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18,700 | In September 1963, the .223 Remington cartridge was officially accepted and named "Cartridge, 5.56mm ball, M193". The specification includes a Remington-designed bullet and the use of IMR4475 powder which resulted in a muzzle velocity of and a chamber pressure of 52,000 psi. | https://en.wikipedia.org/wiki?curid=35022 |
18,701 | In 1970, NATO members signed an agreement to select a second, smaller caliber cartridge to replace the 7.62×51mm NATO cartridge. Of the cartridges tendered, the .223 Remington (M193) was the basis for a new design created by FN Herstal. The FN-created cartridge was named "5.56×45mm NATO" with a military designation of ... | https://en.wikipedia.org/wiki?curid=35022 |
18,702 | The Belgian 62 gr SS109 round was chosen for standardization as the second NATO standard rifle cartridge which led to the October 1980 STANAG 4172. The SS109 used a 62 gr full metal jacket bullet with a seven grain mild steel tip to move the center of gravity rearward, increasing flight stability and thereby the chance... | https://en.wikipedia.org/wiki?curid=35022 |
18,703 | The .223 Remington cartridge inspired an international tendency toward relatively small-sized, lightweight, high-velocity military service cartridges that allow a soldier to carry more ammunition for the same weight compared to their larger and heavier predecessor cartridges, have favourable maximum point-blank range o... | https://en.wikipedia.org/wiki?curid=35022 |
18,704 | The rifling twist rate for this cartridge is 177.8 mm (1 in 7 in), 6 grooves right hand twist, Ø lands = , Ø grooves = . | https://en.wikipedia.org/wiki?curid=35022 |
18,705 | According to STANAG 4172 and the official NATO proofing guidelines the 5.56×45mm NATO case can handle up to piezo service pressure. In NATO regulated organizations every rifle cartridge combination has to be proofed at to certify for service issue. | https://en.wikipedia.org/wiki?curid=35022 |
18,706 | STANAG 4172 defines the Belgian ball cartridge SS109 as the NATO reference cartridge and adds a considerable number of technical requirements like a minimum pressure of at the gas port down the long standard proof barrel and primer sensitivity that are not defined by civilian C.I.P. and SAAMI ammunition rulings and rec... | https://en.wikipedia.org/wiki?curid=35022 |
18,707 | The NATO military alliance uses a NATO-specific recognized class of procedures to control the safety and quality of firearms ammunition called NATO EPVAT testing. The civilian organisations C.I.P. and SAAMI use less comprehensive test procedures than NATO. | https://en.wikipedia.org/wiki?curid=35022 |
18,708 | The "NATO Manual of Proof and Inspection AC/225 (LG/3-SG/1) D/8" stipulates each weapon and component considered vulnerable to the effects of a rapid change in pressure, for example barrels, breech blocks and bolts, will be tested by firing one dry round at a corrected minimum of 25% over pressure and one oiled round a... | https://en.wikipedia.org/wiki?curid=35022 |
18,709 | The US SAAMI lists maximum average pressure (MAP) for the .223 Remington cartridge as piezo pressure with deviation of up to . | https://en.wikipedia.org/wiki?curid=35022 |
18,710 | When 5.56×45mm NATO was adopted as standard in 1980, NATO chose a 178 mm (1:7) rifling twist rate for the 5.56×45mm NATO chambering to adequately stabilize the relatively long NATO L110/M856 5.56×45mm NATO tracer projectile. The US at that time converted all rifles in inventory by replacing the barrels and all new US m... | https://en.wikipedia.org/wiki?curid=35022 |
18,711 | In the US builders of AR type rifles can specify barrels with either .223 Remington, .223 Wylde, 223 Noveske, or 5.56×45mm NATO chambers in lengths from pistol (7.5") to long rifle (24"). These barrels are also available with rifling ranging from 356 mm (1-in-14") to 178 mm (1-in-7"). US makers are moving toward 5.56×4... | https://en.wikipedia.org/wiki?curid=35022 |
18,712 | The 5.56×45mm NATO SS109/M855 cartridge (NATO: SS109; U.S.: M855) with standard 62 gr. lead core bullets with steel penetrator will penetrate about into soft tissue in ideal circumstances. As with all spitzer shaped projectiles, it is prone to yaw in soft tissue. However, at impact velocities above roughly , it may yaw... | https://en.wikipedia.org/wiki?curid=35022 |
