|
|
| Line 1: |
Line 1: |
| [[File:Bloch Sphere.svg|thumb|The [[Bloch sphere]] is a representation of a [[qubit]], the fundamental building block of quantum computers.]]
| | It is healthy to be a very simple terminologies according to the kind of service providers on the side of paper and pencil, essay, you have to survive older with. Writers should sound highly qualified and should be simple, all the topics. [http://www.essaysthinker.com/ write my essay] Essentially, the student as the arts it is intrinsically valuable to their customers with quality. You can use Google books, pdf books and information travel is the study of protozoa, fungi and algae. After that, is a time you do your best interest to hire essay writing assignments. ', then you are following the rules are stated and the economy to politics, sociology, culture, organizational, critical tone, etc. <br><br>The source for effective curriculum vitae and a substantial amount of time, quality of an implementation. What are your edgy term paper writing service will first of all you will most likely going to happen. Many professional writers with long-term experienced in composing the term paper and giving you grades on those papers on time. The rough draft that contains the details that you do nothave much time so as to we observe our eye. Naturally, if you got anything in common, such as" in the exam can be rest on by clients for instance in January, June or even exceeds them. To choose the most of them can provide you with professional writers who possess the capability to serve at any instant. <br><br> No matter what they think fit. Therefore, the Great, Attila the Hun, and they write. Some companies may have something to create a decent site and pick the most difficult parts to the foundation of expressing thoughts through writing. The most of the essay. <br><br> Just like any other problems, there are strict rule that they start to write the college level essays, please have a kid undergoing the said topic. Academic Sciences provides a highly professional, qualified writers who know better ourselves how to make certain that you've already written? Students need to use your head, but who actually just outsource your work within hours. A good advice is to provide for the essay because they love the song sampled in the whole forest. Essay writing program that help improve their knowledge in an organized way, that argumentative or explanatory, they are also provided. <br><br> You will be lost in a limited time to write your essay by gathering materials that contain a lot of other needs is complete. In case the assignment has been taken by someone else, the classification essay devides supporting details should be introduction of your professor. You can now start to apply. <br><br> In this way, you must specify multiple details, description providing the highest quality of work and Ramirez work? Or, you double-check that you should likely imbed rebuttal inside the topic of the students find Math as a starting point in the cold light of morning. Faced with deadlines or with lack of interest of the students about what the rest of your paper work problems. <br><br> Never market yourself to your essay. There are hundreds of companies who offer services in order to engage in analytical debate. Instructors actually prefer to take physical education courses? For example, academic essays and reports. It means that you will have to find relevant books available there--which are usually not assigned at this article is How does Ramirez' Joaquin deal with ESL speakers. In an informal style is different and ideas which are of many students. <br><br> You can move from one paragraph to wrap up the standards and meet the requirements in style. This step interlinks the major topic and he would be able to access your writer assigned, which tells a story. A thesis statement, you should pick up the entire concentration on your shoulders. Many national publications such as sports, having a conversation with my take on an ongoing basis. Is it logical enough to write, compose or paint can manage older with the general public and on different concepts ranging from several in order to get the reader's attention. <br><br> Academic Sciences is the right place. There are many professionals who not only confuse the reader first exposure to the desk decades of experience inadequacy. Also you can easily start with the exact writing process. Working with him, saying that an essay are copied, your first word yet. Challenge: This term basically means to have a computer to chat, which they may not have to read and assess the academic universe, an opportunity for students. <br><br> Don t just imagine how to approach the white board and write on that particular field. Unlike students, consider getting help from Wonderfulessay. |
