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7ff55f4b60ceb004de424140d6a720807ca95b02 | marshall was a golf course owner in his | marshall was a golf course owner in his home state of connecticut. he is deeply rooted in community service in new england. he once served on the board of trustees at his alma mater, the university of connecticut. he is also a member of the board of directors for the first tee of connecticut, a group that provides expo... | wikipedia |
8302123ff21c61229ed4bbdca0f85d7e3aa9e7c2 | marshall has been in television broadcasting for 19 | marshall has been in television broadcasting for 19 years, covering over 1,300 professional and collegiate basketball games. he worked as a color commentator/basketball studio analyst for the boston celtics on comcast sportsnet in new england for 8 years covering over 650 nba games. he was also a color commentator for ... | wikipedia |
5aab6cfb49834da87e898e4e29fa4abeb4eaa815 | after leading his high school basketball team to | after leading his high school basketball team to over 100 wins and being named to washington's all-state team 4 consecutive years (along with being a 4-time all-state selection as a soccer player), marshall graduated from federal way high school, a school in the suburb of seattle. marshall chose to play for the univers... | wikipedia |
b0e23ed07cd6825762f67fc3884f44a2f8f094ec | donny marshall (born july 17, 1972) is an | donny marshall (born july 17, 1972) is an american former professional basketball player who played five seasons in the national basketball association (nba) for the cleveland cavaliers and new jersey nets. he is currently a college basketball television analyst for fox sports 1, westwood one national radio and cbssn. | wikipedia |
90bbc41f263a721c3687bddb668639ada99a02ff | dominic alfred poleon is a footballer who plays | dominic alfred poleon is a footballer who plays as a forward for national league club ebbsfleet united and the saint lucia national team. he played youth football for chelsea and southend united before signing for leeds united in august 2010. whilst at leeds he had loan spells with bury and sheffield united. | wikipedia |
c94ade3149bbc3b414836ef0abb764466173d0b0 | poleon was born in england and is of | poleon was born in england and is of st lucian descent. on 16 june 2023, poleon made his debut for the saint lucia national football team, in a 3–1 defeat to martinique in the 2023 concacaf gold cup preliminary round. on 7 september 2023, he scored his first goals for his country with a hat-trick in a 5–1 victory over ... | wikipedia |
a816437943ea8cb4ef372cdfea5af278e958387b | a successful february 2023 where poleon scored seven | a successful february 2023 where poleon scored seven goals in seven matches, taking ebbsfleet fourteen points clear of the team in second position, saw the striker win the national league south player of the month award. on 7 april 2023, he scored a fourth hat-trick of the season to take his league tally to thirty-six ... | wikipedia |
114201e1dc73411e85434a378e175e36e9bac779 | poleon's contract at crawley was cancelled by mutual | poleon's contract at crawley was cancelled by mutual consent on 2 september 2019 to enable him to join league two newport county on the same day until the end of the 2019–20 season. he made his debut for newport 14 september 2019 in the 2–0 defeat to northampton town as a second-half substitute. | wikipedia |
405130a84cbcc71efba2346b76cdfc4777a8d031 | poleon signed for afc wimbledon on 2 july | poleon signed for afc wimbledon on 2 july 2016. he scored his first goals for wimbledon when he scored twice in an efl trophy tie against swansea city under-23s on 30 august 2016. | wikipedia |
d5e2b036b3c1fabfbbaa8a2eb157027cb8f6f94e | poleon scored his first goal of the 2013–14 | poleon scored his first goal of the 2013–14 season on his first start, in a league cup tie at home to chesterfield. poleon's goal proved to be the winner as leeds won the game 2–1. | wikipedia |
d31eb793e08321d9a1785fa95453aa9f30b18e14 | poleon scored his second goal for leeds at | poleon scored his second goal for leeds at vicarage road on the final day of the season in leeds' 2–1 win against watford after appearing as an early substitute for the injured steve morison. during this match poleon was involved in a controversial collision in which he appeared to push ikechi anya, resulting in him ac... | wikipedia |
2b4497dbfa5566d9d18772563a9dcceaae600836 | poleon joined yorkshire rivals sheffield united on loan | poleon joined yorkshire rivals sheffield united on loan until the end of the season on 12 february 2013. blades boss danny wilson described poleon as being "raw and unpredictable but very quick... he can get in behind the back of people and he can get a goal. we just feel he can add a little bit extra from the bench or... | wikipedia |