18,713 | Fragmentation, if and when it occurs, imparts much greater damage to human tissue than bullet dimensions and velocities would suggest. This fragmentation effect is highly dependent on velocity, and therefore barrel length: short-barreled carbines generate less muzzle velocity and therefore lose wounding effectiveness a... | https://en.wikipedia.org/wiki?curid=35022 |
18,714 | Proponents of the hydrostatic shock theory contend that the shockwave from a high-velocity bullet results in wounding effects beyond the tissue directly crushed and torn by the bullet and fragments. However, others argue that tissue damage from hydrostatic shock is a myth. Critics argue that sonic pressure waves do not... | https://en.wikipedia.org/wiki?curid=35022 |
18,715 | SS109/M855 NATO ball can penetrate up to of steel at 600 meters. According to Nammo, a Finnish-Norwegian ammunition producer, the 5.56×45mm NATO M995 armour piercing cartridge can penetrate up to of RHA steel at 100 meters. | https://en.wikipedia.org/wiki?curid=35022 |
18,716 | The US Army's Ballistic Research Laboratory measured a ballistic coefficient (G7 BC) of 0.151 and form factor (G7 "i") of 1.172 for the SS109/M855 ball projectile. | https://en.wikipedia.org/wiki?curid=35022 |
18,717 | The Swedish military has measured the bullet velocities of SS109/M855 military cartridges at from the muzzle fired from differing barrel lengths. | https://en.wikipedia.org/wiki?curid=35022 |
18,718 | There has been much debate of the allegedly poor performance of the bullet on target in regard to stopping power, lethality, and range. Some of this criticism has been used to advocate an intermediate-sized cartridge between the 5.56 and 7.62 NATO sizes while criticisms of poor barrier penetration and accuracy have bee... | https://en.wikipedia.org/wiki?curid=35022 |
18,719 | The 5.56×45mm NATO standard SS109/M855 cartridge was designed for maximum performance when fired from a long barrel, as was the original 5.56 mm M193 cartridge. Experiments with longer length barrels up to resulted in no improvement or a decrease in muzzle velocities for the SS109/M855 cartridge. Shorter barrels produc... | https://en.wikipedia.org/wiki?curid=35022 |
18,720 | Compared to larger calibers, proponents of the 5.56×45mm NATO round contend that animal studies of the wounding effects of the 5.56×45mm NATO round versus the 7.62×39mm have found that the 5.56×45mm NATO round is more damaging, due to the post-impact behavior of the 5.56 mm projectile resulting in greater cavitation of... | https://en.wikipedia.org/wiki?curid=35022 |
18,721 | Some have contended that shot placement is the most important parameter in determining the lethality of a bullet. Difficulty with the 5.56×45mm NATO at long ranges has been attributed to training; Swedish ISAF units relied on .50 BMG heavy machine guns for long-range shooting due to resilience to factors such as range ... | https://en.wikipedia.org/wiki?curid=35022 |
18,722 | Advances have been made in 5.56 mm ammunition. The U.S. military had adopted for limited issue a 77-grain (5.0 g) "Match" bullet, type classified as the Mk 262. The heavy, lightly constructed bullet fragments more violently at short range and also has a longer fragmentation range. Originally designed for use in the Mk ... | https://en.wikipedia.org/wiki?curid=35022 |
18,723 | U.S. Special Forces had sought to create a round that had increased power out of carbine M4 barrels and compact SCAR-L barrels, while increasing hard target performance. Developmental efforts led to the creation of the Mk318. The bullet uses an open-tip design to inflict damage on soft tissue, and has a brass rear to p... | https://en.wikipedia.org/wiki?curid=35022 |
18,724 | For general issue, the U.S. Army adopted the M855A1 round in 2010 to replace the M855. The primary reason was pressure to use non-lead bullets. The lead slug is replaced by a copper alloy slug in a reverse-drawn jacket, with a hardened steel penetrator extending beyond the jacket, reducing lead contamination to the env... | https://en.wikipedia.org/wiki?curid=35022 |
