D N-400 Completed Application Check-Out List Additional: Fill & Download for Free

GGRE scores and other standardized test scores are used by many graduate programs to try to predict applicants’ academic performance. But low GRE scores can be overcome with strong letters of recommendation from professors and employers who know you well, and by strong academic records and a compelling personal statement.The importance of GRE scores depends on the specific field you want to enter, and on specific program requirements. If you are interested in how graduate school admissions committees make decisions, our CEO Gabe Ignatow, who moonlights as a Sociology Professor (just kidding), is answering questions in the forum on TheGradCafe.com under the alias SocProf. He’s also available on Quora, and of course you can reach us via email at [email protected] information on admissions counseling and application help from GradTrek partners is coming soon. In the meantime, check out some of our preferred graduate school counseling resources, including GradTrain and Accepted.com.How to make the best use of GradTrek’s degree search engine.GradTrek degree search uses program interests, location, GPA and test scores (GRE, TOEFL, GMAT) to find the masters degree programs that fit your criteria. The algorithm shows the programs that best matches the search criteria and will give you an idea of where it would be best to apply. Search recommendation results have extensive content aggregation and include useful information like, University pages, Catalogs, Videos, Inside information and Social media links like Facebook, LinkedIn, Professor Ratings. 15 minutes with this free tool can save you days of research on internet.1. Start on a laptop or desktopGradTrek works well on phones/tablets but a desktop or laptop computer is recommended. GradTrek is a powerful piece of software with many features, and everything goes more smoothly when you have more screen space.2. Focus on the Subjects pageThis is the most important page in the survey. We recommend coming back to this page several times to adjust your subject searches. Our database includes over 400 subjects, and many degrees fall into multiple subject categories. Don’t choose a Specific Degree unless absolutely necessary – there are almost a thousand different degree types in our data set. You’re better off choosing either doctoral-level, masters-level, or certificate-level degrees and then choosing subjects. This way you’re likely to find types of degrees that you may not have known about.3. Enter the preferred locationSpecify your choice of school location – options include distance from zipcode, or choose one or more of the States, Regions or entire US.4. Tuition costSpecify the importantance of tuition cost – Very little, Moderately and A great deal. In general, it is better to choose “Very little” on the slider scale and later narrow down the results based on tuition costs data from University pages.5. Test ScoresOptionally, enter your test scores. Gradtrek is probably the only site which uses your GPA and other standardised test scores to match you to University programs.5. The results of your degree searchA list of recommendations sorted by best fit are provided. The GradTrek database has every accredited university in US to make sure we provide a comprehensive list of results. Scroll down the list to find the next best options. The counter on the top updates in real time as you modify the search criteria. This helps in expanding (or narrowing) your criteria to get to manageable list of programs. You can run the survey multiple times, tweaking the search criteria.Program and Degree Details Page – Clicking a program will take you to program details page has extensive content aggregation and includes useful information like, University page, Catalog, Videos, Social media like Facebook, Professor Ratings, and also inside information. You can takes notes using the notes feature and save a program using the “+” sign. A snapshot of the program details page is below.When you reach GradTrek’s results page, whatever you do–don’t stop! You can click on the program to navigate to the degree program page, or on the “+” button to save the program to your profile. From there you can write notes for each program, and your notes will be automatically saved.GRE Graduate School Requirements was last modified: May 18th, 2016 by Sudhir Nayak« An MBA with a 2.8 GPA?An MBA with low GMAT scores? »Standardized Testing Preparation: The TOEFL Contents Introduction...................................................................................................................................................2 Which test should I take?..............................................................................................................................3 Philadelphia Testing Sites and Fees..............................................................................................................3 Creating a TOEFL Study Plan ......................................................................................................................4 General Testing Vocabulary .........................................................................................................................6 General Testing Speaking Practice ...............................................................................................................7 More Advanced Listening Practice...............................................................................................................9 Practice Speaking Prompts .........................................................................................................................10 General Writing Practice.............................................................................................................................11 TOEFL Overview .......................................................................................................................................12 Speaking Tips..............................................................................................................................................12 Reading Sample Question...........................................................................................................................13 TOEFL Writing: Integrated Tasks and Independent Tasks ........................................................................18 Sample TOEFL Writing Questions:............................................................................................................19 Web Resources............................................................................................................................................32 Writing 2 (last updated August 2014) Introduction This packet reviews basic testing strategies for the TOEFL. It is highly recommended to use this packet in a Conversation Partner session, but it can also be used for self-study. Start with general vocabulary, speaking and reading practice for comprehensive language review relevant to multiple tests. Further practice can be found under “Web Resources.” All answers to grammar exercises are included. You will also need headphones and internet access for some of the listening and speaking prompts. The TOEIC and IELTS packets also offer questions that are similar in nature and could be used for additional practice. Writing 3 (last updated August 2014) Which test should I take? I am a non-native speaker applying to… An undergraduate program in the U.S. TOEFL; ACT or SAT TOEFL is more commonly accepted in U.S. universities, although some schools now take the IELTS too. An undergraduate program in the UK, New Zealand, or Australia IELTS and Cambridge English Language Assessment tests As of 2014, the British council is no longer accepting TOEFL or TOEIC scores to obtain UK visas! A graduate program in the U.S. GRE; TOEFL The GRE is the test required for most native and non-native speakers applying to graduate level programs. In addition, non-native speakers may be required to take the TOEFL or IELTS exam. A graduate program in the UK, New Zealand, or Australia Cambridge English Language Assessment As of 2014, the British council is no longer accepting TOEFL or TOEIC scores to obtain UK visas! Business school GMAT; TOEIC The TOEIC is similar to the TOEFL and IELTS, but it specifically tests workplace English. Law school LSAT The LSAT is taken by native and non-native speakers applying to law school. Philadelphia Testing Sites and Fees TOEFL ibt: $180 Test dates usually offered twice a month Prometric Testing Center 601 Walnut Street Curtis Center Suite 150 West United States of America 19106 215-238-8410 https://www.ets.org/toefl/ibt/register/centers_dates/ Writing 4 (last updated August 2014) Creating a TOEFL Study Plan There are a few different ways to study for the test. First, we recommend the following: 1. First, take a full-length practice test to identify areas that are most difficult for you. You may need to study some portions of the test more than others. Plan to take at least one practice test every 1-2 weeks to familiarize yourself with the test format. 