6556d6c04531c951fdd8a0168322dd03de6c7a9a | poleon was recalled by leeds on 20 november | poleon was recalled by leeds on 20 november due to injuries and suspensions at his parent club, coupled with his own good form at bury. on 18 january 2013, poleon signed a new two-and-a-half-year contract with leeds. | wikipedia |
40216a92cb4023900c19d24c0633c6223ec3bc7b | poleon scored his first goal for the club | poleon scored his first goal for the club in his second game versus yeovil town, equalising on the 74th minute mark at huish park in a 1–2 defeat. he continued his impressive early form over the following games; adding another assist in a 2–1 victory over hartlepool united and his second goal in a 1–1 draw at home to w... | wikipedia |
7217bebafa964342aa0f34d70ef5ec9fcdd72f05 | on 15 october 2012, poleon and teammate zac | on 15 october 2012, poleon and teammate zac thompson joined league one strugglers bury on month-long loan deals. both youngsters would be working under the newly appointed bury manager kevin blackwell, who had a seventeen-year association with warnock as player and coach between 1986 and 2003 and had managed poleon's p... | wikipedia |
8c0f5603c7d779ec82d2b7dcdb2f784d9e694ee1 | poleon made his first start for leeds united | poleon made his first start for leeds united in a league game against nottingham forest on 22 september after impressing as a substitute in a 2–3 league defeat against hull city earlier in the week. he marked the occasion with his first professional goal in the 25th minute. prior to the game against forest, neil warnoc... | wikipedia |
a4041e694f2fff03ba2f4dfff3a524fb99f4fdbd | his performances in further pre-season games would lead | his performances in further pre-season games would lead to the young striker joining fellow prospect sam byram on the fringes of the first team for the start of manager neil warnock 's first full season in charge as he was assigned the number 26 shirt for the campaign. he made his first team début for leeds in the firs... | wikipedia |
f9e8c1d8f4ccda134b4160ed4d98f7acd7b0f871 | after scoring for the club's development team in | after scoring for the club's development team in a 2–0 friendly match victory over alfreton town at north street on 21 july 2012, poleon and several other youngsters including sam byram, nathan turner, lewis turner and monty gimpel, travelled with the senior team the following week on a pre-season tour of cornwall and ... | wikipedia |
304984245c2b1ac3e9365dbe09bc8e841b707bca | poleon joined leeds in the summer of 2010. | poleon joined leeds in the summer of 2010. he gained good reviews in the youth and reserve teams in his first year at the club. in the following 2011–12 season, poleon was the leading scorer for the united youth team with 12 goals. he capped his second season at the club by signing a one-year professional contract alon... | wikipedia |
0e33148cb359b39ef35d93723a8430d5773c380e | poleon attended brampton manor academy in east ham. | poleon attended brampton manor academy in east ham. he began his career in football across the city in the junior teams at chelsea but failed to progress at the premier league club. he would join southend united for the later years of his school life and travelled with them on a tour of france in 2009 aged 15 before be... | wikipedia |
90bbc41f263a721c3687bddb668639ada99a02ff | dominic alfred poleon is a footballer who plays | dominic alfred poleon is a footballer who plays as a forward for national league club ebbsfleet united and the saint lucia national team. he played youth football for chelsea and southend united before signing for leeds united in august 2010. whilst at leeds he had loan spells with bury and sheffield united. | wikipedia |
30956f14653472893c0ffb7d55a2d92d64569a25 | euclid was an ancient greek mathematician active as | euclid was an ancient greek mathematician active as a geometer and logician. considered the "father of geometry", he is chiefly known for the elements treatise, which established the foundations of geometry that largely dominated the field until the early 19th century. his system, now referred to as euclidean geometry,... | wikipedia |
745021dc3a8411f33000d73390dea397bb447e91 | the first english edition of the elements was | the first english edition of the elements was published in 1570 by henry billingsley and john dee. the mathematician oliver byrne published a well-known version of the elements in 1847 entitled the first six books of the elements of euclid in which coloured diagrams and symbols are used instead of letters for the great... | wikipedia |
532cd1efc1bc7e6521b307a96e27d2be1709791d | the elements is often considered after the bible | the elements is often considered after the bible as the most frequently translated, published, and studied book in the western world 's history. with aristotle's metaphysics, the elements is perhaps the most successful ancient greek text, and was the dominant mathematical textbook in the medieval arab and latin worlds. | wikipedia |
