According to Professor Gilles Brassard, an expert in quantum computing: " The time needed to factor an RSA integer is the same order as the time needed to use that same integer as modulus for a single RSA encryption.

According to a poll at a Quantum Mechanics workshop in 1997 ,< ref > the Copenhagen interpretation is the most widely-accepted specific interpretation of quantum mechanics, followed by the many-worlds interpretation.

According to the relational interpretation of quantum mechanics, first proposed by Carlo Rovelli, observations such as those in the double-slit experiment result specifically from the interaction between the observer ( measuring device ) and the object being observed ( physically interacted with ), not any absolute property possessed by the object.

According to the understanding of quantum mechanics known as the Copenhagen interpretation, measurement causes an instantaneous collapse of the wave function describing the quantum system into an eigenstate of the observable state that was measured.

According to quantum mechanics, we can arrange our source so that each emitted pair occupies a quantum state called a spin singlet.

According to the Copenhagen interpretation of quantum mechanics, the quantum state of the system collapses into state I.

According to the present view of the situation, quantum mechanics flatly contradicts Einstein's philosophical postulate that any acceptable physical theory must fulfill " local realism ".

According to the usual rules of quantum mechanics, the actual state of the electron may be any superposition of these states.

According to quantum theory, the particles do not possess definite positions during the periods between measurements.

According to the spin-statistics theorem, particles with integer spin occupy symmetric quantum states, and particles with half-integer spin occupy antisymmetric states ; furthermore, only integer or half-integer values of spin are allowed by the principles of quantum mechanics.

According to the correspondence principle between classical and quantum mechanics, all objects obey the laws of quantum mechanics, and classical mechanics is just an approximation for large systems of objects ( or a statistical quantum mechanics of a large collection of particles ).

According to this interpretation, the probabilistic nature of quantum mechanics is not a temporary feature which will eventually be replaced by a deterministic theory, but instead must be considered a final renunciation of the classical idea of " causality ".

According to the rules of quantum field theory, and the associated Feynman diagrams, the above theory gives rise to three basic interactions: a quark may emit ( or absorb ) a gluon, a gluon may emit ( or absorb ) a gluon, and two gluons may directly interact.

According to the Pauli exclusion principle, fermions cannot share quantum states, so their occupation numbers N < sub > i </ sub > can only take on the value 0 or 1.

According to the Copenhagen interpretation of quantum mechanics, their shared state is indefinite until measured.

According to this vacuum energy explanation, since quantum theory holds that vacuum contains virtual particles, the rapidly moving interface between water and gas converts virtual photons into real photons.

According to Simpson ( 1944 ) quantum evolution relied heavily upon Sewall Wright's theory of random genetic drift.

According to some, quantum mechanics is more strongly ordered than Classical Mechanics, because while Classical Mechanics is chaotic, quantum mechanics is not.

According to Gibbs, the term " statistical ", in the context of mechanics, i. e. statistical mechanics, was first used by the Scottish physicist James Clerk Maxwell in 1871.

According to the theory, wave functions interact with each other and evolve in time in accordance with the laws of quantum mechanics until a measurement is performed, at which point the system takes on one of its possible values, with a probability that's governed by the wave-function.

According to the laws of quantum mechanics, an energy is associated with each electron configuration and, upon certain conditions, electrons are able to move from one orbital to another by emission or absorption of a quantum of energy, in the form of a photon.

According to quantum mechanics, particle pairs are constantly appearing and disappearing as a quantum foam.

According to the principles of quantum mechanics, particles do not actually have trajectories through space.

According to the Copenhagen interpretation of quantum mechanics, quantum evolution is governed by the Schrödinger equation, which is time-symmetric, and by wave function collapse, which is time irreversible.

According to determinism, if someone knows the precise location and momentum of every atom in the universe, their past and future values for any given time are entailed ; they can be calculated from the laws of classical mechanics.

According to an early interview, with the city snowed under during the Great Blizzard of 1978 in Chicago, the two began preliminary work on the Computerized Bulletin Board System, or CBBS.

According to the plans, the Third Army, under general Radko Dimitriev, was deployed east of and behind the First, and was covered by the cavalry division hiding it from the Turkish view.