2. When taking practice tests, pretend it is a real test. Go to a room with no distractions and if taking a paper-based version of the test, set a timer to follow the exact time allotment of the actual test. 3. We also recommend purchasing your own, up-to-date test prep book (check the publication date!). ETS has many book recommendations, as does Amazon. Although there are a lot of online resources, it’s helpful to have a book that you can write in and highlight. 4. Take at least one “rest day” to read fun things in English that aren’t study materials. Read news articles, watch a movie in English, or try reading a short story or poem (Here’s a local literary magazine with fiction stories and poems: http://www.philadelphiastories.org/) Plan 1: Devote each week to a different portion of the test. Example: Week 1: Speaking Week 2: Listening Week 3: Writing Week 4: Vocabulary (it actually helps to study a little vocabulary each week, since you likely won’t remember words if you memorize them quickly and in large quantities). Plan 2: Combine questions from each section for a daily study plan. Here’s one way you could structure a daily study plan that addresses each section of the test. Daily Plan: Study 1-2 new vocabulary words a day from a TOEFL list (10 per week). Don’t just memorize the definitions; practice using them in actual sentences! Most dictionaries have examples of sentences. Study one listening and one speaking question, and outline or write one practice essay. Take time to review the essay for grammatical issues. If you’ve forgotten a grammar rule, pick up a grammar textbook or go online and do a few practice grammar exercises. Learn one or two new idiomatic or transitional phrases a week. A good list can be found here: http://www.elc.byu.edu/classes/buck/w_garden/classes/buck/transitions.html and here: https://owl.english.purdue.edu/owl/resource/574/02/ Writing 5 (last updated August 2014) Learn one or two Latin and Greek roots a week. These are very helpful because even if you don’t know a word’s definition, you can guess its meaning if you know the root! A good list can be found here: http://www.readingrockets.org/article/40406 and here: http://academic.cuesta.edu/acasupp/as/506.HTM Online Study Plans: http://toeflgoanywhere.org/toefl-practice#whats-your-study-personality Using this website, figure out how you learn best, then download a free study guide. The Magoosh TOEFL blog also has a one-month study plan: http://magoosh.com/toefl/2013/one-monthtoefl-study-schedule/ Do NOT try to study the day before the test. Instead, just try watching a TV show you like in English or reading a short news article to keep yourself immersed in the language. Writing 6 (last updated August 2014) General Testing Vocabulary This page includes vocabulary that is good to study for any standardized test, as well as example sentences that might be used on a test. Affect and effect: How does the globalization of English affect other languages? According to the passage, what are the long-term effects of radiation exposure? Analogy: In the passage above, “a pack of wolves” is an analogy for what? Classification: The Dewey Decimal system is a form of book classification used in libraries. Conclude: What did the researchers conclude at the end of their study? Condition: What conditions must be met for a number to be prime? Connotation: In the passage, fast food has a negative connotation with laziness. Determine: How did scientists determine the origin of the fossils? Discourse: In sentence 5, the phrase “academic discourse” refers to language used in the classroom. Draw conclusions: We can draw conclusions about the author’s emotions based on his word choice. e.g. (for example) Legumes (e.g., beans and lentils) contain healthy fats. Genre: What is the genre of the passage? i.e. (in other words): The recent boycott (i.e., the embargo on imported goods) has slowed business. Impact: According to the argument above, how does pollution impact the fishing industry? Metaphor: In the text, “the lion” is a metaphor for the government. Passage: What can we infer from this passage? Significant: What significant changes does the author propose? Symbol/symbolize: What does the color black symbolize in the passage? Text: What is Smith’s analysis of the text? Tone: Which sentence below proves that the author’s tone is humorous? Valid/Invalid: If a=c, which argument is invalid? Period: In what time period does the story take place? Writing 7 (last updated August 2014) General Testing Speaking Practice For this section, you will need headphones and/or a quiet space and an internet connection. Most of these practice questions use 3-minute TED talks and Upworthy videos. Note that there are a variety of accents: non-native, American, and British. Practice 1: Ariana Huffington: How to succeed? Get more sleep http://www.ted.com/talks/arianna_huffington_how_to_succeed_get_more_sleep Based on what the speaker says in the video, decide if the statements below A: support the speaker’s claims B: do not support the speaker’s claims or C: information is not given. 1. Many people think that sleep deprivation is a sign of being productive and busy. 2. People are making poor decisions because they get too much sleep. 3. Having a high I.Q. means that you’re a good leader. Practice 2: Lee Cronin: Print your own medicine http://www.ted.com/talks/lee_cronin_print_your_own_medicine True or False? The 3-D printer in the talk is being used to print: a. Fabrics b. Beakers and test tubes c. Food How will the 3-D printer make medicine? a. Using special ink that prints molecules b. Using hair samples c. Using a superbug Someday, the 3-D printer will be able to print medicine specific to a person by using: a. That person’s special ink b. That person’s DNA c. That person’s image Writing 8 (last updated August 2014) Practice 3: True or False Lalitesh Katragadda: Making Maps to Fight Disaster, Build Economies http://www.ted.com/talks/lalitesh_katragadda_making_maps_to_fight_disaster_build_economies 1. Only 20% of the world was mapped in 2005. 2. Google Map Maker allows people to map things locally. 3. Maps could help in times of disaster by revealing hospitals and unknown roads. Practice 4: Matching 1. GPS 2. Characteristics of storms 3. Names of storms in 2010 4. Early origins of humanizing storms 5. Sixth sense A. Greek gods B. Alex, Bonnie, Collin C. Service area in 0.5 miles D. Mind reading E. Dangerous and unexpected Writing 9 (last updated August 2014) More Advanced Listening Practice Short Answer Listening Practice 5 Sarah Parcak: Archeology from Space http://www.ted.com/talks/sarah_parcak_archeology_from_space a. In what country was this research conducted? b. What kind of data was used to find an ancient city? c. What did the archeologists find five meters down underneath the mud? d. Who is being trained to use the satellite technology so that they can make discovers? Multiple Choice Listening Practice 6 Robin Nagle: What I discovered in New York City Trash http://www.ted.com/talks/robin_nagle_what_i_discovered_in_new_york_city_trash 1. Who cleans up the trash in New York City? a. Private companies b. Volunteers c. The Department of Sanitation 2. What is one reason that being a sanitation worker a dangerous job? Choose the best answer. a. People throw away too much trash b. Motorists do not pay attention when driving around garbage trucks c. People ignore sanitation workers 3. What does the speaker suggest at the end of the talk? a. Clean up your own trash b. Pay sanitation workers more c. Thank sanitation workers for what they do Answer Key: Practice 1: 1. A 2. B (people are making poor decisions because they are getting too little sleep, not too much) 3. B (The speaker says that having a high I.Q. does not mean you are a good leader) Practice 2: 1. B. Beakers and test tubes 2. A. Using special ink that prints molecules 3. B. that person’s DNA Writing 10 (last updated August 2014) Practice 3: 1. False (15% of the world was not mapped in 2005) 2. True 3. True Practice 4: • A: 4 • B: 3 • C: 1 • D: 5 • E: 2 Practice 5: a. Egypt b. Satellite data (or topography data) c. Pottery d. Young Egyptians Practice 6: 1. C. Department of Sanitation 2. B. Motorists do not pay attention when driving around garbage trucks 3. C. Thank sanitation workers for what they do Practice Speaking Prompts Listen to the video “Hannah Brencher: Love letters to strangers.” http://www.ted.com/talks/hannah_brencher_love_letters_to_strangers Do you ever write letters? For whom do you write them and why? Do you think letters are better than writing emails or texts? Why or why not? Writing 11 (last updated August 2014) General Writing Practice Look at a chart or graph and summarize information from the chart by selecting important features and comparing/contrasting them. Read a statement about a specific topic and provide your opinion on the topic. Provide relevant examples from your own knowledge or experience. Should more money be put into space exploration? Why or why not? Writing 12 (last updated August 2014) TOEFL Overview The TOEFL ibt (internet-based test) is the most common test form used, although some countries still use the pbt (paper-based test). The test has a reading, speaking, listening, and writing section. Reading: 60-80 Minutes (36-56 questions) Listening: 60-90 minutes (34-51 questions) Break (10 minutes) Speaking: 20 minutes (6 tasks) Writing: 50 minutes (2 tasks) Speaking Tips For the speaking portion, you have 60 seconds to prepare and respond to a question. Do not use words that you do not know how to pronounce or properly use in a sentence. You lose points for incorrect pronunciation or wrong usage of idioms and vocabulary words. Note that some questions will require you to read a passage, and some will require you to read a passage and then listen to two people discussing the topic. To practice, set a timer and try answering some basic questions first. Basic structure: 1. State your main opinion or argument 2. Provide 2-3 examples (use details to support your answer) 3. Brief concluding statement As you get more practice, you can move on to the difficult questions. Sample questions 1. Who is an important figure in the history of your country? Explain why he/she is or was important. 