Quantum annealing (QA) is an optimization process for finding the global minimum of a given objective function over a given set of candidate solutions (candidate states), by a process using quantum fluctuations. Quantum annealing is used mainly for problems where the search space is discrete (combinatorial optimization problems) with many local minima; such as finding[1] the ground state of a spin glass or the traveling salesman problem. The term "quantum annealing" was first proposed in 1988 by B. Apolloni, N. Cesa Bianchi and D. De Falco as a quantum-inspired classical algorithm.[2][3] It was formulated in its present form by T. Kadowaki and H. Nishimori (ja) in 1998[4] though an imaginary-time variant without quantum coherence had been discussed by A. B. Finnila, M. A. Gomez, C. Sebenik and J. D. Doll in 1994.[5]
Quantum annealing starts from a quantum-mechanical superposition of all possible states (candidate states) with equal weights. Then the system evolves following the time-dependent Schrödinger equation, a natural quantum-mechanical evolution of physical systems. The amplitudes of all candidate states keep changing, realizing a quantum parallelism, according to the time-dependent strength of the transverse field, which causes quantum tunneling between states or essentially tunneling through peaks. If the rate of change of the transverse field is slow enough, the system stays close to the ground state of the instantaneous Hamiltonian (also see adiabatic quantum computation).[6] If the rate of change of the transverse field is accelerated, the system may leave the ground state temporarily but produce a higher likelihood of concluding in the ground state of the final problem Hamiltonian, i.e., Diabatic quantum computation.[7][8] The transverse field is finally switched off, and the system is expected to have reached the ground state of the classical Ising model that corresponds to the solution to the original optimization problem. An experimental demonstration of the success of quantum annealing for random magnets was reported immediately after the initial theoretical proposal.[9] Quantum annealing has also been proven to provide a fast Grover oracle for the square-root speedup in solving many NP-complete problems.[10]
Comparison to Simulated Annealing
Quantum annealing can be compared to simulated annealing, whose "temperature" parameter plays a similar role to QA's tunneling field strength. In simulated annealing, the temperature determines the probability of moving to a state of higher "energy" from a single current state. In quantum annealing, the strength of transverse field determines the quantum-mechanical probability to change the amplitudes of all states in parallel. Analytical[11] and numerical[12] evidence suggests that quantum annealing outperforms simulated annealing under certain conditions (see[13] for a careful analysis, and,[14] for a fully solvable model of quantum annealing to arbitrary target Hamiltonian and comparison of different computation approaches).
Quantum mechanics: analogy and advantage
The tunneling field is basically a kinetic energy term that does not commute with the classical potential energy part of the original glass. The whole process can be simulated in a computer using quantum Monte Carlo (or other stochastic technique), and thus obtain a heuristic algorithm for finding the ground state of the classical glass.
In the case of annealing a purely mathematical objective function, one may consider the variables in the problem to be classical degrees of freedom, and the cost functions to be the potential energy function (classical Hamiltonian). Then a suitable term consisting of non-commuting variable(s) (i.e. variables that have non-zero commutator with the variables of the original mathematical problem) has to be introduced artificially in the Hamiltonian to play the role of the tunneling field (kinetic part). Then one may carry out the simulation with the quantum Hamiltonian thus constructed (the original function + non-commuting part) just as described above. Here, there is a choice in selecting the non-commuting term and the efficiency of annealing may depend on that.
It has been demonstrated experimentally as well as theoretically, that quantum annealing can indeed outperform thermal annealing (simulated annealing) in certain cases, especially where the potential energy (cost) landscape consists of very high but thin barriers surrounding shallow local minima.[15] Since thermal transition probabilities (proportional to , with the temperature and the Boltzmann constant) depend only on the height of the barriers, for very high barriers, it is extremely difficult for thermal fluctuations to get the system out from such local minima. However, as argued earlier in 1989 by Ray, Chakrabarti & Chakrabarti,[1] the quantum tunneling probability through the same barrier (considered in isolation) depends not only on the height of the barrier, but also on its width and is approximately given by , where is the tunneling field.[16] This additional handle through the width , in presence of quantum tunneling, can be of major help: If the barriers are thin enough (i.e. ), quantum fluctuations can surely bring the system out of the shallow local minima. For an -spin glass, the barrier height becomes of order . For constant value of one gets proportional to for the annealing time (instead of proportional to for thermal annealing), while can even become -independent for cases where decreases as .[17][18]
It is speculated that in a quantum computer, such simulations would be much more efficient and exact than that done in a classical computer, because it can perform the tunneling directly, rather than needing to add it by hand. Moreover, it may be able to do this without the tight error controls needed to harness the quantum entanglement used in more traditional quantum algorithms. Some confirmation of this is found in exactly solvable models.[19][20]
Timeline of ideas related to quantum annealing in Ising spin glasses:
1989 Idea was presented that quantum fluctuations could help explore rugged energy landscapes of the classical Ising spin glasses by escaping from local minima (having tall but thin barriers) using tunneling;[1]
1998 Formulation of quantum annealing and numerical test demonstrating its advantages in Ising glass systems;[4]
1999 First experimental demonstration of quantum annealing in LiHoYF Ising glass magnets;[21]
2011 Superconducting-circuit quantum annealing machine built and marketed by D-Wave Systems.[22]
In 2011, D-Wave Systems announced the first commercial quantum annealer on the market by the name D-Wave One and published a paper in Nature on its performance.[22] The company claims this system uses a 128 qubit processor chipset.[23] On May 25, 2011, D-Wave announced that Lockheed Martin Corporation entered into an agreement to purchase a D-Wave One system.[24] On October 28, 2011 USC's Information Sciences Institute took delivery of Lockheed's D-Wave One.