b7849b759582a8ce1ccecdd414c9c36e524cae0b | euclid is generally considered with archimedes and apollonius | euclid is generally considered with archimedes and apollonius of perga as among the greatest mathematicians of antiquity. many commentators cite him as one of the most influential figures in the history of mathematics. the geometrical system established by the elements long dominated the field; however, today that syst... | wikipedia |
6b298300734c1a691e97154010d243fe4207dab7 | the final three books (11–13) primarily discuss solid | the final three books (11–13) primarily discuss solid geometry. by introducing a list of 37 definitions, book 11 contextualizes the next two. although its foundational character resembles book 1, unlike the latter it features no axiomatic system or postulates. the three sections of book 11 include content on solid geom... | wikipedia |
d729131d071edc4ce6f80e149c5df511c8f206ff | from book 7 onwards, the mathematician benno artmann | from book 7 onwards, the mathematician benno artmann notes that "euclid starts afresh. nothing from the preceding books is used". number theory is covered by books 7 to 10, the former beginning with a set of 22 definitions for parity, prime numbers and other arithmetic-related concepts. book 7 includes the euclidean al... | wikipedia |
9d4e87fd82aa5f2d87d610d631c9a1949fa7ccd6 | book 2 is traditionally understood as concerning " | book 2 is traditionally understood as concerning " geometric algebra ", though this interpretation has been heavily debated since the 1970s; critics describe the characterization as anachronistic, since the foundations of even nascent algebra occurred many centuries later. the second book has a more focused scope and m... | wikipedia |
0b16c6fe6c411be673b6d02114ec81f96ccf3e47 | book 1 of the elements is foundational for | book 1 of the elements is foundational for the entire text. it begins with a series of 20 definitions for basic geometric concepts such as lines, angles and various regular polygons. euclid then presents 10 assumptions (see table, right), grouped into five postulates (axioms) and five common notions. these assumptions ... | wikipedia |
9bb4b7e6ccd6aee90b28f7992ba976510014615b | the elements does not exclusively discuss geometry as | the elements does not exclusively discuss geometry as is sometimes believed. it is traditionally divided into three topics: plane geometry (books 1–6), basic number theory (books 7–10) and solid geometry (books 11–13)—though book 5 (on proportions) and 10 (on irrational lines) do not exactly fit this scheme. the heart ... | wikipedia |
521dae720179c3734d557badc0d0f770ad363dcb | euclid is best known for his thirteen-book treatise, | euclid is best known for his thirteen-book treatise, the elements (greek: Στοιχεῖα; stoicheia), considered his magnum opus. much of its content originates from earlier mathematicians, including eudoxus, hippocrates of chios, thales and theaetetus, while other theorems are mentioned by plato and aristotle. it is difficu... | wikipedia |
52aa9781a248a771703bd892d21fdbf50e4f00e0 | any firm dating of euclid's activity c. 300 | any firm dating of euclid's activity c. 300 bc is called into question by a lack of contemporary references. the earliest original reference to euclid is in apollonius' prefatory letter to the conics (early 2nd century bc): "the third book of the conics contains many astonishing theorems that are useful for both the sy... | wikipedia |
53e956fdaa94c056aded6e522e9277f05f15f104 | medieval arabic sources give vast amounts of information | medieval arabic sources give vast amounts of information concerning euclid's life, but are completely unverifiable. most scholars consider them of dubious authenticity; heath in particular contends that the fictionalization was done to strengthen the connection between a revered mathematician and the arab world. there ... | wikipedia |
6c322a8a65d8991b2eaf57b5fc1f4c26993f34c2 | euclid is often referred to as 'euclid of | euclid is often referred to as 'euclid of alexandria' to differentiate him from the earlier philosopher euclid of megara, a pupil of socrates included in dialogues of plato with whom he was historically conflated. valerius maximus, the 1st century ad roman compiler of anecdotes, mistakenly substituted euclid's name for... | wikipedia |
850c59c1f6d375f0fe1cc00440c2ff212cef1a5a | in his collection, pappus mentions that apollonius studied | in his collection, pappus mentions that apollonius studied with euclid's students in alexandria, and this has been taken to imply that euclid worked and founded a mathematical tradition there. the city was founded by alexander the great in 331 bc, and the rule of ptolemy i from 306 bc onwards gave it a stability which ... | wikipedia |
d27da7b955a4922cc94f75db3e56ada28c10629e | according to proclus, euclid lived shortly after several | according to proclus, euclid lived shortly after several of plato 's (d. 347 bc) followers and before the mathematician archimedes (c. 287 – c. 212 bc); specifically, proclus placed euclid during the rule of ptolemy i (r. 305/304–282 bc). euclid's birthdate is unknown; some scholars estimate around 330 or 325 bc, but o... | wikipedia |
