serie A club Napoli and the Scotland
Billy_Gilmour
Group of unitary complex matrices with determinant of 1
to the rotation group SO(3) whose kernel is {+I, −I}. Since the quaternions can be identified as the even subalgebra of the Clifford algebra Cl(3), SU(2)
Special_unitary_group
British far-right group
activist group in the United Kingdom, established in summer 2026 by far-right activist Daniel Thomas, known as Danny Tommo. Tommo founded the group after
Patriot_Platform
Charity for homeless people
sometimes known as the Cyreneans). It was founded in 1963 by Anton Wallich-Clifford, who had encountered many homeless people while working for the Probation
Simon_Community
Clifford Corporation purchased the Ansair bus bodybuilding business from Ansett Transport Industries. That was followed by the Austral Pacific Group,
Clifford_Corporation
British actor (1933–2015)
Kenneth Clifford Earl (29 August 1933 – 30 July 2015) was an English actor who appeared in numerous television programmes and films. Earl was born in Romney
Clifford_Earl
travel, tourism, insurance
CLIFFORD GROUP
CLIFFORD GROUP
CLIFFORD GROUP
CLIFFORD GROUP
CLIFFORD GROUP
CLIFFORD GROUP
CLIFFORD GROUP
CLIFFORD GROUP
CLIFFORD GROUP
travel, tourism, insurance