2. Air pollution is a huge problem in many big cities. What are three ways that people can lessen pollution in their everyday life? 3. Online courses are becoming popular alternatives to studying in a classroom. Would you prefer to study online or in a class? Provide examples and details to support your answer. 4. Describe a hobby you love. Why is it so important to you? Why does it interest you? Writing 13 (last updated August 2014) Example of a question and answer: Reading books is one of my favorite hobbies because there is always something new and interesting to read. First, reading is important to me because I can learn about new topics that I might not study in school. I can learn about new worlds, cultures, and vocabulary just from reading. Second, I love to read because it reduces my stress. I love to enter a new world and follow the characters in their emotional journey. Third, reading allows me to practice my English and better understand English grammar. In conclusion, I never get bored while I’m reading. There are so many new worlds to explore. Reading Sample Question Despite Protests, Canada Approves Northern Gateway Oil Pipeline By Ian Austin Excerpted from: http://www.nytimes.com/2014/06/18/business/energy-environment/canada-approvesnorthern-gateway-pipeline.html?ref=science&_r=0 1 The Canadian government’s approval of a major pipeline running from the Alberta oil sands to a new port on the coast of British Columbia has intensified opposition from aboriginal groups, environmentalists and community advocates. 4 The Northern Gateway project, which the government approved on Tuesday as expected, would send heavy, oil-bearing bitumen to Asia, giving Canadian producers better access to the world markets. The pipeline, being built by Enbridge, has been championed by the federal government as a way to diversify Canada’s energy industry from its current dependence on exports to the United States. 10 But opponents in British Columbia, who span the political spectrum, threatened to block the pipeline altogether. The fear is that the pipeline would make the province vulnerable to an oil spill, damaging the rugged and scenic coastline. 13 Tom Mulcair, the leader of the opposition New Democratic Party, said that Prime Minister Stephen Harper and his Conservative government had ignored broad public opinion. 16 “Stephen Harper continues to act as if this is 1948,” Mr. Mulcair told reporters outside of the House of Commons. “You can no longer force pipelines from the top down.” Calling oil tankers off the coast of British Columbia “madness,” Mr. Mulcair said that the decision was a “severe threat to social order, social peace.” Writing 14 (last updated August 2014) 20 In the statement, Greg Rickford, the minister of natural resources, acknowledged that Enbridge’s efforts to win over British Columbia and native groups had fallen short. “The proponent clearly has more work to do in order to fulfill the public commitment it has made to engage with aboriginal groups and local communities.” 25 The president and chief of Enbridge, Al Monaco, seemed to agree during a conference call with reporters. “The economic benefits are not enough to secure public support,” he said. 28 The company must meet about 100 conditions imposed by the regulator before construction begins. Mr. Monaco declined to say how long that would delay construction, but he suggested at one point that it would take at least four years. 31 The most pressing problem is addressing the concerns of the native Canadian tribes. About a decade ago, the Supreme Court of Canada ruled that such native groups must be consulted and accommodated about projects that cross their land. The definition of both terms remains fuzzy, but most legal experts say that the native groups do not have a veto. 36 Still, such groups are preparing for a fight. Art Sterritt, the executive director of Coastal First Nations, an alliance of nine native groups opposed to the pipeline, said his organization would take legal action and form political alliances to block the project. On Monday, the Coastal First Nations formed a group with Unifor, formerly the Canadian Auto Workers union, and several environmental groups to quash the project. 42 The main issue for his members, Mr. Sterritt said, was the oil industry’s inability to demonstrate that it could effectively clean up coastal oil spills. If legal and political challenges are ultimately unsuccessful, Mr. Sterritt added, “our people will be out there stopping the bulldozers.” 1. The word “championed” in line 7 is closest in meaning to: a. Won b. Supported c. Competed d. Agreed 2. In paragraph 9, why does the author include that the native groups must be consulted and accommodated? a. To support the claim that environmentalists fear oil spills b. To support the economic benefits of the pipeline c. To explain why aboriginal groups have a stake in the discussion d. To explain why aboriginal groups are powerless Writing 15 (last updated August 2014) 3. Which of the following can be inferred from paragraph 2 about the federal government’s support of the pipeline? a. The pipeline has full support b. The pipeline will be built quickly with the help of the Northern Gateway project c. Lessening U.S. imports will strengthen the Canadian economy d. The Asian oil market is failing 4. According to paragraph 3, who opposes the construction of the pipeline? a. Aboriginal groups b. Politicians c. Various stakeholders d. The Northern Gateway project 5. The word “spectrum” on line 10 is closest in meaning to: a. Range b. Diversity c. Level d. Ratio 6. The word “pressing” on line 31 is closest in meaning to: a. Forceful b. Desperate c. Urgent d. Complex 7. According to paragraph 2, all of the following phrases are true EXCEPT: a. Canada will now have access to Asian oil markets. b. The Canadian government wants to diversify its energy industry. c. The energy industry will stop exporting to the U.S. d. Enridge will be building the pipeline. 8. The phrase “from the top down” on lines 17 and 18 is closest in meaning to: a. Power relationships that move from the weakest to the strongest group b. Lying face-down c. Analyzing in detail d. Power relationships that move from the strongest to the weakest group 9. The word “fuzzy” on line 34 is closest in meaning to: a. Furry b. Unclear c. Mysterious d. Diverging Writing 16 (last updated August 2014) 10. Paragraph 5 supports which of the following statements? a. Building the pipeline could lead to an oil spill. b. The decision-making process used to approve the pipeline is antiquated. c. The pipeline must be approved from the top down. d. Oil tankers off the coast of British Columbia are angry. 11. Which of the sentences below best expresses the essential information in the following sentence? The definition of both terms remains fuzzy, but most legal experts say that the native groups do not have a veto. Incorrect choices change the meaning in important ways or leave out essential information. a. Although legal experts agree that native groups cannot overturn the decision, their other rights are clear. b. The native groups’ rights are weak, but the native groups have legal rights. c. The native groups’ rights are in disagreement, but the majority of legal experts agree that no one can oppose the vote. d. The native groups’ rights remain unclear, but most legal experts agree that the native group cannot vote against the decision. 