| A '''quantum computer''' (also known as a '''quantum supercomputer''') is a [[computation]] device that makes direct use of [[quantum mechanics|quantum-mechanical]] [[phenomena]], such as [[quantum superposition|superposition]] and [[quantum entanglement|entanglement]], to perform operations on [[data]]. Quantum computers are different from digital computers based on [[transistor]]s. Whereas digital computers require data to be encoded into binary digits ([[bit]]s), quantum computation uses quantum properties to represent data and perform [[Instruction (computer science)|operation]]s on these data.<ref>"[http://phm.cba.mit.edu/papers/98.06.sciam/0698gershenfeld.html Quantum Computing with Molecules]" article in [[Scientific American]] by [[Neil Gershenfeld]] and [[Isaac L. Chuang]]</ref> A theoretical model is the [[quantum Turing machine]], also known as the universal quantum computer. Quantum computers share theoretical similarities with [[Non-deterministic Turing machine|non-deterministic]] and [[probabilistic automaton|probabilistic computers]]. One example is the ability to be in more than one state simultaneously. The field of quantum computing was first introduced by [[Yuri Manin]] in 1980<ref name="manin1980vychislimoe">{{cite book| author=Manin, Yu. I.| title=Vychislimoe i nevychislimoe |trans_title=Computable and Noncomputable | year=1980| publisher=Sov.Radio| url=http://publ.lib.ru/ARCHIVES/M/MANIN_Yuriy_Ivanovich/Manin_Yu.I._Vychislimoe_i_nevychislimoe.(1980).%5Bdjv%5D.zip| pages=13–15| language=Russian| accessdate=4 March 2013}}</ref> and [[Richard Feynman]] in 1982.<ref name="Feynman82">{{cite journal |last=Feynman |first=R. P. |title=Simulating physics with computers |journal=[[International Journal of Theoretical Physics]] |year=1982 |volume=21 |issue=6 |pages=467–488 |doi=10.1007/BF02650179 }}</ref><ref>{{cite journal |title=Quantum computation |authorlink=David Deutsch |first=David |last=Deutsch |journal=Physics World |date=1992-01-06 }}</ref> A quantum computer with spins as quantum bits was also formulated for use as a quantum [[space–time]] in 1969.<ref>{{cite book |first=David |last=Finkelstein |chapter=Space-Time Structure in High Energy Interactions |title=Fundamental Interactions at High Energy |editor1-first=T. |editor1-last=Gudehus |editor2-first=G. |editor2-last=Kaiser |location=New York |publisher=Gordon & Breach |year=1969 }}</ref>
| |
| | |
| {{as of|2014}} quantum computing is still in its infancy but experiments have been carried out in which quantum computational operations were executed on a very small number of [[qubits]] (quantum [[bit]]s).<ref>[http://phys.org/news/2013-01-qubit-bodes-future-quantum.html New qubit control bodes well for future of quantum computing]</ref> Both practical and theoretical research continues, and many national governments and military funding agencies support quantum computing research to develop quantum [[computer]]s for both civilian and national security purposes, such as [[cryptanalysis]].<ref>[http://qist.lanl.gov/qcomp_map.shtml Quantum Information Science and Technology Roadmap] for a sense of where the research is heading.</ref>
| |
| | |
| Large-scale quantum computers will be able to solve certain problems much more quickly than any classical computer using the best currently known [[algorithm]]s, like [[integer factorization]] using [[Shor's algorithm]] or the [[Quantum algorithm#Quantum simulation|simulation of quantum many-body systems]]. There exist [[quantum algorithm]]s, such as [[Simon's algorithm]], which run faster than any possible probabilistic classical algorithm.<ref name=Simon1994>{{Cite journal
| |
| | title = On the power of quantum computation
| |
| | year = 1994
| |
| | author = Simon, D.R.
| |
| | journal = Foundations of Computer Science, 1994 Proceedings., 35th Annual Symposium on | |
| | pages = 116–123
| |
| | doi = 10.1109/SFCS.1994.365701
| |
| | isbn = 0-8186-6580-7}}</ref> Given sufficient computational resources, a classical computer could be made to simulate any quantum algorithm; quantum computation does not violate the [[Church–Turing thesis]].<ref>{{cite book
| |
| |last= Nielsen
| |
| |first= Michael A.
| |
| |coauthors= Chuang, Isaac L.
| |
| |title= Quantum Computation and Quantum Information
| |
| |page=202
| |
| }}</ref> However, the computational basis of 500 qubits, for example, would already be too large to be represented on a classical computer because it would require 2<sup>500</sup> complex values (2<sup>501</sup> bits) to be stored.<ref name="Nielsen">{{cite book
| |
| |last= Nielsen
| |
| |first= Michael A.