In May 2013 it was announced that a consortium of Google, NASA Ames and the non-profit Universities Space Research Association purchased an adiabatic quantum computer from D-Wave Systems with 512 qubits.[25][26] An extensive study of its performance as quantum annealer, compared to some classical annealing algorithms, is already available.[27]
In June 2014, D-Wave announced a new quantum applications ecosystem with computational finance firm 1QB Information Technologies (1QBit) and cancer research group DNA-SEQ to focus on solving real-world problems with quantum hardware.[28] As the first company dedicated to producing software applications for commercially available quantum computers, 1QBit's research and development arm has focused on D-Wave's quantum annealing processors and has successfully demonstrated that these processors are suitable for solving real-world applications.[29]
With demonstrations of entanglement published,[30] the question of whether or not the D-Wave machine can demonstrate quantum speedup over all classical computers remains unanswered. A study published in Science in June 2014, described as "likely the most thorough and precise study that has been done on the performance of the D-Wave machine"[31] and "the fairest comparison yet", attempted to define and measure quantum speedup. Several definitions were put forward as some may be unverifiable by empirical tests, while others, though falsified, would nonetheless allow for the existence of performance advantages. The study found that the D-Wave chip "produced no quantum speedup" and did not rule out the possibility in future tests.[32] The researchers, led by Matthias Troyer at the Swiss Federal Institute of Technology, found "no quantum speedup" across the entire range of their tests, and only inconclusive results when looking at subsets of the tests. Their work illustrated "the subtle nature of the quantum speedup question". Further work[33] has advanced understanding of these test metrics and their reliance on equilibrated systems, thereby missing any signatures of advantage due to quantum dynamics.
There are many open questions regarding quantum speedup. The ETH reference in the previous section is just for one class of benchmark problems. Potentially there may be other classes of problems where quantum speedup might occur. Researchers at Google, LANL, USC, Texas A&M, and D-Wave are working to find such problem classes.[34]
D-Wave's architecture differs from traditional quantum computers. It is not known to be polynomially equivalent to a universal quantum computer and, in particular, cannot execute Shor's algorithm because Shor's algorithm is not a hillclimbing process.[citation needed] Shor's algorithm requires a universal quantum computer. During the Qubits 2021 conference held by D-Wave, it was announced[36] that the company is developing their first universal quantum computers, capable of running Shor's algorithm in addition to other gate-model algorithms such as QAOA and VQE.
"A cross-disciplinary introduction to quantum annealing-based algorithms" [37] presents an introduction to combinatorial optimization (NP-hard) problems, the general structure of quantum annealing-based algorithms and two examples of this kind of algorithms for solving instances of the max-SAT and Minimum Multicut problems, together with an overview of the quantum annealing systems manufactured by D-Wave Systems. Hybrid quantum-classic algorithms for large-scale discrete-continuous optimization problems were reported to illustrate the quantum advantage.[38][39]
^Apolloni, Bruno; Cesa-Bianchi, Nicolo; De Falco, Diego (July 1988). "A numerical implementation of quantum annealing". Stochastic Processes, Physics and Geometry, Proceedings of the Ascona-Locarno Conference.
^Smelyanskiy, Vadim N.; Rieffel, Eleanor G.; Knysh, Sergey I.; Williams, Colin P.; Johnson, Mark W.; Thom, Murray C.; Macready, William G.; Pudenz, Kristen L. (2012). "A Near-Term Quantum Computing Approach for Hard Computational Problems in Space Exploration". arXiv:1204.2821 [quant-ph].