12. According to the passage, who is opposed to the pipeline for environmental reasons? a. Al Monaco b. Greg Rickford c. Steven Harper d. Art Sterritt 13. Look at the four letters (A, B, C, and D) that indicate where the following sentence could be added to the passage in paragraph 6. If the environment were harmed, this could reduce tourism to the region and also affect wildlife habitats. Where would the sentence best fit? (A)But opponents in British Columbia, who span the political spectrum, threatened to block the pipeline altogether. (B) The fear is that the pipeline would make the province vulnerable to an oil spill, damaging the rugged and scenic coastline. (C) Tom Mulcair, the leader of the opposition New Democratic Party, said that Prime Minister Stephen Harper and his Conservative government had ignored broad public opinion. (D) Choose the place where the sentence fits best. a. Option A b. Option B c. Option C d. Option D Writing 17 (last updated August 2014) 14. An introductory sentence for a brief summary of the passage is provided below. Complete the summary by selecting the THREE answer choices that express the most important ideas in the passage. Some sentences do not belong in the summary because they express ideas that are not presented in the passage or are minor ideas in the passage. This question is worth 2 points. Write your answer choices in the spaces where they belong. You can write in the number of the answer choice or the whole sentence. A pipeline through Canada has been approved by the federal government, but faces opposition from environmentalists, aboriginal groups, and local communities. • • • Answer choices (1) The government has elected to open up its world market by expanding exports to Asia, which will lessen its reliance on the U.S. for business. (2) Aboriginal communities have a stake in the decision, although the exact outcome is still unclear. (3) Local groups will be out there stopping bulldozers if the pipeline is built. (4) Aboriginal groups have a right to accommodations if certain projects cross their land. (5) Environmental groups fear that oil spills and damage to the landscape could result from the pipeline construction. (6) Enbridge and Northern Gateway Project were both approved by the government. Writing 18 (last updated August 2014) TOEFL Writing: Integrated Tasks and Independent Tasks Integrated tasks ask you to summarize and compare/contrast information. Learn paraphrasing skills to master these questions. You will have three minutes to read an academic text. Then you will listen to a lecture on the same topic. Take notes while you listen. Independent tasks ask you to form your own opinions and evidence in response to a single question. General Tips: 1. For note-taking, it’s okay to abbreviate words so that you can write faster. Focus on keywords, not whole sentences. Some note-taking shortcuts: = equal to ex. Example > greater than b/n between

Quantum computing is computing using quantum-mechanical phenomena, such as superposition and entanglement.[1]A quantum computer is a device that performs quantum computing. Such a computer is different from binary digital electronic computers based on transistors. Whereas common digital computing requires that the data be encoded into binary digits (bits), each of which is always in one of two definite states (0 or 1), quantum computation uses quantum bits or qubits, which can be in superpositions of states. A quantum Turing machine is a theoretical model of such a computer and is also known as the universal quantum computer. The field of quantum computing was initiated by the work of Paul Benioff[2]and Yuri Manin in 1980,[3]Richard Feynman in 1982,[4]and David Deutsch in 1985.[5]As of 2018, the development of actual quantum computers is still in its infancy, but experiments have been carried out in which quantum computational operations were executed on a very small number of quantum bits.[6]Both practical and theoretical research continues, and many national governments and military agencies are funding quantum computing research in additional effort to develop quantum computers for civilian, business, trade, environmental and national security purposes, such as cryptanalysis.[7]Noisy devices with a small number of qubits have been developed by a number of companies, including IBM, Intel, and Google.[8]IBM has made 5-qubit and 16-qubit quantum computing devices available to the public for experiments via the cloud on the IBM Q Experience. D-Wave Systems has been developing their own version of a quantum computer that uses annealing.[9]Large-scale quantum computers would theoretically be able to solve certain problems much more quickly than any classical computers that use even the best currently known algorithms, like integer factorization using Shor's algorithm (which is a quantum algorithm) and the simulation of quantum many-body systems. There exist quantum algorithms, such as Simon's algorithm, that run faster than any possible probabilistic classical algorithm.[10]A classical computer could in principle (with exponential resources) simulate a quantum algorithm, as quantum computation does not violate the Church–Turing thesis.[11]:202On the other hand, quantum computers may be able to efficiently solve problems which are not practically feasible on classical computers.Contents1Basics2Principles of operation3Operation4Potential4.1Cryptography4.2Quantum search4.3Quantum simulation4.4Quantum annealing and adiabatic optimisation4.5Solving linear equations4.6Quantum supremacy5Obstacles5.1Quantum decoherence6Developments6.1Quantum computing models6.2Physical realizations6.3Timeline7Relation to computational complexity theory8See also9References10Further reading11External linksBasics[edit]A classical computer has a memory made up of bits, where each bit is represented by either a one or a zero. A quantum computer, on the other hand, maintains a sequence of qubits, which can represent a one, a zero, or any quantum superposition of those two qubit states;[11]:13–16a pair of qubits can be in any quantum superposition of 4 states,[11]:16and three qubits in any superposition of 8 states. In general, a quantum computer with [math]{\displaystyle n}[/math] qubits can be in an arbitrary superposition of up to [math]{\displaystyle 2^{n}}[/math] different states simultaneously.[11]:17(This compares to a normal computer that can only be in one of these [math]{\displaystyle 2^{n}}[/math] states at any one time).A quantum computer operates on its qubits using quantum gates and measurement (which also alters the observed state). An algorithm is composed of a fixed sequence of quantum logic gates and a problem is encoded by setting the initial values of the qubits, similar to how a classical computer works. The calculation usually ends with a measurement, collapsing the system of qubits into one of the [math]{\displaystyle 2^{n}}[/math] eigenstates, where each qubit is zero or one, decomposing into a classical state. The outcome can, therefore, be at most [math]{\displaystyle n}[/math] classical bits of information (or, if the algorithm did not end with a measurement, the result is an unobserved quantum state).Quantum algorithms are often probabilistic, in that they provide the correct solution only with a certain known probability.[12]Note that the term non-deterministic computing must not be used in that case to mean probabilistic (computing) because the term non-deterministic has a different meaning in computer science.An example of an implementation of qubits of a quantum computer could start with the use of particles with two spin states: "down" and "up" (typically written [math]{\displaystyle |{\downarrow }\rangle }[/math] and [math]{\displaystyle |{\uparrow }\rangle }[/math], or [math]{\displaystyle |0{\rangle }}[/math] and [math]{\displaystyle |1{\rangle }}[/math]). This is true because any such system can be mapped onto an effective spin-1/2 system.Principles of operation[edit]This section includes a list of references, but its sources remain unclear because it has insufficient inline citations.Please help to improve this section by introducing more precise citations.(February 2018)(Learn how and when to remove this template message)A quantum computer with a given number of qubits is fundamentally different from a classical computer composed of the same number of classical bits. For example, representing the state of an n-qubit system on a classical computer requires the storage of 2ncomplex coefficients, while to characterize the state of a classical n-bit system it is sufficient to provide the values of the n bits, that is, only n numbers. Although this fact may seem to indicate that qubits can hold exponentially more information than their classical counterparts, care must be taken not to overlook the fact that the qubits are only in a probabilistic superposition of all of their states. This means that when the final state of the qubits is measured, they will only be found in one of the possible configurations they were in before the measurement. It is generally incorrect to think of a system of qubits as being in one particular state before the measurement. Since the fact that they were in a superposition of states before the measurement was made directly affects the possible outcomes of the computation.Qubits are made up of controlled particles and the means of control (e.g. devices that trap particles and switch them from one state to another).