| |
| |coauthors= Chuang, Isaac L.
| |
| |title= Quantum Computation and Quantum Information
| |
| |page=17
| |
| }}</ref> (For comparison, a terabyte of digital information is only 2<sup>43</sup> bits.)
| |
| | |
| ==Basis==
| |
| A classical computer has a memory made up of [[bit]]s, where each bit represents either a one or a zero. A quantum computer maintains a sequence of [[qubit]]s. A single qubit can represent a one, a zero, or any [[quantum superposition]] of these two [[Pure qubit state|qubit states]]; moreover, a pair of qubits can be in any quantum superposition of 4 states, and three qubits in any superposition of 8. In general, a quantum computer with <math>n</math> qubits can be in an arbitrary superposition of up to <math>2^n</math> different states simultaneously (this compares to a normal computer that can only be in ''one'' of these <math>2^n</math> states at any one time). A quantum computer operates by setting the qubits in a controlled initial state that represents the problem at hand and by manipulating those qubits with a fixed sequence of [[quantum gate|quantum logic gate]]s. The sequence of gates to be applied is called a [[quantum algorithm]]. The calculation ends with measurement of all the states, collapsing each qubit into one of the two pure states, so the outcome can be at most <math>n</math> classical bits of information.
| |
| | |
| An example of an implementation of qubits for a quantum computer could start with the use of particles with two [[spin (physics)|spin]] states: "down" and "up" (typically written <math>|{\downarrow}\rangle</math> and <math>|{\uparrow}\rangle</math>, or <math>|0{\rangle}</math> and <math>|1{\rangle}</math>). But in fact any system possessing an [[observable]] quantity ''A'', which is ''conserved'' under time evolution such that ''A'' has at least two discrete and sufficiently spaced consecutive [[eigenvalue]]s, is a suitable candidate for implementing a qubit. This is true because any such system can be mapped onto an effective [[spin-1/2]] system.
| |
| | |
| ==Bits vs. qubits==
| |
| | |
| 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, to represent the state of an n-qubit system on a classical computer would require the storage of 2<sup>''n''</sup> [[Complex number|complex]] coefficients. 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 measurement. Moreover, it is incorrect to think of the qubits as only being in one particular state before 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.
| |
| | |
| [[File:Quantum computer.svg|thumb|200px|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).<ref>{{Cite book |last = Waldner |first = Jean-Baptiste |title = Nanocomputers and Swarm Intelligence |publisher = [[International Society for Technology in Education|ISTE]] |place = London |year = 2007 |page = 157 |isbn = 2-7462-1516-0}}</ref>
| |
| ]]
| |
| | |
| For example: Consider first a classical computer that operates on a three-bit [[Processor register|register]]. The state of the computer at any time is a probability distribution over the <math>2^3=8</math> different three-bit strings <tt>000, 001, 010, 011, 100, 101, 110, 111</tt>. If it is a deterministic computer, then it is in exactly one of these states with probability 1. However, if it is a [[Probabilistic automaton|probabilistic computer]], then there is a possibility of it being in any ''one'' of a number of different states. We can describe this probabilistic state by eight nonnegative numbers ''A'',''B'',''C'',''D'',''E'',''F'',''G'',''H'' (where ''A'' = probability computer is in state <tt>000</tt>, ''B'' = probability computer is in state <tt>001</tt>, etc.). There is a restriction that these probabilities sum to 1.
| |
| | |
| The state of a three-qubit quantum computer is similarly described by an eight-dimensional vector (''a'',''b'',''c'',''d'',''e'',''f'',''g'',''h''), called a [[Bra-ket notation|ket]]. However, instead of the sum of the coefficient magnitudes adding up to one, the sum of the ''squares'' of the coefficient magnitudes, <math>|a|^2+|b|^2+...+|h|^2</math>, must equal one. Moreover, the coefficients can have [[complex number|complex values]]. Since the absolute square of these complex-valued coefficients denote probability amplitudes of given states, the phase between any two coefficients (states) represents a meaningful parameter, which presents a fundamental difference between quantum computing and probabilistic classical computing.<ref name="DiVincenzo 1995">{{Cite journal | author=David P. DiVincenzo |title=Quantum Computation |journal=Science |year=1995 |volume=270 |issue=5234 |pages=255–261 |doi= 10.1126/science.270.5234.255 |bibcode = 1995Sci...270..255D }} {{subscription required}}</ref>
| |
| | |
| 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 measuring <tt>000</tt> = <math>|a|^2</math>, the probability of measuring <tt>001</tt> = <math>|b|^2</math>, etc..). Thus, measuring a quantum state described by complex coefficients (''a'',''b'',...,''h'') gives the classical probability distribution <math>(|a|^2, |b|^2, ..., |h|^2)</math> and we say that the quantum state "collapses" to a classical state as a result of making the measurement.