18,725 | The U.S. Marines adopted the Mk318 in early 2010 due to delays with the M855A1. This was a temporary measure until the M855A1 was available for them, which occurred in mid-2010 when the Army began to receive the rounds. Both the Mk318 and M855A1 weigh the same and have similar performance, and both have better performa... | https://en.wikipedia.org/wiki?curid=35022 |
18,726 | If the 5.56 mm bullet is moving too slowly to reliably yaw, expand, or fragment on impact, the wound size and potential to incapacitate a person is greatly reduced. There have been numerous attempts to create an intermediate cartridge that addresses the complaints of 5.56 NATO's lack of stopping power along with lack o... | https://en.wikipedia.org/wiki?curid=35022 |
18,727 | By late 2004, the 6.8mm Remington SPC (6.8×43mm) was in limited use with U.S. Special Operators. However, it was not adopted for widespread use due to resistance from officials on changing calibers. In 2007, both the U.S. SOCOM and the U.S. Marine Corps decided not to field weapons chambered in 6.8×43mm due to logistic... | https://en.wikipedia.org/wiki?curid=35022 |
18,728 | In April 2022, the U.S. Army selected a new rifle and light machine gun as part of the Next Generation Squad Weapon Program. They will replace 5.56 mm weapons, being chambered in 6.8×51mm Fury that has greater accuracy and range while being more lethal than 5.56×45mm NATO and 7.62×51mm NATO against emerging threats. | https://en.wikipedia.org/wiki?curid=35022 |
18,729 | The exterior dimensions of the 5.56mm NATO and .223 Remington cartridges are identical. While the cartridges are identical other than powder load, the chamber leade, i.e. the area where the rifling begins, is cut to a sharper angle on some .223 commercial chambers. Because of this, a cartridge loaded to generate 5.56mm... | https://en.wikipedia.org/wiki?curid=35022 |
18,730 | The dimensional specifications of 5.56 NATO and .223 commercial brass cases are identical. The cases tend to have similar case capacity when measured, with variations chiefly due to brand, not 5.56 vs .223 designation. The result of this is that there is no such thing as "5.56 brass" or ".223 brass", the differences in... | https://en.wikipedia.org/wiki?curid=35022 |
18,731 | In July 2012, the US Army made a request for vendors to supply alternative cartridge cases to reduce the weight of an M855A1 5.56 mm round by at least 10 percent, as well as for the 7.62 NATO and .50 BMG rounds. The cartridge cases must maintain all performance requirements when fully assembled, be able to be used by t... | https://en.wikipedia.org/wiki?curid=35022 |
18,732 | C.I.P. defines the maximum service and proof test pressures of the .223 Remington cartridge equal to the 5.56mm NATO, at . This differs from the SAAMI maximum pressure specification for .223 Remington of , due to CIP test protocols measuring pressure using a drilled case, rather than an intact case with a conformal pis... | https://en.wikipedia.org/wiki?curid=35022 |
18,733 | Differences in testing methodology have led to widespread confusion, however when measured with identical measuring equipment using identical methodologies, .223 Remington yields peak average pressures about 5,000 psi lower than 5.56 NATO. | https://en.wikipedia.org/wiki?curid=35022 |
18,734 | The 5.56mm NATO chamber, known as a NATO or mil-spec chamber, has a longer leade, which is the distance between the mouth of the cartridge and the point at which the rifling engages the bullet. The .223 Remington chamber, known as SAAMI chamber, is allowed to have a shorter leade, and is only required to be proof teste... | https://en.wikipedia.org/wiki?curid=35022 |
18,735 | Using commercial .223 Remington cartridges in a 5.56mm NATO chambered rifle should work reliably, but until recently, it was believed this was less accurate than when fired from a .223 Remington chambered gun due to the longer leade. Although that may have been true in the early 1960s when the two rounds were developed... | https://en.wikipedia.org/wiki?curid=35022 |
18,736 | The upper receiver (to which the barrel with its chamber are attached) and the lower receiver are entirely separate parts in AR-15 style rifles. If the lower receiver has either .223 or 5.56 stamped on it, it does not guarantee the upper assembly is rated for the same caliber, because the upper and the lower receiver i... | https://en.wikipedia.org/wiki?curid=35022 |