81a0ee509279b4ee32ae4c0ce31d25e7de49ca2d | as with many ancient greek mathematicians, the details | as with many ancient greek mathematicians, the details of euclid's life are mostly unknown. he is accepted as the author of four mostly extant treatises—the elements, optics, data, phaenomena —but besides this, there is nothing known for certain of him. the traditional narrative mainly follows the 5th century ad accoun... | wikipedia |
a013c614e0f4d71308d23bb8c65067cafb5b6658 | the english name 'euclid' is the anglicized version | the english name 'euclid' is the anglicized version of the ancient greek name eukleídes (Εὐκλείδης). it is derived from ' eu- ' (εὖ; 'well') and 'klês' (-κλῆς; 'fame'), meaning "renowned, glorious". in english, by metonymy, 'euclid' can mean his most well-known work, euclid's elements, or a copy thereof, and is sometim... | wikipedia |
ce909cecb7303c91c769bf4308616d189c78b473 | in the elements, euclid deduced the theorems from | in the elements, euclid deduced the theorems from a small set of axioms. he also wrote works on perspective, conic sections, spherical geometry, number theory, and mathematical rigour. in addition to the elements, euclid wrote a central early text in the optics field, optics, and lesser-known works including data and p... | wikipedia |
5c7ca1987df13bf99c4ddd71e05c87768f22a86a | very little is known of euclid's life, and | very little is known of euclid's life, and most information comes from the scholars proclus and pappus of alexandria many centuries later. medieval islamic mathematicians invented a fanciful biography, and medieval byzantine and early renaissance scholars mistook him for the earlier philosopher euclid of megara. it is ... | wikipedia |
add17d804c01556cedfd00d18bc8274930ff67ca | euclid (/ ˈ j uː k l ɪ | euclid (/ ˈ j uː k l ɪ d /; greek: Εὐκλείδης; fl. 300 bc) was an ancient greek mathematician active as a geometer and logician. considered the "father of geometry", he is chiefly known for the elements treatise, which established the foundations of geometry that largely dominated the field until the early 19th century.... | wikipedia |
9080b64c0d0dfd965f8ef86a1b51ba5f4ffce195 | julius nättinen is a finnish professional ice hockey | julius nättinen is a finnish professional ice hockey forward who is currently playing with hifk of the liiga. he was drafted by the anaheim ducks in the second round, 59th overall, in the 2015 nhl entry draft. | wikipedia |
136ac5ee87288316b7332ba62ea609828173ac97 | on july 3, 2020, nättinen signed a one-year | on july 3, 2020, nättinen signed a one-year contract with hc ambrì-piotta of the national league (nl). he was forced to sit out the first two weeks of the regular season in early october with a groin strain. nättinen then went on to score 12 goals in his first 10 regular season games. he finished his lone season in swi... | wikipedia |
e9ffa0d6e7c420c2e443d8bfdba800f7b165694f | following the termination of his nhl contract, nättinen | following the termination of his nhl contract, nättinen returned to his original liiga club, jyp jyväskylä, securing a three-year contract on 25 september 2018. nättinen led liiga with 33 goals scored in the 2019–20 season. | wikipedia |
ec53869ecc5f5743b65a5f1755ebdea9b33d79c4 | in his first north american professional season, nättinen | in his first north american professional season, nättinen was assigned to the ducks' american hockey league (ahl) affiliate, the san diego gulls, for the duration of the 2017–18 season. unable to find his scoring touch, nättinen produced just 4 goals in 55 games. following the ducks' 2018 training camp, nättinen was am... | wikipedia |
0fd31f79d91f2cf1cfd273e0b462b8ff8f9dd763 | after his rookie season in the ohl with | after his rookie season in the ohl with the colts in the 2015–16 season and having scored 71 points in just 52 games, nättinen was traded to the windsor spitfires on 26 june 2016. | wikipedia |
095fb18208fdaa76a22e39e39c2a0f826c708536 | on 16 july 2015, nättinen was signed to | on 16 july 2015, nättinen was signed to a three-year entry-level contract by the anaheim ducks. he left finland after the draft to continue his development playing major junior hockey in the ontario hockey league (ohl) after he was selected by the barrie colts, 51st overall in the chl import draft in 2015. | wikipedia |
99e8906355ae3429ea3edf82f88635d5b43ea979 | julius nättinen (born 14 january 1997) is a | julius nättinen (born 14 january 1997) is a finnish professional ice hockey forward who is currently playing with hifk of the liiga. he was drafted by the anaheim ducks in the second round, 59th overall, in the 2015 nhl entry draft. | wikipedia |