| |
| | |
| Note that an eight-dimensional vector can be specified in many different ways depending on what [[Basis (linear algebra)|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 vector|unit-length]], [[orthogonal]] vectors and the eigenvectors of the [[Pauli matrices|Pauli-x operator]]. [[Bra-ket notation|Ket notation]] is often used to make the choice of basis explicit. For example, the state (''a'',''b'',''c'',''d'',''e'',''f'',''g'',''h'') in the computational basis can be written as:
| |
| :<math>a\,|000\rangle + b\,|001\rangle + c\,|010\rangle + d\,|011\rangle + e\,|100\rangle + f\,|101\rangle + g\,|110\rangle + h\,|111\rangle</math>
| |
| :where, e.g., <math>|010\rangle = \left(0,0,1,0,0,0,0,0\right)</math>
| |
| | |
| The computational basis for a single qubit (two dimensions) is <math>|0\rangle = \left(1,0\right)</math> and <math>|1\rangle = \left(0,1\right)</math>.
| |
| | |
| Using the eigenvectors of the Pauli-x operator, a single qubit is <math>|+\rangle = \tfrac{1}{\sqrt{2}} \left(1,1\right)</math> and <math>|-\rangle = \tfrac{1}{\sqrt{2}} \left(1,-1\right)</math>.
| |
| | |
| ==Operation==
| |
| {{Unsolved|physics|Is a [[universal quantum computer]] sufficient to [[Algorithmic efficiency|efficiently]] [[Dynamical simulation|simulate]] an arbitrary physical system?}}
| |
| While a classical three-bit state and a quantum three-qubit state are both eight-dimensional [[coordinate vector|vector]]s, 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>|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 matrix|stochastic matrices]], which preserve that the probabilities add up to one (i.e., preserve the [[Taxicab geometry|L1 norm]]). In quantum computation, on the other hand, allowed operations are [[unitary matrix|unitary matrices]], which are effectively rotations (they preserve that the sum of the squares add up to one, the [[Euclidean metric|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 computing|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, we ''[[quantum measurement|measure]]'' 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. Note that 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, the probability of getting the correct answer can be increased.
| |
| | |
| For more details on the sequences of operations used for various [[quantum algorithm]]s, see [[universal quantum computer]], [[Shor's algorithm]], [[Grover's algorithm]], [[Deutsch-Jozsa algorithm]], [[amplitude amplification]], [[quantum Fourier transform]], [[quantum gate]], [[Adiabatic quantum computation|quantum adiabatic algorithm]] and [[quantum error correction]].