^Steiger, Damian; Heim, Bettina; Rønnow, Troels; Troyer, Matthias (October 22, 2015). "Performance of quantum annealing hardware". In Huckridge, David A.; Ebert, Reinhard; Gruneisen, Mark T.; Dusek, Miloslav; Rarity, John G. (eds.). Electro-Optical and Infrared Systems: Technology and Applications XII; and Quantum Information Science and Technology. Vol. 9648. p. 964816. Bibcode:2015SPIE.9648E..16S. doi:10.1117/12.2202661. S2CID57916974.
Li, Fuxiang; Chernyak, V. Y.; Sinitsyn, N. A. (2013). "Quantum Annealing and Computation: A Brief Documentary Note". Science and Culture. 79: 485–500. arXiv:1310.1339. Bibcode:2013arXiv1310.1339G..
Suzuki, S.; Inoue, J.-I. & Chakrabarti, B. K. (2013). "Chapter 8 on Quantum Annealing". Quantum Ising Phases & Transitions in Transverse Ising Models (2nd ed.). Heidelberg: Springer. ISBN978-3-64233-038-4.
Monumen peringatan Avro Anson RI-003 di Gadut, Tilatang Kamang, Agam, Sumatera Barat (0°16′18″S 100°22′03″E / 0.2717868°S 100.3675655°E / -0.2717868; 100.3675655) Avro Anson RI-003 adalah sebuah pesawat terbang multifungsi bermesin ganda keluaran Inggris, yang merupakan pesawat terbang ketiga yang dimiliki oleh pemerintah Republik Indonesia.[1] Pesawat Avro Anson tersebut dibeli pada awal bulan Desember 1947, diberi nomor register RI-003, dan digunakan…
Municipality in Southern, BrazilRibeirão ClaroMunicipalityCountry BrazilRegionSouthernStateParanáMesoregionNorte Pioneiro ParanaensePopulation (2020 [1]) • Total10,645Time zoneUTC−3 (BRT) Ribeirão Claro is a municipality in the state of Paraná in the Southern Region of Brazil.[2][3][4][5] See also List of municipalities in Paraná References ^ IBGE 2020 ^ Divisão Territorial do Brasil (in Portuguese). Divisão Territorial d…
لمعانٍ أخرى، طالع نيكولا يوفانوفيتش (توضيح). نيكولا يوفانوفيتش معلومات شخصية الميلاد 18 سبتمبر 1952 (العمر 71 سنة)ستنيي الطول 6 قدم 3 بوصة (1.91 م) مركز اللعب مدافع الجنسية يوغوسلافيا الجبل الأسود المسيرة الاحترافية1 سنوات فريق م. (هـ.) 1972–1975 بودوتشنوست بودغوريت…
Ekolog NMFS SE Panama City Laboratory mengambil sampel darah hiu di Teluk Meksiko. National Marine Fisheries Service (NMFS) adalah badan federal Amerika Serikat yang bertugas menataguna dan memanajemen sumber daya laut hidup dan habitatnya di Zona Ekonomi Eksklusif Amerika Serikat, yang membentang 200 mil laut dari garis pantai (sekitar 370 kilometer). Dengan menggunakan alat yang disediakan oleh Magnuson-Stevens Fishery Conservation and Management Act, NMFS menilai dan memprediksi status persed…
Artikel ini membutuhkan judul dalam bahasa Indonesia yang sepadan dengan judul aslinya. Sebuah B-17 Flying Fortress AS diserang oleh bom-bom yang dijatuhkan oleh penerbang pengebom yang terbang di atasnya Friendly fire adalah sebuah serangan oleh sebuah pasukan militer terhadap pasukan sendiri, non-musuh, sekutu atau netral, yang disangka target saat pertikaian, atau karena ketidakakuratan atau kesalahan. Tembakan yang tidak ditujukan untuk menyerang musuh, dan tembakan terhadap pasukan sendiri …
Эта статья — о городе Косовска-Митровица в целом. О его сербской части см. Северная Косовска-Митровица. ГородКосовска-Митровицасерб. Косовска Митровица, алб. Mitrovica Герб 42°53′ с. ш. 20°52′ в. д.HGЯO Страна Республика Косово/ Сербия[1] Округ Косовс…
Cette cathédrale n’est pas la seule cathédrale Notre-Dame. CathédraleNotre-Dame de Luxembourg Cathédrale de Luxembourg avec, à gauche, le bâtiment de l'ancien collège Présentation Nom local Kathedral Notre-Dame vu Lëtzebuerg Culte catholique Dédicataire Vierge Marie Type Église cathédrale Rattachement Archidiocèse de Luxembourg Début de la construction 1613 Fin des travaux 1938 (Agrandissement) Architecte Jean Du Blocq, Hubert Schumacher Style dominant baroque tardif Site web sit…