0728603d9e656ecd269fa5a0aed4bf2a2f21961b | edward james conlin was an american basketball player | edward james conlin was an american basketball player and coach. a 6'5" guard/forward from fordham university, conlin played in the national basketball association from 1955 to 1962 as a member of the syracuse nationals, detroit pistons, and philadelphia warriors. on february 13, 1959, conlin was traded from syracuse t... | wikipedia |
f54e7c5a248a13c667f5009c187cd8e7c2cd2275 | conlin returned to fordham when he joined the | conlin returned to fordham when he joined the coaching staff of johnny bach in 1967. he assumed the position of head coach from 1968 to 1970. conlin was dismissed from the team in 1970 with a record of 27–24 during his two seasons. | wikipedia |
cc04d83c2c8d17b5013b8da64cb78651049812df | a 6'5" guard / forward from fordham university, | a 6'5" guard / forward from fordham university, conlin played in the national basketball association from 1955 to 1962 as a member of the syracuse nationals, detroit pistons, and philadelphia warriors. on february 13, 1959, conlin was traded from syracuse to detroit for eventual hall-of-famer george yardley. he average... | wikipedia |
6bbe1cec2a4036c97c4a49d4015187bec0040cec | in quantum mechanics, a singlet state usually refers | in quantum mechanics, a singlet state usually refers to a system in which all electrons are paired. the term 'singlet' originally meant a linked set of particles whose net angular momentum is zero, that is, whose overall spin quantum number s = 0 . as a result, there is only one spectral line of a singlet state. in con... | wikipedia |
2231e8ac45f7edbb40cd5d98a46739963c1f0d6e | a weaker form of einstein's locality principle remains | a weaker form of einstein's locality principle remains intact, which is this: classical information cannot be transmitted faster than the speed of light c, not even by using quantum entanglement events. this form of locality is weaker than the notion of "einstein locality" or "local realism" used in the epr and bell's ... | wikipedia |
87d5bc359853d036e53e08a0415522fb1e22165c | the difficulty captured by the epr-bohm thought experiment | the difficulty captured by the epr-bohm thought experiment was that by measuring a spatial component of the angular momentum of either of two particles that have been prepared in a spatially distributed singlet state, the quantum state of the remaining particle, conditioned on the measurement result obtained, appears t... | wikipedia |
ea9511ceb117563076d9eb453d3d713b589820b4 | the possibility of spatially extended unbound singlet states | the possibility of spatially extended unbound singlet states has considerable historical and even philosophical importance, since considering such states contributed importantly to the theoretical and experimental exploration and verification of what is now called quantum entanglement. along with podolsky and rosen, ei... | wikipedia |
a053846e9ac8e0e4ba64ade0794f1d35f7976252 | particles in singlet states do not need to | particles in singlet states do not need to be locally bound to each other. for example, when the spin states of two electrons are correlated by their emission from a single quantum event that conserves angular momentum, the resulting electrons remain in a shared singlet state even as their separation in space increases... | wikipedia |
f68e5f7c9cb38c618055db41cea4cf3559a5b6f5 | similarly, for a system of two electrons, it | similarly, for a system of two electrons, it is possible to measure the total spin by applying (s → 1 + s → 2) 2 {\displaystyle \left({\vec {s}}_{1}+{\vec {s}}_{2}\right)^{2}}, where s → 1 {\displaystyle {\vec {s}}_{1}} acts on electron 1 and s → 2 {\displaystyle {\vec {s}}_{2}} acts on electron 2. since this system ha... | wikipedia |
9e63660679bede591b6c4ef43d077ce50d4f7e37 | this greater mathematical precision for example makes it | this greater mathematical precision for example makes it possible to assess how singlets and doublets behave under rotation operations. since a spin-1/2 electron transforms as a doublet under rotation, its experimental response to rotation can be predicted by using the fundamental representation of that doublet, specif... | wikipedia |
1a4d657a011fd0edad6ca4afc7b1916b332dbf51 | the ability of positronium to form both singlet | the ability of positronium to form both singlet and triplet states is described mathematically by saying that the product of two doublet representations (meaning the electron and positron, which are both spin-1/2 doublets) can be decomposed into the sum of an adjoint representation (the triplet or spin 1 state) and a t... | wikipedia |
c3c93f1fb63843693c31b6f662c789e02f461e7e | any spin value can be used for the | any spin value can be used for the pair, but the entanglement effect will be strongest both mathematically and experimentally if the spin magnitude is as small as possible, with the maximum possible effect occurring for entities with spin-1/2 (such as electrons and positrons). early thought experiments for unbound sing... | wikipedia |