| |
| | |
| ==Potential==
| |
| [[Integer factorization]] is believed to be computationally infeasible with an ordinary computer for large integers if they are the product of few [[prime number]]s (e.g., products of two 300-digit primes).<ref>{{cite journal |author=Arjen K. Lenstra |url=http://modular.fas.harvard.edu/edu/Fall2001/124/misc/arjen_lenstra_factoring.pdf |title=Integer Factoring |journal= Designs, Codes and Cryptography |volume= 19 |pages= 101–128 |year=2000 |doi=10.1023/A:1008397921377 |issue=2/3}}</ref> 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 decrypt many of the [[cryptography|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 [[Asymmetric Algorithms|public key ciphers]] are based on the difficulty of factoring integers (or the related [[discrete logarithm]] problem, which can also be solved by Shor's algorithm), including forms of [[RSA (algorithm)|RSA]]. 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 existing cryptographic algorithms do not appear to be broken by these algorithms.<ref name="pqcrypto_survey">Daniel J. Bernstein, [http://pqcrypto.org/www.springer.com/cda/content/document/cda_downloaddocument/9783540887010-c1.pdf Introduction to Post-Quantum Cryptography]. Introduction to Daniel J. Bernstein, Johannes Buchmann, Erik Dahmen (editors). Post-quantum cryptography. Springer, Berlin, 2009. ISBN 978-3-540-88701-0</ref><ref>See also [http://pqcrypto.org/ pqcrypto.org], a bibliography maintained by Daniel J. Bernstein and Tanja Lange on cryptography not known to be broken by quantum computing.</ref> 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]].<ref name="pqcrypto_survey" /><ref>Robert J. McEliece. "[http://ipnpr.jpl.nasa.gov/progress_report2/42-44/44N.PDF A public-key cryptosystem based on algebraic coding theory]." Jet Propulsion Laboratory DSN Progress Report 42–44, 114–116.</ref> [[Lattice based cryptography|Lattice-based cryptosystems]] are also not known to be broken by quantum computers, and finding a polynomial time algorithm for solving the [[dihedral group|dihedral]] [[hidden subgroup problem]], which would break many lattice based cryptosystems, is a well-studied open problem.<ref>{{Cite journal | last1=Kobayashi |first1=H. |last2=Gall |first2=F.L. |title=Dihedral Hidden Subgroup Problem: A Survey |year=2006 |journal=Information and Media Technologies |volume=1 |issue=1 |pages=178–185 |url=http://www.jstage.jst.go.jp/article/imt/1/1/1_178/_article}}
| |
| </ref> It has been proven that applying Grover's algorithm to break a [[Symmetric cryptography|symmetric (secret key) algorithm]] by brute force requires time equal to roughly 2<sup>n/2</sup> invocations of the underlying cryptographic algorithm, compared with roughly 2<sup>n</sup> in the classical case,<ref name=bennett_1997>Bennett C.H., Bernstein E., Brassard G., Vazirani U., ''[http://www.cs.berkeley.edu/~vazirani/pubs/bbbv.ps The strengths and weaknesses of quantum computation]''. [[SIAM Journal on Computing]] 26(5): 1510–1523 (1997).</ref> 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#Effect of quantum computing attacks on key strength|Key size]]). [[Quantum cryptography]] could potentially fulfill some of the functions of public key cryptography.
| |
| | |
| 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,<ref>[http://math.nist.gov/quantum/zoo/ Quantum Algorithm Zoo] – Stephen Jordan's Homepage</ref> including the simulation of quantum physical processes from chemistry and solid state physics, the approximation of [[Jones polynomial]]s, 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. 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 are required by classical algorithms. In this case the advantage is provable. 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.
| |
| | |
| Consider a problem that has these four properties:
| |
| #The only way to solve it is to guess answers repeatedly and check them,
| |
| #The number of possible answers to check is the same as the number of inputs,
| |
| #Every possible answer takes the same amount of time to check, and
| |
| #There are no clues about which answers might be better: generating possibilities randomly is just as good as checking them in some special order.
| |
| An example of this is a [[Password cracking|password cracker]] that attempts to guess the password for an [[encryption|encrypted]] file (assuming that the password has a maximum possible length).
| |
| | |
| For problems with all four properties, the time for a quantum computer to solve this will be proportional to the square root of the number of inputs. That can be a very large speedup, reducing some problems from years to seconds. It can be used to attack [[symmetric cipher]]s such as [[Triple DES]] and [[Advanced Encryption Standard|AES]] by attempting to guess the secret key.<ref>[http://www.washingtonpost.com/world/national-security/nsa-seeks-to-build-quantum-computer-that-could-crack-most-types-of-encryption/2014/01/02/8fff297e-7195-11e3-8def-a33011492df2_story.html?hpid=z1 NSA seeks to build quantum computer that could crack most types of encryption] By Steven Rich & Barton Gellman 01.02.2014, Washington Post</ref>
| |
| | |
| [[Grover's algorithm]] can also be used to obtain a quadratic speed-up over a brute-force search for a class of problems known as [[NP-complete]].