18,737 | In more practical terms, most AR-15 parts suppliers engineer their complete upper assemblies (not to be confused with stripped uppers where the barrel is not included) to support both calibers in order to satisfy market demand and prevent any potential problems. Some manufacturers have begun offering a hybrid .223 Wyld... | https://en.wikipedia.org/wiki?curid=35022 |
18,738 | The first confrontations between the AK-47 and the M14 rifle came in the early part of the Vietnam War. Battlefield reports indicated that the M14 was uncontrollable in full-auto and that soldiers could not carry enough ammo to maintain fire superiority over the AK-47. A replacement was needed, as a result, the Army wa... | https://en.wikipedia.org/wiki?curid=35022 |
18,739 | This request ultimately resulted in the development of a scaled-down version of the Armalite AR-10, called ArmaLite AR-15 rifle. During testing it was found that a 5- to 7-man team armed with the ArmaLite AR-15s has the same firepower as 11-man team armed with M14s. Also, soldiers armed with ArmaLite AR-15s could carry... | https://en.wikipedia.org/wiki?curid=35022 |
18,740 | Hit probability refers to the ability of a soldier to concentrate on firing in spite of their weapon's recoil and noise, which is noticeably different between the two cartridges. The 7.62 NATO has twice the impact energy of the 5.56 NATO, preferable if a target is protected by higher level armor, especially at "medium"... | https://en.wikipedia.org/wiki?curid=35022 |
18,741 | Military ammunition was packed exclusively in 20-round cartons from 1963 to 1966. In late 1966 the 10-round stripper clip and magazine-charging adapter were introduced and ammunition began being packed in clips in bandoleers. | https://en.wikipedia.org/wiki?curid=35022 |
18,742 | In 1970, NATO decided to standardize a second rifle caliber. Tests were conducted from 1977 to 1980 using U.S. XM777 5.56 mm, Belgian SS109 5.56 mm, British 4.85×49mm, and German 4.7×33mm caseless. No weapon could be agreed upon, as many were prototypes, but the SS109 was found to be the best round and standardized on ... | https://en.wikipedia.org/wiki?curid=35022 |
18,743 | The maximum effective point target range of an M4 carbine with M855 rounds is , with a maximum effective area target range of . These mark the greatest distances the rounds can be expected to accurately hit the target, not the ranges that they have terminal effectiveness against them. Because the M855 is yaw dependent ... | https://en.wikipedia.org/wiki?curid=35022 |
18,744 | The M855A1 Enhanced Performance Round (EPR) was introduced in June 2010. It features a lead-free 62 grain (4.0 g) projectile with a solid copper core, and is tailored for use in rifles with shorter barrels such as the M4 carbine. It provides more consistent performance compared to the M855. | https://en.wikipedia.org/wiki?curid=35022 |
18,745 | On 24 June 2010, the United States Army announced it began shipping its new 5.56 mm cartridge, the M855A1 Enhanced Performance Round (EPR), to active combat zones. During testing, the M855A1 performed better than M80 7.62×51mm NATO ball ammunition against certain types of targets (particularly hardened steel). However,... | https://en.wikipedia.org/wiki?curid=35022 |
18,746 | The United States Marine Corps purchased 1.8 million rounds in 2010, with plans to adopt the round to replace the interim MK318 SOST rounds used in Afghanistan when the M855A1 project was delayed. The Marine Corps plans to adopt the M855A1 round in 2018; although testing revealed it caused "some durability issues" with... | https://en.wikipedia.org/wiki?curid=35022 |
18,747 | On a media day at Aberdeen Proving Ground on 4 May 2011, reports were given about the M855A1's performance in the field since it was issued 11 months earlier. One primary advantage given by the round is its consistent performance against soft targets. While the older SS109/M855 was yaw-dependent, which means its effect... | https://en.wikipedia.org/wiki?curid=35022 |