[13]To better understand this point, consider a classical computer that operates on a three-bit register. If the exact state of the register at a given time is not known, it can be described as a probability distribution over the [math]{\displaystyle 2^{3}=8}[/math] different three-bit strings000, 001, 010, 011, 100, 101, 110,and111. If there is no uncertainty over its state, then it is in exactly one of these states with probability 1. However, if it is a probabilistic computer, then there is a possibility of it being in any one of a number of different states.The state of a three-qubit quantum computer is similarly described by an eight-dimensional vector [math]{\displaystyle (a_{0},a_{1},a_{2},a_{3},a_{4},a_{5},a_{6},a_{7})}[/math](or a one dimensional vector with each vector node holding the amplitude and the state as the bit string of qubits). Here, however, the coefficients [math]{\displaystyle a_{i}}[/math] are complex numbers, and it is the sum of the squares of the coefficients' absolute values, [math]{\displaystyle \sum _{i}|a_{i}|^{2}}[/math], that must equal 1. For each [math]{\displaystyle i}[/math], the absolute value squared [math]{\displaystyle \left|a_{i}\right|^{2}}[/math] gives the probability of the system being found in the [math]{\displaystyle i}[/math]-th state after a measurement. However, because a complex number encodes not just a magnitude but also a direction in the complex plane, the phase difference between any two coefficients (states) represents a meaningful parameter. This is a fundamental difference between quantum computing and probabilistic classical computing.[14]If you measure the three qubits, you will observe a three-bit string. The probability of measuring a given string is the squared magnitude of that string's coefficient (i.e., the probability of measuring000= [math]{\displaystyle |a_{0}|^{2}}[/math], the probability of measuring001= [math]{\displaystyle |a_{1}|^{2}}[/math], etc.). Thus, measuring a quantum state described by complex coefficients [math]{\displaystyle (a_{0},a_{1},a_{2},a_{3},a_{4},a_{5},a_{6},a_{7})}[/math] gives the classical probability distribution [math]{\displaystyle (|a_{0}|^{2},|a_{1}|^{2},|a_{2}|^{2},|a_{3}|^{2},|a_{4}|^{2},|a_{5}|^{2},|a_{6}|^{2},|a_{7}|^{2})}[/math] and we say that the quantum state "collapses" to a classical state as a result of making the measurement.An eight-dimensional vector can be specified in many different ways depending on what basis is chosen for the space. The basis of bit strings (e.g.,000,001, …,111) is known as the computational basis. Other possible bases are unit-length, orthogonal vectors and the eigenvectors of the Pauli-x operator. Ket notation is often used to make the choice of basis explicit. For example, the state [math]{\displaystyle (a_{0},a_{1},a_{2},a_{3},a_{4},a_{5},a_{6},a_{7})}[/math] in the computational basis can be written as:[math]{\displaystyle a_{0}\,|000\rangle +a_{1}\,|001\rangle +a_{2}\,|010\rangle +a_{3}\,|011\rangle +a_{4}\,|100\rangle +a_{5}\,|101\rangle +a_{6}\,|110\rangle +a_{7}\,|111\rangle }[/math]where, e.g., [math]{\displaystyle |010\rangle =\left(0,0,1,0,0,0,0,0\right)}[/math]The computational basis for a single qubit (two dimensions) is [math]{\displaystyle |0\rangle =\left(1,0\right)}[/math] and [math]{\displaystyle |1\rangle =\left(0,1\right)}[/math].Using the eigenvectors of the Pauli-x operator, a single qubit is [math]{\displaystyle |+\rangle ={\tfrac {1}{\sqrt {2}}}\left(1,1\right)}[/math] and [math]{\displaystyle |-\rangle ={\tfrac {1}{\sqrt {2}}}\left(1,-1\right)}[/math].Operation[edit]This section does not cite any sources. Please help improve this section by adding citations to reliable sources. Unsourced material may be challenged and removed.(February 2018)(Learn how and when to remove this template message)Unsolved problem in physics:Is a universal quantum computer sufficient to efficiently simulate an arbitrary physical system?(more unsolved problems in physics)While a classical 3-bit state and a quantum 3-qubit state are each eight-dimensional vectors, they are manipulated quite differently for classical or quantum computation. For computing in either case, the system must be initialized, for example into the all-zeros string, [math]{\displaystyle |000\rangle }[/math], corresponding to the vector (1,0,0,0,0,0,0,0). In classical randomized computation, the system evolves according to the application of stochastic matrices, which preserve that the probabilities add up to one (i.e., preserve the L1 norm). In quantum computation, on the other hand, allowed operations are unitary matrices, which are effectively rotations (they preserve that the sum of the squares add up to one, the Euclidean or L2 norm). (Exactly what unitaries can be applied depend on the physics of the quantum device.) Consequently, since rotations can be undone by rotating backward, quantum computations are reversible. (Technically, quantum operations can be probabilistic combinations of unitaries, so quantum computation really does generalize classical computation. See quantum circuit for a more precise formulation.)Finally, upon termination of the algorithm, the result needs to be read off. In the case of a classical computer, we sample from the probability distribution on the three-bit register to obtain one definite three-bit string, say 000. Quantum mechanically, one measures the three-qubit state, which is equivalent to collapsing the quantum state down to a classical distribution (with the coefficients in the classical state being the squared magnitudes of the coefficients for the quantum state, as described above), followed by sampling from that distribution. This destroys the original quantum state. Many algorithms will only give the correct answer with a certain probability. However, by repeatedly initializing, running and measuring the quantum computer's results, the probability of getting the correct answer can be increased. In contrast, counterfactual quantum computation allows the correct answer to be inferred when the quantum computer is not actually running in a technical sense, though earlier initialization and frequent measurements are part of the counterfactual computation protocol.For more details on the sequences of operations used for various quantum algorithms, see universal quantum computer, Shor's algorithm, Grover's algorithm, Deutsch–Jozsa algorithm, amplitude amplification, quantum Fourier transform, quantum gate, quantum adiabatic algorithm and quantum error correction.Potential[edit]Cryptography[edit]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 few prime numbers (e.g., products of two 300-digit primes).[15]By comparison, a quantum computer could efficiently solve this problem using Shor's algorithm to find its factors. This ability would allow a quantum computer to break many of the cryptographic systems in use today, in the sense that there would be a polynomial time (in the number of digits of the integer) algorithm for solving the problem. In particular, most of the popular public key ciphers are based on the difficulty of factoring integers or the discrete logarithm problem, both of which can be solved by Shor's algorithm. In particular, the RSA, Diffie–Hellman, and elliptic curve Diffie–Hellman algorithms could be broken. These are used to protect secure Web pages, encrypted email, and many other types of data. Breaking these would have significant ramifications for electronic privacy and security.However, other cryptographic algorithms do not appear to be broken by those algorithms.[16][17]Some public-key algorithms are based on problems other than the integer factorization and discrete logarithm problems to which Shor's algorithm applies, like the McEliece cryptosystem based on a problem in coding theory.[16][18]Lattice-based cryptosystems are also not known to be broken by quantum computers, and finding a polynomial time algorithm for solving the dihedral hidden subgroup problem, which would break many lattice based cryptosystems, is a well-studied open problem.[19]It has been proven that applying Grover's algorithm to break a symmetric (secret key) algorithm by brute force requires time equal to roughly 2n/2invocations of the underlying cryptographic algorithm, compared with roughly 2nin the classical case,[20]meaning that symmetric key lengths are effectively halved: AES-256 would have the same security against an attack using Grover's algorithm that AES-128 has against classical brute-force search (see Key size). 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.[21]Quantum search[edit]Besides factorization and discrete logarithms, quantum algorithms offering a more than polynomial speedup over the best known classical algorithm have been found for several problems,[22]including the simulation of quantum physical processes from chemistry and solid state physics, the approximation of Jones polynomials, and solving Pell's equation. No mathematical proof has been found that shows that an equally fast classical algorithm cannot be discovered, although this is considered unlikely.