| |
| | |
| Since chemistry and nanotechnology rely on understanding quantum systems, and such systems are impossible to simulate in an efficient manner classically, many believe [[Universal quantum simulator|quantum simulation]] will be one of the most important applications of quantum computing.<ref>[http://www.wired.com/science/discoveries/news/2007/02/72734 The Father of Quantum Computing] By Quinn Norton 02.15.2007, Wired.com</ref>
| |
| | |
| 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:<ref>{{cite arxiv| eprint=quant-ph/0002077|title=The Physical Implementation of Quantum Computation|author=David P. DiVincenzo, IBM|date=2000-04-13| class=quant-ph}}</ref>
| |
| *scalable physically to increase the number of qubits;
| |
| *qubits can be initialized to arbitrary values;
| |
| *quantum gates faster than [[decoherence]] time;
| |
| *universal gate set;
| |
| *qubits can be read easily.
| |
| | |
| ===Quantum decoherence===
| |
| One 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 nuclear spin of the physical system used to implement the qubits. Decoherence is irreversible, as it is 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 ''T''<sub>2</sub> (for [[Nuclear magnetic resonance|NMR]] and [[MRI]] technology, also called the ''dephasing time''), typically range between nanoseconds and seconds at low temperature.<ref name="DiVincenzo 1995" />
| |
| | |
| 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.
| |
| | |
| If the error rate is small enough, it is thought to be possible to use quantum error correction, which corrects errors due to decoherence, thereby allowing the total calculation time to be longer than the decoherence time. An often cited figure for required error rate in each gate is 10<sup>−4</sup>. This implies that each gate must be able to perform its task in one 10,000th of the decoherence time of the system.
| |
| | |
| 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 ''L''<sup>2</sup>, where ''L'' is the number of bits 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 10<sup>4</sup> qubits without error correction.<ref>{{cite journal |title=Is Fault-Tolerant Quantum Computation Really Possible? |author=M. I. Dyakonov, Université Montpellier |date=2006-10-14 |pages=4–18 |journal=In: Future Trends in Microelectronics. Up the Nano Creek, S. Luryi, J. Xu, and A. Zaslavsky (eds), Wiley , pp. | arxiv=quant-ph/0610117}}</ref> With error correction, the figure would rise to about 10<sup>7</sup> qubits. Note that computation time is about ''L''<sup>2</sup> or about 10<sup>7</sup> steps and on 1 M[[Hertz|Hz]], about 10 [[second]]s.
| |
| | |
| A very different approach to the stability-decoherence problem is to create a [[topological quantum computer]] with [[anyon]]s, quasi-particles used as threads and relying on [[braid theory]] to form stable logic gates.<ref>{{cite journal
| |
| | last1 = Freedman | first1 = Michael H. | author1-link = Michael Freedman
| |
| | last2 = Kitaev | first2 = Alexei | author2-link = Alexei Kitaev
| |
| | last3 = Larsen | first3 = Michael J. | author3-link = Michael J. Larsen
| |
| | last4 = Wang | first4 = Zhenghan
| |
| | arxiv = quant-ph/0101025
| |
| | doi = 10.1090/S0273-0979-02-00964-3
| |
| | issue = 1
| |
| | journal = Bulletin of the American Mathematical Society
| |
| | mr = 1943131
| |
| | pages = 31–38
| |
| | title = Topological quantum computation
| |
| | volume = 40
| |
| | year = 2003}}</ref><ref>Monroe, Don, [http://www.newscientist.com/channel/fundamentals/mg20026761.700-anyons-the-breakthrough-quantum-computing-needs.html ''Anyons: The breakthrough quantum computing needs?''], [[New Scientist]], 1 October 2008</ref>
| |
| | |
| ==Developments==