380b651d4a27cc0bef4ff4ee4e4728b9f8aed77b | the simplest possible bound particle pair capable of | the simplest possible bound particle pair capable of exhibiting the singlet state is positronium, which consists of an electron and positron (antielectron) bound by their opposite electric charges. the electron and positron in positronium can also have identical or parallel spin orientations, which results in an experi... | wikipedia |
f8d8dbac7b9fa5bb52018be4c8483a2f47d97655 | the simplest possible angular momentum singlet is a | the simplest possible angular momentum singlet is a set (bound or unbound) of two spin-1/2 (fermion) particles that are oriented so that their spin directions ("up" and "down") oppose each other; that is, they are antiparallel. | wikipedia |
972547120ac95f6d10d45da05567794caef29ea2 | while for angular momentum states the singlet-style terminology | while for angular momentum states the singlet-style terminology is seldom used beyond triplets (spin=1), it has proven historically useful for describing much larger particle groups and subgroups that share certain features and are distinguished from each other by quantum numbers beyond spin. an example of this broader... | wikipedia |
971659369e92944b1b695682107b599b30bf368b | singlet-style terminology is also used for systems whose | singlet-style terminology is also used for systems whose mathematical properties are similar or identical to angular momentum spin states, even when traditional spin is not involved. in particular, the concept of isospin was developed early in the history of particle physics to address the remarkable similarities of pr... | wikipedia |
e987db40172a68e7257d09e8de0cca265f0c4940 | the origin of the term "singlet" is that | the origin of the term "singlet" is that bound quantum systems with zero net angular momentum emit photons within a single spectral line, as opposed to double lines (doublet state) or triple lines (triplet state). the number of spectral lines n {\displaystyle n} in this singlet-style terminology has a simple relationsh... | wikipedia |
e021e8121fba4feb7fea3ca289d711c21af89cc9 | singlets and the related spin concepts of doublets | singlets and the related spin concepts of doublets and triplets occur frequently in atomic physics and nuclear physics, where one often needs to determine the total spin of a collection of particles. since the only observed fundamental particle with zero spin is the extremely inaccessible higgs boson, singlets in every... | wikipedia |
c7cbd6a4de6e8393783dee0ce5bdf5c4588276fb | in quantum mechanics, a singlet state usually refers | in quantum mechanics, a singlet state usually refers to a system in which all electrons are paired. the term 'singlet' originally meant a linked set of particles whose net angular momentum is zero, that is, whose overall spin quantum number s = 0 {\displaystyle s=0}. as a result, there is only one spectral line of a si... | wikipedia |
1f3a9a22a2ca16c2dca1cb893a4122d290fb70e2 | in computer science, the controlled not gate, controlled-x | in computer science, the controlled not gate, controlled-x gate, controlled-bit-flip gate, feynman gate or controlled pauli-x is a quantum logic gate that is an essential component in the construction of a gate-based quantum computer. it can be used to entangle and disentangle bell states. any quantum circuit can be si... | wikipedia |
421ba2e4973da982644ced77620e578f627f0518 | in may, 2024, canada implemented export restrictions on | in may, 2024, canada implemented export restrictions on the sale of quantum computers containing more than 34 qubits and error rates below a certain cnot error threshold, along with restrictions for quantum computers with more qubits and higher error rates. the same restrictions quickly popped up in the uk, france, spa... | wikipedia |
c764c795176a7af3264622cb3df76f90a145d9c9 | = 1 2 2 ((| 00 ⟩ + | = 1 2 2 ((| 00 ⟩ + | 01 ⟩ + | 10 ⟩ + | 11 ⟩) + (| 00 ⟩ − | 01 ⟩ − | 10 ⟩ + | 11 ⟩)) {\displaystyle ={\frac {1}{2{\sqrt {2}}}}((|00\rangle +|01\rangle +|10\rangle +|11\rangle)+(|00\rangle -|01\rangle -|10\rangle +|11\rangle))} | wikipedia |
1ae7dc753101b695d5b4051d7e41f9f3d8224e5a | = 1 2 2 ((| 0 ⟩ a | = 1 2 2 ((| 0 ⟩ a + | 1 ⟩ a) (| 0 ⟩ b + | 1 ⟩ b) + (| 0 ⟩ a − | 1 ⟩ a) (| 0 ⟩ b − | 1 ⟩ b)) {\displaystyle ={\frac {1}{2{\sqrt {2}}}}((|0\rangle _{a}+|1\rangle _{a})(|0\rangle _{b}+|1\rangle _{b})+(|0\rangle _{a}-|1\rangle _{a})(|0\rangle _{b}-|1\rangle _{b}))} | wikipedia |
ae144b8f6cf4dbf66b00ee6ea77b697b6640b572 | = 1 2 (| + ⟩ a | | = 1 2 (| + ⟩ a | + ⟩ b + | − ⟩ a | − ⟩ b) {\displaystyle ={\frac {1}{\sqrt {2}}}(|+\rangle _{a}|+\rangle _{b}+|-\rangle _{a}|-\rangle _{b})} | wikipedia |
4dd44d3d99150b9899e134bd68730e7cdd45e81d | in the hadamard view, the control and target | in the hadamard view, the control and target qubits have conceptually swapped and qubit a is inverted when qubit b is | − ⟩ b {\displaystyle |-\rangle _{b}}. the output state after applying the c gate is 1 2 (| + + ⟩ + | − − ⟩) {\textstyle {\frac {1}{\sqrt {2}}}(|++\rangle +|--\rangle)} which can be shown as follows: | wikipedia |