18,748 | The M855A1 was put to the test at the 2012 National Rifle Association's National High-Power Rifle Championship at Camp Perry, Ohio in August 2012. The shooter for the Army was Rob Harbison, a contractor supporting small caliber ammunition capability development at Fort Benning Georgia. This was a special event for the ... | https://en.wikipedia.org/wiki?curid=35022 |
18,749 | From fielding in June 2010 to September 2012, Alliant Techsystems delivered over 350 million M855A1 Enhanced Performance Rounds. | https://en.wikipedia.org/wiki?curid=35022 |
18,750 | Since its introduction, the M855A1 has been criticized for its St. Mark's SMP842 propellant causing increased fouling of the gun barrel. Post-combat surveys have reported no issues with the EPR in combat. A series of tests found no significant difference in fouling between the old M855 and the M855A1. However, manufact... | https://en.wikipedia.org/wiki?curid=35022 |
18,751 | From June 2010 to June 2013, issuing of the M855A1 Enhanced Performance Round removed 1,994 metric tons of lead from the waste stream. of lead are eliminated from each M855A1 projectile. | https://en.wikipedia.org/wiki?curid=35022 |
18,752 | The Mk 262 is a match-quality round manufactured by Black Hills Ammunition made originally for the Special Purpose Rifle (SPR). It uses a Sierra MatchKing bullet that is more effective at longer ranges than the standard issue M855 round. | https://en.wikipedia.org/wiki?curid=35022 |
18,753 | In 1999, SOCOM requested Black Hills Ammunition to develop ammunition for the Mk 12 SPR that SOCOM was designing. For the rifle to be accurate out to 700 yards, Black Hills "militarized" a cartridge that used the Sierra 77 grain OTM (Open Tip Match) projectile; it switched from a .223 Remington to 5.56 mm case, increas... | https://en.wikipedia.org/wiki?curid=35022 |
18,754 | According to US DoD sources, the Mk 262 round is capable of making kills at 700 meters. Ballistics tests found that the round caused "consistent initial yaw in soft tissue" between 3 and 4 in at ranges from 15 feet to 300 meters. Apparently it is superior to the standard M855 round when fired from an M4 or M16 rifle, i... | https://en.wikipedia.org/wiki?curid=35022 |
18,755 | Following early engagements in Afghanistan and Iraq, U.S. Special Operations Forces reported that M855 ammunition used in M4A1 rifles was ineffective. In 2005, the Pentagon issued a formal request to the ammunition industry for "enhanced" ammunition. The only business that responded was the Federal Cartridge Company, o... | https://en.wikipedia.org/wiki?curid=35022 |
18,756 | Officially designated the Mk318 MOD 0 "Cartridge, Caliber 5.56mm Ball, Carbine, Barrier", and called "SOST (Special Operations Science and Technology)" ammunition, the 62-grain bullet fragments consistently, even out of a 10.5 in barrel. The lead portion fragments in the first few inches of soft tissue, then the solid ... | https://en.wikipedia.org/wiki?curid=35022 |
18,757 | In February 2010, the U.S. Marine Corps adopted the Mk318 for use by infantry. To be fielded by an entire branch of the military, the round is classified as having an "open-tip" bullet, similar to the M118LR 7.62 NATO round. The SOST bullet uses a "reverse drawn" forming process. The base of the bullet is made first, t... | https://en.wikipedia.org/wiki?curid=35022 |
18,758 | As the issue of environmentally friendly ammo grew, the Marines looked to see if the Mk318's lead could be replaced while still meeting specifications. They found that by replacing the lead with copper and slightly stretching the jacket around to crimp the nose even more, the bullet's ballistic coefficient increased. T... | https://en.wikipedia.org/wiki?curid=35022 |
18,759 | The 5.6mm "Gewehr Patrone" 90 or 5,6mm Gw Pat 90 (5.6 mm Rifle Cartridge 90), is the standard round used by the Swiss military in its rifle, the SIG SG 550. The cartridge is also known as the Cart 5,6mm 90 F (French: "Cartouche pour Fusil" / Italian: "Cartuccia per Fucile") to the French- and Italian-speaking Swiss mil... | https://en.wikipedia.org/wiki?curid=35022 |
18,760 | The Gw Pat 90 was designed for the SIG SG 550 when it came into production in 1987, replacing the SIG SG 510. Previous experience of a change in standard rifle had proved that changing the distance of fire for the training ranges was more expensive than the design of a new ammunition; this prompted the design of a cart... | https://en.wikipedia.org/wiki?curid=35022 |