[23]For some problems, quantum computers offer a polynomial speedup. The most well-known example of this is quantum database search, which can be solved by Grover's algorithm using quadratically fewer queries to the database than that are required by classical algorithms. In this case, the advantage is not only provable but also optimal, it has been shown that Grover's algorithm gives the maximal possible probability of finding the desired element for any number of oracle lookups. Several other examples of provable quantum speedups for query problems have subsequently been discovered, such as for finding collisions in two-to-one functions and evaluating NAND trees.Problems that can be addressed with Grover's algorithm have the following properties:There is no searchable structure in the collection of possible answers,The number of possible answers to check is the same as the number of inputs to the algorithm, andThere exists a boolean function which evaluates each input and determines whether it is the correct answerFor problems with all these properties, the running time of Grover's algorithm on a quantum computer will scale as the square root of the number of inputs (or elements in the database), as opposed to the linear scaling of classical algorithms. A general class of problems to which Grover's algorithm can be applied[24]is Boolean satisfiability problem. In this instance, the database through which the algorithm is iterating is that of all possible answers. An example (and possible) application of this is a password cracker that attempts to guess the password or secret key for an encrypted file or system. Symmetric ciphers such as Triple DES and AES are particularly vulnerable to this kind of attack.[25]This application of quantum computing is a major interest of government agencies.[26]Quantum simulation[edit]Since chemistry and nanotechnology rely on understanding quantum systems, and such systems are impossible to simulate in an efficient manner classically, many believe quantum simulation will be one of the most important applications of quantum computing.[27]Quantum simulation could also be used to simulate the behavior of atoms and particles at unusual conditions such as the reactions inside a collider.[28]Quantum annealing and adiabatic optimisation[edit]Adiabatic quantum computation relies on the adiabatic theorem to undertake calculations. A system is placed in the ground state for a simple Hamiltonian, which is slowly evolved to a more complicated Hamiltonian whose ground state represents the solution to the problem in question. The adiabatic theorem states that if the evolution is slow enough the system will stay in its ground state at all times through the process.Solving linear equations[edit]The Quantum algorithm for linear systems of equations or "HHL Algorithm", named after its discoverers Harrow, Hassidim, and Lloyd, is expected to provide speedup over classical counterparts.[29]Quantum supremacy[edit]John Preskill has introduced the term quantum supremacy to refer to the hypothetical speedup advantage that a quantum computer would have over a classical computer in a certain field.[30]Google announced in 2017 that it expected to achieve quantum supremacy by the end of the year, and IBM says that the best classical computers will be beaten on some task within about five years.[31]Quantum supremacy has not been achieved yet, and skeptics like Gil Kalai doubt that it will ever be.[32][33]Bill Unruh doubted the practicality of quantum computers in a paper published back in 1994.[34]Paul Davies pointed out that a 400-qubit computer would even come into conflict with the cosmological information bound implied by the holographic principle.[35]Those such as Roger Schlafly have pointed out that the claimed theoretical benefits of quantum computing go beyond the proven theory of quantum mechanics and imply non-standard interpretations, such as the many-worlds interpretation and negative probabilities. Schlafly maintains that the Born rule is just "metaphysical fluff" and that quantum mechanics does not rely on probability any more than other branches of science but simply calculates the expected values of observables. He also points out that arguments about Turing complexity cannot be run backwards.[36][37][38]Those who prefer Bayesian interpretations of quantum mechanics have questioned the physical nature of the mathematical abstractions employed.[39]Obstacles[edit]There are a number of technical challenges in building a large-scale quantum computer, and thus far quantum computers have yet to solve a problem faster than a classical computer. David DiVincenzo, of IBM, listed the following requirements for a practical quantum computer:[40]scalable physically to increase the number of qubits;qubits that can be initialized to arbitrary values;quantum gates that are faster than decoherence time;universal gate set;qubits that can be read easily.Quantum decoherence[edit]Main article: Quantum decoherenceOne of the greatest challenges is controlling or removing quantum decoherence. This usually means isolating the system from its environment as interactions with the external world cause the system to decohere. However, other sources of decoherence also exist. Examples include the quantum gates, and the lattice vibrations and background thermonuclear spin of the physical system used to implement the qubits. Decoherence is irreversible, as it is effectively non-unitary, and is usually something that should be highly controlled, if not avoided. Decoherence times for candidate systems in particular, the transverse relaxation time T2(for NMR and MRItechnology, also called the dephasing time), typically range between nanoseconds and seconds at low temperature.[14]Currently, some quantum computers require their qubits to be cooled to 20 millikelvins in order to prevent significant decoherence.[41]As a result, time-consuming tasks may render some quantum algorithms inoperable, as maintaining the state of qubits for a long enough duration will eventually corrupt the superpositions.[42]These issues are more difficult for optical approaches as the timescales are orders of magnitude shorter and an often-cited approach to overcoming them is optical pulse shaping. Error rates are typically proportional to the ratio of operating time to decoherence time, hence any operation must be completed much more quickly than the decoherence time.As described in the Quantum threshold theorem, if the error rate is small enough, it is thought to be possible to use quantum error correction to suppress errors and decoherence. This allows the total calculation time to be longer than the decoherence time if the error correction scheme can correct errors faster than decoherence introduces them. An often cited figure for the required error rate in each gate for fault-tolerant computation is 10−3, assuming the noise is depolarizing.Meeting this scalability condition is possible for a wide range of systems. However, the use of error correction brings with it the cost of a greatly increased number of required qubits. The number required to factor integers using Shor's algorithm is still polynomial, and thought to be between L and L2, where L is the number of qubits in the number to be factored; error correction algorithms would inflate this figure by an additional factor of L. For a 1000-bit number, this implies a need for about 104bits without error correction.[43]With error correction, the figure would rise to about 107bits. Computation time is about L2or about 107steps and at 1 MHz, about 10 seconds.A very different approach to the stability-decoherence problem is to create a topological quantum computer with anyons, quasi-particles used as threads and relying on braid theory to form stable logic gates.[44][45]Developments[edit]Quantum computing models[edit]There are a number of quantum computing models, distinguished by the basic elements in which the computation is decomposed. The four main models of practical importance are:Quantum gate array (computation decomposed into a sequence of few-qubit quantum gates)One-way quantum computer (computation decomposed into a sequence of one-qubit measurements applied to a highly entangled initial state or cluster state)Adiabatic quantum computer, based on quantum annealing (computation decomposed into a slow continuous transformation of an initial Hamiltonian into a final Hamiltonian, whose ground states contain the solution)[46]Topological quantum computer[47] (computation decomposed into the braiding of anyons in a 2D lattice)The quantum Turing machine is theoretically important but the direct implementation of this model is not pursued. All four models of computation have been shown to be equivalent; each can simulate the other with no more than polynomial overhead.Physical realizations[edit]For physically implementing a quantum computer, many different candidates are being pursued, among them (distinguished by the physical system used to realize the qubits):Superconducting quantum computing[48][49] (qubit implemented by the state of small superconducting circuits (Josephson junctions))Trapped ion quantum computer (qubit implemented by the internal state of trapped ions)Optical lattices (qubit implemented by internal states of neutral atoms trapped in an optical lattice)Quantum dot computer, spin-based (e.g. the Loss-DiVincenzo quantum computer[50]) (qubit given by the spin states of trapped electrons)Quantum dot computer, spatial-based (qubit given by electron position in double quantum dot)[51]Coupled Quantum Wire (qubit implemented by a pair of Quantum Wires coupled by a Quantum Point Contact)[52][53][54]Nuclear magnetic resonance quantum computer (NMRQC) implemented with the nuclear magnetic resonance of molecules in solution, where qubits are provided by nuclear spins within the dissolved molecule and probed with radio wavesSolid-state NMR Kane quantum computers (qubit realized by the nuclear spin state of phosphorus donors in silicon)Electrons-on-helium quantum computers (qubit