d7dc65401d0d4a6897c0cf9cb8df15b23df5801f | | + ⟩ a {\displaystyle |+\rangle _{a}} and | | + ⟩ a {\displaystyle |+\rangle _{a}} and 1 2 (| + ⟩ + | − ⟩) b {\displaystyle {\frac {1}{\sqrt {2}}}(|+\rangle +|-\rangle)_{b}} | wikipedia |
e5bb5731aa44f39f51e66fc600b18b538e10eb68 | after applying c, the resulting bell state 1 | after applying c, the resulting bell state 1 2 (| 00 ⟩ + | 11 ⟩) {\textstyle {\frac {1}{\sqrt {2}}}(|00\rangle +|11\rangle)} has the property that the individual qubits can be measured using any basis and will always present a 50/50 chance of resolving to each state. in effect, the individual qubits are in an undefined... | wikipedia |
2d93dbe4927ca350e686306a2b468bcf160d339d | 1 2 (| 0 ⟩ + | 1 | 1 2 (| 0 ⟩ + | 1 ⟩) a {\displaystyle {\frac {1}{\sqrt {2}}}(|0\rangle +|1\rangle)_{a}} and | 0 ⟩ b {\displaystyle |0\rangle _{b}} | wikipedia |
2594d8216fa61a9644b044af1306b5e2d4c57b73 | a common application of the c gate is | a common application of the c gate is to maximally entangle two qubits into the | Φ + ⟩ {\displaystyle |\phi ^{+}\rangle } bell state; this forms part of the setup of the superdense coding, quantum teleportation, and entangled quantum cryptography algorithms. | wikipedia |
e18fd5f4f7a3c0372232eabe979f7bfed0c5d636 | 1 2.. 1 2 = {\displaystyle {\frac {1}{2}}{\begin{bmatrix}{\begin{array}{rrrr}1&1&1&1\\1&-1&1&-1\\1&1&-1&-1\\1&-1&-1&1\en | 1 2.. 1 2 = {\displaystyle {\frac {1}{2}}{\begin{bmatrix}{\begin{array}{rrrr}1&1&1&1\\1&-1&1&-1\\1&1&-1&-1\\1&-1&-1&1\end{array}}\end{bmatrix}}.{\begin{bmatrix}1&0&0&0\\0&1&0&0\\0&0&0&1\\0&0&1&0\end{bmatrix}}.{\frac {1}{2}}{\begin{bmatrix}{\begin{array}{rrrr}1&1&1&1\\1&-1&1&-1\\1&1&-1&-1\\1&-1&-1&1\end{array}}\end{bmat... | wikipedia |
f3b9db134f5abc949d69ae562a53003cdd12388c | when multiplied out, this yields a matrix that | when multiplied out, this yields a matrix that swaps the | 01 ⟩ {\displaystyle |01\rangle } and | 11 ⟩ {\displaystyle |11\rangle } terms over, while leaving the | 00 ⟩ {\displaystyle |00\rangle } and | 10 ⟩ {\displaystyle |10\rangle } terms alone. this is equivalent to a cnot gate where qubit 2 is the control qubit and... | wikipedia |
b6dd949127a5a5d54a285893a6e43a2fcc1b7f3f | the single-qubit hadamard transform, h, is hermitian and | the single-qubit hadamard transform, h, is hermitian and therefore its own inverse. the tensor product of two hadamard transforms operating (independently) on two qubits is labelled h. we can therefore write the matrices as: | wikipedia |
525a4dd8d8c567140a9651ec77186409268e5a8d | we now proceed to give the details of | we now proceed to give the details of the computation. working through each of the hadamard basis states, the results on the right column show that the first qubit flips between | + ⟩ {\displaystyle |+\rangle } and | − ⟩ {\displaystyle |-\rangle } when the second qubit is | − ⟩ {\displaystyle |-\rangle }: | wikipedia |
e465bafdedc399009c4557df8a58ec0e37278908 | the "computational" basis { | 0 ⟩, | | the "computational" basis { | 0 ⟩, | 1 ⟩ } {\displaystyle \{|0\rangle,|1\rangle \}} is the eigenbasis for the spin in the z-direction, whereas the hadamard basis { | + ⟩, | − ⟩ } {\displaystyle \{|+\rangle,|-\rangle \}} is the eigenbasis for spin in the x-direction. switching x and z and qubits 1 and 2, then, recovers ... | wikipedia |
035bf8dc51ca1a47331808007e5e6b606921d8fa | etc. viewing cnot in this basis, the state | etc. viewing cnot in this basis, the state of the second qubit remains unchanged, and the state of the first qubit is flipped, according to the state of the second bit. (for details see below.) "thus, in this basis the sense of which bit is the control bit and which the target bit has reversed. but we have not changed ... | wikipedia |
63f4157845c91952dd06e1172ddb6830c25d8d5f | insight can be won by expressing the cnot | insight can be won by expressing the cnot gate with respect to a hadamard transformed basis { | + ⟩, | − ⟩ } {\displaystyle \{|+\rangle,|-\rangle \}}. the hadamard transformed basis of a one-qubit register is given by | wikipedia |
0350f081f87035be67f534571273fc41bbd3c744 | when viewed only in the computational basis { | when viewed only in the computational basis { | 0 ⟩, | 1 ⟩ } {\displaystyle \{|0\rangle,|1\rangle \}}, the behaviour of the c appears to be like the equivalent classical gate. however, the simplicity of labelling one qubit the control and the other the target does not reflect the complexity of what happens for most inp... | wikipedia |
0dcb0e03b834a3c34ec4b2256f98103a8584cc71 | in addition to a regular controlled not gate, | in addition to a regular controlled not gate, one could construct a function-controlled not gate, which accepts an arbitrary number n +1 of qubits as input, where n +1 is greater than or equal to 2 (a quantum register). this gate flips the last qubit of the register if and only if a built-in function, with the first n ... | wikipedia |