18,761 | The ammunition is currently (2009) produced by RUAG Ammotec, a subsidiary of the RUAG group. The ammunition is manufactured in three variations: the standard FMJ round, the tracer round, and a blank round. | https://en.wikipedia.org/wiki?curid=35022 |
18,762 | The FMJ cartridge has a Copper-Zinc alloy case and uses a double base propellant. The bullet is a 4.1 g (63 gr) tombac jacketed FMJ projectile with a G1 ballistic coefficient of 0.331 (ICAO) / 0.337 (Army Metro). The projectile contains approximately 95% Pb, 2% Sb, 3% Cu, and was designed for terminal ballistic instabi... | https://en.wikipedia.org/wiki?curid=35022 |
18,763 | The Gw Pat 90 is used both in the Swiss military and in sport shooting. The very high level of individual training in the Swiss militia (every single soldier bearing a weapon has to shoot in order to maintain his ability once a year; see Gun laws in Switzerland) and the overall use of the Gw Pat 90 by the many Swiss ci... | https://en.wikipedia.org/wiki?curid=35022 |
18,764 | Quantum computing is a type of computation whose operations can harness the phenomena of quantum mechanics, such as superposition, interference, and entanglement. Devices that perform quantum computations are known as quantum computers. Though current quantum computers are too small to outperform usual (classical) comp... | https://en.wikipedia.org/wiki?curid=25220 |
18,765 | There are several models of quantum computation with the most widely used being quantum circuits. Other models include the quantum Turing machine, quantum annealing, and adiabatic quantum computation. Most models are based on the quantum bit, or "qubit", which is somewhat analogous to the bit in classical computation. ... | https://en.wikipedia.org/wiki?curid=25220 |
18,766 | Efforts towards building a physical quantum computer focus on technologies such as transmons, ion traps and topological quantum computers, which aim to create high-quality qubits. These qubits may be designed differently, depending on the full quantum computer's computing model, as to whether quantum logic gates, quant... | https://en.wikipedia.org/wiki?curid=25220 |
18,767 | Any computational problem that can be solved by a classical computer can also be solved by a quantum computer. Conversely, any problem that can be solved by a quantum computer can also be solved by a classical computer, at least in principle given enough time. In other words, quantum computers obey the Church–Turing th... | https://en.wikipedia.org/wiki?curid=25220 |
18,768 | Quantum computing began in 1980 when physicist Paul Benioff proposed a quantum mechanical model of the Turing machine. Richard Feynman and Yuri Manin later suggested that a quantum computer had the potential to simulate things a classical computer could not feasibly do. In 1986 Feynman introduced an early version of th... | https://en.wikipedia.org/wiki?curid=25220 |
18,769 | In December 2021 McKinsey & Company analysis states that "..investment dollars are pouring in, and quantum-computing start-ups are proliferating". They go on to note that "While quantum computing promises to help businesses solve problems that are beyond the reach and speed of conventional high-performance computers, u... | https://en.wikipedia.org/wiki?curid=25220 |
18,770 | Computer engineers typically describe a modern computer's operation in terms of classical electrodynamics. | https://en.wikipedia.org/wiki?curid=25220 |
18,771 | Within these "classical" computers, some components (such as semiconductors and random number generators) may rely on quantum behavior, but these components are not isolated from their environment, so any quantum information quickly decoheres. | https://en.wikipedia.org/wiki?curid=25220 |
18,772 | While programmers may depend on probability theory when designing a randomized algorithm, quantum mechanical notions like superposition and interference are largely irrelevant for program analysis. | https://en.wikipedia.org/wiki?curid=25220 |
18,773 | Complex numbers model probability amplitudes, vectors model quantum states, and matrices model the operations that can be performed on these states. | https://en.wikipedia.org/wiki?curid=25220 |