According to accounts which vary in some of the details, in 340 BC the Byzantines and their allies the Athenians were under siege by the troops of Philip of Macedon.

According to the Jewish Encyclopedia, " a comparison of the Masoretic text with the Septuagint throws some light on the last phase in the history of the origin of the Book of Jeremiah, inasmuch as the translation into Greek was already under way before the work on the Hebrew book had come to an end ...

According to the book of Ezra-Nehemiah they did so under the joint leadership of a descendant of the last king and the last High Priest, rebuilding the Temple and reconstituting Judah ( now called Yehud ) as a holy community ruled by priests.

According to Coogan, Hosea falls under a unique genre called “ covenant lawsuit ” where God accuses Israel of breaking their previously made agreement.

According to its Memorandum & Articles of Association, its objectives are :- “ To act as Nominee or agent or attorney either solely or jointly with others, for any person or persons, partnership, company, corporation, government, state, organisation, sovereign, province, authority, or public body, or any group or association of them ....” Bank of England Nominees Limited was granted an exemption by Edmund Dell, Secretary of State for Trade, from the disclosure requirements under Section 27 ( 9 ) of the Companies Act 1976, because, “ it was considered undesirable that the disclosure requirements should apply to certain categories of shareholders .” The Bank of England is also protected by its Royal Charter status, and the Official Secrets Act.

According to Blair ( 1997 ) British Steel faced serious problems at the time of its formation, including obsolescent plants ; plants operating under capacity and thus at low efficiency ; outdated technology ; price controls that reduced marketing flexibility ; soaring coal and oil costs ; lack of capital investment funds ; and increasing competition on the world market.

According to the authors of the study, " Probably Napoléon also knew his remote oriental patrilineal origins, because Francesco Buonaparte ( the Giovanni son ), who was a mercenary under the orders of the Genoa Republic in Ajaccio in 1490, was nicknamed The Maure of Sarzane ".

According to his website, three extended periods of his fasting have been observed under control of scientific and medical teams, the first lasting 211 days in 1995 – 96, in Calicut, India, under the direction of Dr C. K. Ramachandran.

According to historian Yuki Tanaka, " cannibalism was often a systematic activity conducted by whole squads and under the command of officers ".

According to George Cameron Stone, " Entire suits of mail kusari gusoku were worn on occasions, sometimes under the ordinary clothing ".

According to this viewpoint, citizens are sovereign, morally autonomous beings with duties to pay taxes, obey the law, engage in business transactions, and defend the nation if it comes under attack, but are essentially passive politically, and their primary focus is on economic betterment.

According to Suetonius, Caligula's body was placed under turf until it was burned and entombed by his sisters.

According to Bancroft, Mather had been influential in gaining politically unpopular Stoughton his appointment as lieutenant governor under Phips by appealing to his politically powerful father, Increase Mather.

According to Edward Barlow, a captain employed by the English East India Company, Kidd attacked a Mughal convoy here under escort by Barlow's East Indiaman, and was repelled.

According to Bernal Díaz del Castillo, a conquistador serving under Cortés who recorded his experiences in his book The Conquest of New Spain, the supposed plot was revealed by two men, named Tapia and Juan Velásquez.

According to non-Orthodox Jews and critical historians, Jewish law too has been affected by surrounding cultures ( for example, some scholars argue that the establishment of absolute monotheism in Judaism was a reaction against the dualism of Zoroastrianism that Jews encountered when living under Persian rule ; Jews rejected polygamy during the Middle Ages, influenced by their Christian neighbors ).

According to Suetonius, the imperial bureaucracy never ran more efficiently than under Domitian, whose exacting standards and suspicious nature maintained historically low corruption among provincial governors and elected officials.

According to observations of structures larger than solar systems, as well as Big Bang cosmology interpreted under the Friedmann equations and the FLRW metric, dark matter accounts for 23 % of the mass-energy content of the observable universe.

According to distributists, property ownership is a fundamental right and the means of production should be spread as widely as possible among the general populace, rather than being centralized under the control of the state ( state socialism ) or by an elite of wealthy property owners ( laissez-faire capitalism ).

According to the CIA, the Afar constitute under 5 % of the nation's population.

According to the Talmud, however, the point of Qoheleth is to state that all is futile under the Sun.