c038e6c3858f41e9ddbea7c66f6af73c44bc64ff | the first experimental realization of a cnot gate | the first experimental realization of a cnot gate was accomplished in 1995. here, a single beryllium ion in a trap was used. the two qubits were encoded into an optical state and into the vibrational state of the ion within the trap. at the time of the experiment, the reliability of the cnot-operation was measured to b... | wikipedia |
bfa9c1b36d8f596bc57a2f3ce7d8f487d50f5814 | a | 00 ⟩ + b | 01 | a | 00 ⟩ + b | 01 ⟩ + c | 11 ⟩ + d | 10 ⟩ {\displaystyle a|00\rangle +b|01\rangle +c|11\rangle +d|10\rangle } | wikipedia |
53a48cd20bc23f5b273683f7d7333597007c283d | a | 00 ⟩ + b | 01 | a | 00 ⟩ + b | 01 ⟩ + c | 10 ⟩ + d | 11 ⟩ {\displaystyle a|00\rangle +b|01\rangle +c|10\rangle +d|11\rangle } | wikipedia |
338231ba4eb49c806c8f76373173d082876df39d | more generally, the inputs are allowed to be | more generally, the inputs are allowed to be a linear superposition of { | 0 ⟩, | 1 ⟩ } {\displaystyle \{|0\rangle,|1\rangle \}}. the cnot gate transforms the quantum state: | wikipedia |
120d7b97c74787324c2a65f153c850db566e6b3d | if { | 0 ⟩, | 1 ⟩ | if { | 0 ⟩, | 1 ⟩ } {\displaystyle \{|0\rangle,|1\rangle \}} are the only allowed input values for both qubits, then the target output of the cnot gate corresponds to the result of a classical xor gate. fixing control as | 1 ⟩ {\displaystyle |1\rangle }, the target output of the cnot gate yields the result of a classic... | wikipedia |
387f31d08f4242f8c4eb2995ec7d5018eea92448 | the cnot gate operates on a quantum register | the cnot gate operates on a quantum register consisting of 2 qubits. the cnot gate flips the second qubit (the target qubit) if and only if the first qubit (the control qubit) is | 1 ⟩ {\displaystyle |1\rangle }. | wikipedia |
825156aca0622726d6c4fb83a189e91db62ca042 | in general, any single qubit unitary gate can | in general, any single qubit unitary gate can be expressed as u = e i h {\displaystyle u=e^{ih}}, where h is a hermitian matrix, and then the controlled u is c u = e i 1 2 (i 1 − z 1) h 2 {\displaystyle cu=e^{i{\frac {1}{2}}(i_{1}-z_{1})h_{2}}}. | wikipedia |
a617de5b341f1e691c4990b032b905d9a8158ddd | being both unitary and hermitian, cnot has the | being both unitary and hermitian, cnot has the property e i θ u = (cos θ) i + (i sin θ) u {\displaystyle e^{i\theta u}=(\cos \theta)i+(i\sin \theta)u} and u = e i π 2 (i − u) = e − i π 2 (i − u) {\displaystyle u=e^{i{\frac {\pi }{2}}(i-u)}=e^{-i{\frac {\pi }{2}}(i-u)}}, and is involutory. | wikipedia |
370667da85fc3c4ecb128051ec726dc452ed2bd6 | in computer science, the controlled not gate (also | in computer science, the controlled not gate (also c-not or cnot), controlled- x gate, controlled-bit-flip gate, feynman gate or controlled pauli-x is a quantum logic gate that is an essential component in the construction of a gate-based quantum computer. it can be used to entangle and disentangle bell states. any qua... | wikipedia |
8a3b2155a2ac4e9989a45c6c7b3dbe0158ae1cae | in chemistry, a reducing agent is a chemical | in chemistry, a reducing agent is a chemical species that "donates" an electron to an electron recipient. examples of substances that are common reducing agents include hydrogen, the alkali metals, formic acid, oxalic acid, and sulfite compounds. in their pre-reaction states, reducers have extra electrons and oxidizers... | wikipedia |
f7da0f573cba5ccbcd0c3b58c724afba8296da84 | thus in a redox reaction, the agent whose | thus in a redox reaction, the agent whose oxidation state increases, that "loses/donates electrons", that "is oxidized", and that "reduces" is called the reducer or reducing agent, while the agent whose oxidation state decreases, that "gains/accepts/receives electrons", that "is reduced", and that "oxidizes" is called ... | wikipedia |
0e7ca416b9f234bcc1a7f13a16dd6a218080a6ce | iron (fe) has been oxidized because the oxidation | iron (fe) has been oxidized because the oxidation number increased. iron is the reducing agent because it gave electrons to the oxygen (o).oxygen (o) has been reduced because the oxidation number has decreased and is the oxidizing agent because it took electrons from iron (fe). | wikipedia |
45686e4fa3e2910bde998a4f1aa1f409048fa0c5 | in the above equation, the iron (fe) has | in the above equation, the iron (fe) has an oxidation number of 0 before and 3+ after the reaction. for oxygen (o) the oxidation number began as 0 and decreased to 2−. these changes can be viewed as two " half-reactions " that occur concurrently: | wikipedia |
d1c9b75049df9449cb6b5052025cc46919f39b89 | historically, reduction referred to the removal of oxygen | historically, reduction referred to the removal of oxygen from a compound, hence the name 'reduction'. an example of this phenomenon occurred during the great oxidation event, in which biologically−produced molecular oxygen (dioxygen (o), an oxidizer and electron recipient) was added to the early earth's atmosphere, wh... | wikipedia |
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