UFC mixed martial arts event in 2021 UFC on ABC: Vettori vs. HollandThe poster for UFC on ABC: Vettori vs. HollandInformationPromotionUltimate Fighting ChampionshipDateApril 10, 2021 (2021-04-10)VenueUFC ApexCityEnterprise, Nevada, United StatesAttendanceNone (behind closed doors)[1]Event chronology UFC 260: Miocic vs. Ngannou 2 UFC on ABC: Vettori vs. Holland UFC on ESPN: Whittaker vs. Gastelum UFC on ABC: Vettori vs. Holland (also known as UFC on ABC 2 and UFC Vegas 23) …
Arabic-language feed of Cartoon Network EMEA Television channel Cartoon Network Arabic كرتون نتورك بالعربيةCountryIraqUnited Arab EmiratesEgyptSaudi ArabiaBroadcast areaArab WorldHeadquartersGreat Marlborough Street, London, United Kingdom (Turner Broadcasting System EMEA)Dubai Media City, United Arab Emirates (Turner Broadcasting System Arabia FZ-LLC)ProgrammingLanguage(s)ArabicEnglishPicture format1080i HDTVTimeshift serviceCartoon Network Arabic +2 (defunct as of 2016)Owners…
National road in Bangladesh This article may require cleanup to meet Wikipedia's quality standards. No cleanup reason has been specified. Please help improve this article if you can. (May 2011) (Learn how and when to remove this message) Part of a series onTransport in Bangladesh Modes Rail Lines Station Trains Roads Boat Aviation History Airlines Air Astra Biman Bangladesh Fly Dhaka Airlines Novoair US-Bangla Airlines South Asian Airlines Bismillah Airlines Easy Fly Express SkyAir Airports Bari…
Cet article est une ébauche concernant l’histoire et un homme politique français. Vous pouvez partager vos connaissances en l’améliorant (comment ?) selon les recommandations des projets correspondants. Louis Grivart Louis Grivart photographié par Jean Nicolas Truchelut. Fonctions Sénateur français 30 janvier 1876 – 4 août 1901(25 ans, 6 mois et 5 jours) Élection 30 janvier 1876 Réélection 5 janvier 18795 janvier 18885 janvier 1897 Circonscription Ille-et-Vila…
Catedral de Nuestra Señora de la Inmaculada Concepción Catedral de Nossa Senhora da Imaculada Conceição patrimonio de influencia portuguesa Vista de la CatedralLocalizaciónPaís MozambiqueImperio portuguésDivisión Distrito Urbano de KaMpfumoDirección Maputo MozambiqueCoordenadas 25°58′08″S 32°34′30″E / -25.969, 32.575Información religiosaCulto Iglesia católicaDiócesis Arquidiócesis de MaputoPropietario Arquidiócesis de MaputoAdvocación Virgen MaríaHi…
Government complex in Houston Harris County, Texas jails701 Jail, one of the jails in the complexLocationHouston, Texas, United StatesGoverning bodyHarris County Sheriff's Office The government of Harris County, Texas maintains its main jail complex in Downtown Houston, Texas. The complex, operated by the Harris County Sheriff's Office (HCSO), lies in the peninsula formed by the Buffalo Bayou in northern Downtown. While most of the complex is based on county jails serving Harris County, Joe…
Role of the trombone in jazz music Craig Harris playing trombone The trombone is a musical instrument from the brass instrument family. Trombone's first premiere in jazz was with Dixieland jazz as a supporting role within the Dixie Group. This role later grew into the spotlight as players such as J.J. Johnson and Jack Teagarden began to experiment more with the instrument, finding that it can fill in roles along with the saxophone and trumpet in bebop. The trombone has since grown to be featured…
For the character as portrayed in literature, see James Bond (literary character). Fictional character James BondJames Bond characterThe gun barrel sequence from the Eon Productions film Dr. No (1962)First appearanceDr. No (1962)Created byIan FlemingPortrayed by Sean Connery (1962–1967, 1971, 1983) David Niven (1967) George Lazenby (1969) Roger Moore (1973–1985) Timothy Dalton (1987–1989) Pierce Brosnan (1995–2002) Daniel Craig (2006–2021) In-universe informationAlias007TitleCommander …
أوسامو شيمومورا (باليابانية: 下村脩) أوسامو شيمومورا خلال مؤتمر صحفي سنة 2008 في أكاديمية العلوم السويدية معلومات شخصية الميلاد 27 أغسطس 1928 [1][2] فوكوتشياما، كيوتو الوفاة 19 أكتوبر 2018 (90 سنة) ناغاساكي، ناغاساكي سبب الوفاة شيخوخة[3] مواطن…