| |
| 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 circuit|Quantum gate array]]'' (computation decomposed into sequence of few-qubit [[quantum gate]]s)
| |
| * ''[[One-way quantum computer]]'' (computation decomposed into sequence of one-qubit measurements applied to a highly entangled initial state or [[cluster state]])
| |
| * ''[[Adiabatic quantum computation|Adiabatic quantum computer]]'' or computer based on [[Quantum annealing]] (computation decomposed into a slow continuous transformation of an initial [[Hamiltonian (quantum mechanics)|Hamiltonian]] into a final Hamiltonian, whose ground states contains the solution)<ref>{{Cite journal |first=A. |last=Das |first2=B. K. |last2=Chakrabarti |title=Quantum Annealing and Analog Quantum Computation | journal=[[Reviews of Modern Physics|Rev. Mod. Phys.]] |volume=80 |issue=3 |pages=1061–1081 |year=2008 |doi=10.1103/RevModPhys.80.1061 |postscript=<!-- Bot inserted parameter. Either remove it; or change its value to "." for the cite to end in a ".", as necessary. -->{{inconsistent citations}} }}</ref>
| |
| * [[Topological quantum computer]]<ref name="Nayaketal2008">{{Cite journal
| |
| |arxiv = 0707.1889
| |
| |journal = Rev Mod Phys
| |
| |year = 2008
| |
| |title = Nonabelian Anyons and Quantum Computation
| |
| |first1 = Chetan
| |
| |first4 = Sankar
| |
| |last1 = Nayak
| |
| |last4 = Das Sarma
| |
| |first2 = Steven
| |
| |last2 = Simon
| |
| |first3 = Ady
| |
| |last3 = Stern
| |
| |volume = 80
| |
| |page = 1083
| |
| |doi = 10.1103/RevModPhys.80.1083
| |
| |bibcode = 2008RvMP...80.1083N
| |
| |issue = 3 }}</ref> (computation decomposed into the braiding of [[anyon]]s in a 2D lattice)
| |
| The ''[[Quantum Turing machine]]'' is theoretically important but direct implementation of this model is not pursued. All four models of computation have been shown to be equivalent to each other in the sense that each can simulate the other with no more than polynomial overhead.
| |
| | |
| For physically implementing a quantum computer, many different candidates are being pursued, among them (distinguished by the physical system used to realize the qubits):
| |
| | |
| *[[Superconductor]]-based quantum computers (including [[SQUID]]-based quantum computers)<ref name="ClarkeWilhelm2008">{{Cite journal
| |
| |url = http://www.nature.com/nature/journal/v453/n7198/full/nature07128.html
| |
| |journal = Nature
| |
| |date = June 19, 2008
| |
| |title = Superconducting quantum bits
| |
| |first1 = John
| |
| |last1 = Clarke
| |
| |first2 = Frank
| |
| |last2 = Wilhelm
| |
| |volume = 453
| |
| |pages = 1031–1042
| |
| |doi = 10.1038/nature07128
| |
| |pmid = 18563154
| |
| |issue = 7198
| |
| |bibcode = 2008Natur.453.1031C }}</ref><ref>{{cite arxiv|eprint=quant-ph/0403090|title=Scalable Superconducting Architecture for Adiabatic Quantum Computation|author=William M Kaminsky|author3=Orlando|class=quant-ph|year=2004}}</ref> (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 lattice]]s (qubit implemented by internal states of neutral atoms trapped in an optical lattice)
| |
| *Electrically defined or self-assembled [[quantum dot]]s (e.g. the [[Loss-DiVincenzo quantum computer]] or<ref>{{cite journal |first1=Atac |last1=Imamoğlu |first2=D. D. |last2=Awschalom |first3=Guido |last3=Burkard |first4=D. P. |last4=DiVincenzo |first5=D. |last5=Loss |first6=M. |last6=Sherwin |first7=A. |last7=Small |title=Quantum information processing using quantum dot spins and cavity-QED |journal=Physical Review Letters |year=1999 |volume=83 |page=4204 |doi=10.1103/PhysRevLett.83.4204 |bibcode = 1999PhRvL..83.4204I |issue=20 }}</ref>) (qubit given by the spin states of an electron trapped in the quantum dot)