is the electron spin)Cavity quantum electrodynamics (CQED) (qubit provided by the internal state of trapped atoms coupled to high-finesse cavities)Molecular magnet[55] (qubit given by spin states)Fullerene-based ESR quantum computer (qubit based on the electronic spin of atoms or molecules encased in fullerenes)Linear optical quantum computer (qubits realized by processing states of different modes of light through linear elements e.g. mirrors, beam splitters and phase shifters)[56]Diamond-based quantum computer[57][58][59] (qubit realized by the electronic or nuclear spin of nitrogen-vacancy centers in diamond)Bose-Einstein condensate-based quantum computer[60]Transistor-based quantum computer – string quantum computers with entrainment of positive holes using an electrostatic trapRare-earth-metal-ion-doped inorganic crystal based quantum computers[61][62] (qubit realized by the internal electronic state of dopants in optical fibers)Metallic-like carbon nanospheres based quantum computers[63]A large number of candidates demonstrates that the topic, in spite of rapid progress, is still in its infancy. There is also a vast amount of flexibility.Timeline[edit]Main article: Timeline of quantum computingIn 1959 Richard Feynman in his lecture "There's Plenty of Room at the Bottom" states the possibility of using quantum effects for computation.In 1980 Paul Benioff described quantum mechanical Hamiltonian models of computers[64]and the Russian mathematician Yuri Manin motivated the development of quantum computers.[65]In 1981, at a conference co-organized by MIT and IBM, physicist Richard Feynman urged the world to build a quantum computer. He said, "Nature isn't classical, dammit, and if you want to make a simulation of nature, you'd better make it quantum mechanical, and by golly, it's a wonderful problem because it doesn't look so easy."[66]In 1984, BB84 is published, the world's first quantum cryptography protocol by IBM scientists Charles Bennett and Gilles Brassard.In 1993, an international group of six scientists, including Charles Bennett, showed that perfect quantum teleportation is possible[67]in principle, but only if the original is destroyed.In 1994 Peter Shor, at AT&T's Bell Labs discovered an important quantum algorithm, which allows a quantum computer to factor large integers exponentially much faster than the best known classical algorithm. Shor's algorithm can theoretically break many of the public-key cryptosystems in use today.[68]Its invention sparked a tremendous interest in quantum computers.In 1996, The DiVincenzo's criteria are published which is a list of conditions that are necessary for constructing a quantum computer proposed by the theoretical physicist David P. DiVincenzo in his 2000 paper "The Physical Implementation of Quantum Computation".In 2001, researchers demonstrated Shor's algorithm to factor 15 using a 7-qubit NMR computer.[69]In 2005, researchers at the University of Michigan built a semiconductor chip ion trap. Such devices from standard lithography may point the way to scalable quantum computing.[70]In 2009, researchers at Yale University created the first solid-state quantum processor. The two-qubit superconducting chip had artificial atom qubits made of a billion aluminum atoms that acted like a single atom that could occupy two states.[71][72]A team at the University of Bristol also created a silicon chip based on quantum optics, able to run Shor's algorithm.[73]Further developments were made in 2010.[74]Springer publishes a journal (Quantum Information Processing) devoted to the subject.[75]In February 2010, Digital Combinational Circuits like an adder, subtractor etc. are designed with the help of Symmetric Functions organized from different quantum gates.[76][77]In April 2011, a team of scientists from Australia and Japan made a breakthrough in quantum teleportation. They successfully transferred a complex set of quantum data with full transmission integrity, without affecting the qubits' superpositions.[78][79]Photograph of a chip constructed by D-Wave Systems Inc. Mounted and wire-bonded in a sample holder. The D-Wave processor is designed to use 128 superconducting logic elements that exhibit controllable and tunable coupling to perform operations.In 2011, D-Wave Systems announced the first commercial quantum annealer, the D-Wave One, claiming a 128 qubit processor. On May 25, 2011, Lockheed Martin agreed to purchase a D-Wave One system.[80]Lockheed and the University of Southern California (USC) will house the D-Wave One at the newly formed USC Lockheed Martin Quantum Computing Center.[81]D-Wave's engineers designed the chips with an empirical approach, focusing on solving particular problems. Investors liked this more than academics, who said D-Wave had not demonstrated they really had a quantum computer. Criticism softened after a D-Wave paper in Nature, that proved the chips have some quantum properties.[82][83]Two published papers have suggested that the D-Wave machine's operation can be explained classically, rather than requiring quantum models.[84][85]Later work showed that classical models are insufficient when all available data is considered.[86]Experts remain divided on the ultimate classification of the D-Wave systems though their quantum behavior was established concretely with a demonstration of entanglement.[87]During the same year, researchers at the University of Bristol created an all-bulk optics system that ran a version of Shor's algorithm to successfully factor 21.[88]In September 2011 researchers proved quantum computers can be made with a Von Neumann architecture (separation of RAM).[89]In November 2011 researchers factorized 143 using 4 qubits.[90]In February 2012 IBM scientists said that they had made several breakthroughs in quantum computing with superconducting integrated circuits.[91]In April 2012 a multinational team of researchers from the University of Southern California, Delft University of Technology, the Iowa State University of Science and Technology, and the University of California, Santa Barbara, constructed a two-qubit quantum computer on a doped diamond crystal that can easily be scaled up and is functional at room temperature. Two logical qubit directions of electron spin and nitrogen kernels spin were used, with microwave impulses. This computer ran Grover's algorithm generating the right answer from the first try in 95% of cases.[92]In September 2012, Australian researchers at the University of New South Wales said the world's first quantum computer was just 5 to 10 years away, after announcing a global breakthrough enabling the manufacture of its memory building blocks. A research team led by Australian engineers created the first working qubit based on a single atom in silicon, invoking the same technological platform that forms the building blocks of modern-day computers.[93][94]In October 2012, Nobel Prizes were presented to David J. Wineland and Serge Haroche for their basic work on understanding the quantum world, which may help make quantum computing possible.[95][96]In November 2012, the first quantum teleportation from one macroscopic object to another was reported by scientists at the University of Science and Technology of China in Hefei.[97][98]In December 2012, the first dedicated quantum computing software company, 1QBit was founded in Vancouver, BC.[99]1QBit is the first company to focus exclusively on commercializing software applications for commercially available quantum computers, including the D-Wave Two. 1QBit's research demonstrated the ability of superconducting quantum annealing processors to solve real-world problems.[100]In February 2013, a new technique, boson sampling, was reported by two groups using photons in an optical lattice that is not a universal quantum computer but may be good enough for practical problems. Science Feb 15, 2013In May 2013, Google announced that it was launching the Quantum Artificial Intelligence Lab, hosted by NASA's Ames Research Center, with a 512-qubit D-Wave quantum computer. The USRA (Universities Space Research Association) will invite researchers to share time on it with the goal of studying quantum computing for machine learning.[101]Google added that they had "already developed some quantum machine learning algorithms" and had "learned some useful principles", such as that "best results" come from "mixing quantum and classical computing".[101]In early 2014 it was reported, based on documents provided by former NSA contractor Edward Snowden, that the U.S. National Security Agency (NSA) is running a $79.7 million research program (titled "Penetrating Hard Targets") to develop a quantum computer capable of breaking vulnerable encryption.[102]In 2014, a group of researchers from ETH Zürich, USC, Google ,and Microsoft reported a definition of quantum speedup, and were not able to measure quantum speedup with the D-Wave Two device, but did not explicitly rule it out.[103][104]In 2014, researchers at University of New South Wales used silicon as a protectant shell around qubits, making them more accurate, increasing the length of time they will hold information, and possibly making quantum computers easier to build.