18,774 | Programming a quantum computer is then a matter of composing operations in such a way that the resulting program computes a useful result in theory and is implementable in practice. | https://en.wikipedia.org/wiki?curid=25220 |
18,775 | The prevailing model of quantum computation describes the computation in terms of a network of quantum logic gates. This model is a complex linear-algebraic generalization of boolean circuits. | https://en.wikipedia.org/wiki?curid=25220 |
18,776 | A memory consisting of formula_1 bits of information has formula_2 possible states. A vector representing all memory states thus has formula_2 entries (one for each state). This vector is viewed as a "probability vector" and represents the fact that the memory is to be found in a particular state. | https://en.wikipedia.org/wiki?curid=25220 |
18,777 | The bits of classical computers are not capable of being in superposition, so one entry must have a value of 1 (i.e. a 100% probability of being in this state) and all other entries would be zero. | https://en.wikipedia.org/wiki?curid=25220 |
18,778 | In quantum mechanics, probability vectors can be generalized to density operators. The quantum state vector formalism is usually introduced first because it is conceptually simpler, and because it can be used instead of the density matrix formalism "for pure states," where the whole quantum system is known. | https://en.wikipedia.org/wiki?curid=25220 |
18,779 | We begin by considering a simple memory consisting of only one quantum bit. When measured, this memory may be found in one of two states: the zero state or the one state. We may represent the state of this memory using Dirac notation so that | https://en.wikipedia.org/wiki?curid=25220 |
18,780 | A quantum memory may then be found in any quantum superposition formula_5 of the two classical states formula_6 and formula_7: | https://en.wikipedia.org/wiki?curid=25220 |
18,781 | The coefficients formula_9 and formula_10 are complex numbers. The state formula_5 is not itself a probability vector but can be connected with a probability vector via the measurement operation. If the quantum memory is measured to determine whether the state is formula_6 or formula_7 (this is known as a computational... | https://en.wikipedia.org/wiki?curid=25220 |
18,782 | The state of this one-qubit quantum memory can be manipulated by applying quantum logic gates, analogous to how classical memory can be manipulated with classical logic gates. One important gate for both classical and quantum computation is the NOT gate, which can be represented by a matrix | https://en.wikipedia.org/wiki?curid=25220 |
18,783 | Mathematically, the application of such a logic gate to a quantum state vector is modelled with matrix multiplication. Thus formula_19 and formula_20. | https://en.wikipedia.org/wiki?curid=25220 |
18,784 | The mathematics of single qubit gates can be extended to operate on multi-qubit quantum memories in two important ways. One way is simply to select a qubit and apply that gate to the target qubit whilst leaving the remainder of the memory unaffected. Another way is to apply the gate to its target only if another part o... | https://en.wikipedia.org/wiki?curid=25220 |
18,785 | As a mathematical consequence of this definition, formula_23, formula_24, formula_25, and formula_26. In other words, the CNOT applies a NOT gate (formula_27 from before) to the second qubit if and only if the first qubit is in the state formula_7. If the first qubit is formula_6, nothing is done to either qubit. | https://en.wikipedia.org/wiki?curid=25220 |
18,786 | In summary, a quantum computation can be described as a network of quantum logic gates and measurements. However, any measurement can be deferred to the end of quantum computation, though this deferment may come at a computational cost, so most quantum circuits depict a network consisting only of quantum logic gates an... | https://en.wikipedia.org/wiki?curid=25220 |
18,787 | There are a number of models of computation for quantum computing, distinguished by the basic elements in which the computation is decomposed. | https://en.wikipedia.org/wiki?curid=25220 |