[105]In April 2015 IBM scientists claimed two critical advances towards the realization of a practical quantum computer. They claimed the ability to detect and measure both kinds of quantum errors simultaneously, as well as a new, square quantum bit circuit design that could scale to larger dimensions.[106]In October 2015, QuTech successfully conducts the Loophole-free Bell inequality violation test using electron spins separated by 1.3 kilometres.[107]In October 2015 researchers at the University of New South Wales built a quantum logic gate in silicon for the first time.[108]In December 2015 NASA publicly displayed the world's first fully operational $15-million quantum computer made by the Canadian company D-Wave at the Quantum Artificial Intelligence Laboratory at its Ames Research Center in California's Moffett Field. The device was purchased in 2013 via a partnership with Google and Universities Space Research Association. The presence and use of quantum effects in the D-Wave quantum processing unit is more widely accepted.[109]In some tests, it can be shown that the D-Wave quantum annealing processor outperforms Selby’s algorithm.[110]Only two of this computer have been made so far.In May 2016, IBM Research announced[111]that for the first time ever it is making quantum computing available to members of the public via the cloud, who can access and run experiments on IBM’s quantum processor. The service is called the IBM Quantum Experience. The quantum processor is composed of five superconducting qubits and is housed at the IBM T. J. Watson Research Center in New York.In August 2016, scientists at the University of Maryland successfully built the first reprogrammable quantum computer.[112]In October 2016 Basel University described a variant of the electron-hole based quantum computer, which instead of manipulating electron spins uses electron holes in a semiconductor at low (mK) temperatures which are a lot less vulnerable to decoherence. This has been dubbed the "positronic" quantum computer as the quasi-particle behaves like it has a positive electrical charge.[113]In March 2017, IBM announced an industry-first initiative to build commercially available universal quantum computing systems called IBM Q. The company also released a new API (Application Program Interface) for the IBM Quantum Experience that enables developers and programmers to begin building interfaces between its existing five quantum bit (qubit) cloud-based quantum computer and classical computers, without needing a deep background in quantum physics.In May 2017, IBM announced[114]that it has successfully built and tested its most powerful universal quantum computing processors. The first is a 16 qubit processor that will allow for more complex experimentation than the previously available 5 qubit processor. The second is IBM's first prototype commercial processor with 17 qubits and leverages significant materials, device, and architecture improvements to make it the most powerful quantum processor created to date by IBM.In July 2017, a group of U.S. researchers announced a quantum simulator with 51 qubits. The announcement was made by Mikhail Lukin of Harvard University at the International Conference on Quantum Technologies in Moscow.[115]A quantum simulator differs from a computer. Lukin’s simulator was designed to solve one equation. Solving a different equation would require building a new system. A computer can solve many different equations.In September 2017, IBM Research scientists use a 7 qubit device to model the largest molecule,[116]Beryllium hydride, ever by a quantum computer. The results were published as the cover story in the peer-reviewed journal Nature.In October 2017, IBM Research scientists successfully "broke the 49-qubit simulation barrier" and simulated 49- and 56-qubit short-depth circuits, using the Lawrence Livermore National Laboratory's Vulcan supercomputer, and the University of Illinois' Cyclops Tensor Framework (originally developed at the University of California). The results were published in arxiv.[117]In November 2017, the University of Sydney research team in Australia successfully made a microwave circulator, an important quantum computer part, 1000 times smaller than a conventional circulator by using topological insulators to slow down the speed of light in a material.[118]In December 2017, IBM announced[119]its first IBM Q Network clients. The companies, universities, and labs to explore practical quantum applications, using IBM Q 20 qubit commercial systems, for business and science include: JPMorgan Chase, Daimler AG, Samsung, JSR Corporation, Barclays, Hitachi Metals, Honda, Nagase, Keio University, Oak Ridge National Lab, Oxford University and University of Melbourne.In December 2017, Microsoft released a preview version of a "Quantum Development Kit".[120]It includes a programming language, Q#, which can be used to write programs that are run on an emulated quantum computer.In 2017 D-Wave reported to start selling a 2000 qubit quantum computer.[121]In late 2017 and early 2018 IBM,[122]Intel,[123]and Google[124]each reported testing quantum processors containing 50, 49, and 72 qubits, respectively, all realized using superconducting circuits. By number of qubits, these circuits are approaching the range in which simulating their quantum dynamics is expected to become prohibitive on classical computers, although it has been argued that further improvements in error rates are needed to put classical simulation out of reach.[125]In February 2018, scientists reported, for the first time, the discovery of a new form of light, which may involve polaritons, that could be useful in the development of quantum computers.[126][127]In February 2018, QuTech reported successfully testing a silicon-based two-spin-qubits quantum processor.[128]In June 2018, Intel begins testing silicon-based spin-qubit processor, manufactured in the company's D1D Fab in Oregon.[129]In July 2018, a team led by the University of Sydney has achieved the world's first multi-qubit demonstration of a quantum chemistry calculation performed on a system of trapped ions, one of the leading hardware platforms in the race to develop a universal quantum computer.[130]Relation to computational complexity theory[edit]Main article: Quantum complexity theoryThe suspected relationship of BQP to other problem spaces.[131]The class of problems that can be efficiently solved by quantum computers is called BQP, for "bounded error, quantum, polynomial time". Quantum computers only run probabilistic algorithms, so BQP on quantum computers is the counterpart of BPP ("bounded error, probabilistic, polynomial time") on classical computers. It is defined as the set of problems solvable with a polynomial-time algorithm, whose probability of error is bounded away from one half.[132]A quantum computer is said to "solve" a problem if, for every instance, its answer will be right with high probability. If that solution runs in polynomial time, then that problem is in BQP.BQP is contained in the complexity class #P (or more precisely in the associated class of decision problems P#P),[133]which is a subclass of PSPACE.BQP is suspected to be disjoint from NP-complete and a strict superset of P, but that is not known. Both integer factorizationand discrete log are in BQP. Both of these problems are NP problems suspected to be outside BPP, and hence outside P. Both are suspected to not be NP-complete. There is a common misconception that quantum computers can solve NP-complete problems in polynomial time. That is not known to be true, and is generally suspected to be false.[133]The capacity of a quantum computer to accelerate classical algorithms has rigid limits—upper bounds of quantum computation's complexity. The overwhelming part of classical calculations cannot be accelerated on a quantum computer.[134]A similar fact takes place for particular computational tasks, like the search problem, for which Grover's algorithm is optimal.[135]Bohmian Mechanics is a non-local hidden variable interpretation of quantum mechanics. It has been shown that a non-local hidden variable quantum computer could implement a search of an N-item database at most in [math]{\displaystyle O({\sqrt[{3}]{N}})}[/math] steps. This is slightly faster than the [math]{\displaystyle O({\sqrt {N}})}[/math] steps taken by Grover's algorithm. Neither search method will allow quantum computers to solve NP-Complete problems in polynomial time.[136]Although quantum computers may be faster than classical computers for some problem types, those described above cannot solve any problem that classical computers cannot already solve. A Turing machine can simulate these quantum computers, so such a quantum computer could never solve an undecidable problemlike the halting problem. The existence of "standard" quantum computers does not disprove the Church–Turing thesis.[137]It has been speculated that theories of quantum gravity, such as M-theory or loop quantum gravity, may allow even faster computers to be built. Currently, defining computation in such theories is an open problem due to the problem of time, i.e., there currently exists no obvious way to describe what it means for an observer to submit input to a computer and later receive output.[138][80]