18,788 | A quantum computation can be described as a network of quantum logic gates and measurements. However, any measurement can be deferred to the end of quantum computation, though this deferment may come at a computational cost, so most quantum circuits depict a network consisting only of quantum logic gates and no measure... | https://en.wikipedia.org/wiki?curid=25220 |
18,789 | Any quantum computation (which is, in the above formalism, any unitary matrix of size formula_30 over formula_31 qubits) can be represented as a network of quantum logic gates from a fairly small family of gates. A choice of gate family that enables this construction is known as a universal gate set, since a computer t... | https://en.wikipedia.org/wiki?curid=25220 |
18,790 | A measurement-based quantum computer decomposes computation into a sequence of Bell state measurements and single-qubit quantum gates applied to a highly entangled initial state (a cluster state), using a technique called quantum gate teleportation. | https://en.wikipedia.org/wiki?curid=25220 |
18,791 | An adiabatic quantum computer, based on quantum annealing, decomposes computation into a slow continuous transformation of an initial Hamiltonian into a final Hamiltonian, whose ground states contain the solution. | https://en.wikipedia.org/wiki?curid=25220 |
18,792 | The quantum Turing machine is theoretically important but the physical implementation of this model is not feasible. All of these models of computation—quantum circuits, one-way quantum computation, adiabatic quantum computation, and topological quantum computation—have been shown to be equivalent to the quantum Turing... | https://en.wikipedia.org/wiki?curid=25220 |
18,793 | Quantum cryptography could potentially fulfill some of the functions of public key cryptography. Quantum-based cryptographic systems could, therefore, be more secure than traditional systems against quantum hacking. | https://en.wikipedia.org/wiki?curid=25220 |
18,794 | Progress in finding quantum algorithms typically focuses on this quantum circuit model, though exceptions like the quantum adiabatic algorithm exist. Quantum algorithms can be roughly categorized by the type of speedup achieved over corresponding classical algorithms. | https://en.wikipedia.org/wiki?curid=25220 |
18,795 | Quantum algorithms that offer more than a polynomial speedup over the best-known classical algorithm include Shor's algorithm for factoring and the related quantum algorithms for computing discrete logarithms, solving Pell's equation, and more generally solving the hidden subgroup problem for abelian finite groups. The... | https://en.wikipedia.org/wiki?curid=25220 |
18,796 | Other problems, including the simulation of quantum physical processes from chemistry and solid-state physics, the approximation of certain Jones polynomials, and the quantum algorithm for linear systems of equations have quantum algorithms appearing to give super-polynomial speedups and are BQP-complete. Because these... | https://en.wikipedia.org/wiki?curid=25220 |
18,797 | Some quantum algorithms, like Grover's algorithm and amplitude amplification, give polynomial speedups over corresponding classical algorithms. Though these algorithms give comparably modest quadratic speedup, they are widely applicable and thus give speedups for a wide range of problems. Many examples of provable quan... | https://en.wikipedia.org/wiki?curid=25220 |
18,798 | A notable application of quantum computation is for attacks on cryptographic systems that are currently in use. Integer factorization, which underpins the security of public key cryptographic systems, is believed to be computationally infeasible with an ordinary computer for large integers if they are the product of fe... | https://en.wikipedia.org/wiki?curid=25220 |
18,799 | Identifying cryptographic systems that may be secure against quantum algorithms is an actively researched topic under the field of "post-quantum cryptography". Some public-key algorithms are based on problems other than the integer factorization and discrete logarithm problems to which Shor's algorithm applies, like th... | https://en.wikipedia.org/wiki?curid=25220 |
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