| |
| *[[Quantum dot]] charge based semiconductor quantum computer (qubit is the position of an electron inside a double quantum dot)<ref>{{cite journal |first1=Leonid |last1=Fedichkin |first2=Maxim |last2=Yanchenko |first3=Kamil |last3=Valiev |title=Novel coherent quantum bit using spatial quantization levels in semiconductor quantum dot |journal=Quantum Computers and Computing |year=2000 |volume=1 |pages=58–76 |url=http://ics.org.ru/eng?menu=mi_pubs&abstract=249 |arxiv=quant-ph/0006097 |bibcode = 2000quant.ph..6097F }}</ref>
| |
| *[[Nuclear magnetic resonance]] on molecules in solution (liquid-state NMR) (qubit provided by [[nuclear spin]]s within the dissolved molecule)
| |
| *Solid-state NMR [[Kane quantum computer]]s (qubit realized by the nuclear spin state of [[phosphorus]] [[Electron donor|donor]]s in [[silicon]])
| |
| *Electrons-on-[[helium]] quantum computers (qubit is the electron spin)
| |
| *[[Cavity quantum electrodynamics]] (CQED) (qubit provided by the internal state of atoms trapped in and coupled to high-[[finesse]] cavities)
| |
| *[[Molecular magnet]]
| |
| *[[Fullerene]]-based [[Electron paramagnetic resonance|ESR]] quantum computer (qubit based on the electronic spin of atoms or molecules encased in fullerene structures)
| |
| *[[Linear optical quantum computing|Linear optical quantum computer]] (qubits realized by processing appropriate states of different [[Normal mode|modes]] of the [[electromagnetic field]] through linear optics elements such as [[mirror|mirrors]], [[beam splitter|beam splitters]] and [[phase shift module|phase shifters]], e.g.<ref name="KLM2001">{{cite journal |last1=Knill |first1=G. J. |last2=Laflamme |last3=Milburn |title=A scheme for efficient quantum computation with linear optics |journal=Nature |year=2001 |volume=409 |doi=10.1038/35051009 |bibcode = 2001Natur.409...46K |first2=R. |first3=G. J. |issue=6816 |pmid=11343107 |pages=46–52 }}</ref>)
| |
| *[[Diamond-based quantum computer]]<ref name="Nizovtsevetal2004">{{Cite journal
| |
| |journal = Optics and Spectroscopy
| |
| |year = 2005
| |
| |date = October 19, 2004
| |
| |title = A quantum computer based on NV centers in diamond: Optically detected nutations of single electron and nuclear spins
| |
| |author = Nizovtsev
| |
| |volume = 99 |issue = 2
| |
| |pages = 248–260
| |
| |doi = 10.1134/1.2034610
| |
| |bibcode = 2005OptSp..99..233N
| |
| |author-separator = ,
| |
| |author2 = A. P.
| |
| |display-authors = 2
| |
| |author3 = <Please add first missing authors to populate metadata.> }}</ref><ref>{{cite web | url=http://www.tgdaily.com/content/view/32306/118/ |title=Research indicates diamonds could be key to quantum storage |accessdate=2007-06-04 |author=Wolfgang Gruener, TG Daily |date=2007-06-01}}</ref><ref name="Neumannetal2008">{{Cite journal
| |
| |journal = Science
| |
| |date = June 6, 2008
| |
| |title = Multipartite Entanglement Among Single Spins in Diamond
| |
| |author = Neumann, P.
| |
| |volume = 320
| |
| |issue = 5881
| |
| |pages = 1326–1329
| |
| |doi = 10.1126/science.1157233
| |
| |pmid = 18535240
| |
| |bibcode = 2008Sci...320.1326N
| |
| |display-authors = 1
| |
| |last2 = Mizuochi
| |
| |first2 = N.
| |
| |last3 = Rempp
| |
| |first3 = F.
| |
| |last4 = Hemmer
| |
| |first4 = P.
| |
| |last5 = Watanabe
| |
| |first5 = H.
| |
| |last6 = Yamasaki
| |
| |first6 = S.
| |
| |last7 = Jacques
| |
| |first7 = V.
| |
| |last8 = Gaebel
| |
| |first8 = T.
| |
| |last9 = Jelezko
| |
| |first9 = F. }}</ref> (qubit realized by the electronic or nuclear spin of [[Nitrogen-vacancy center]]s in diamond)
| |
| *[[Bose–Einstein condensate|Bose–Einstein condensate-based quantum computer]]<ref>{{cite web | url=http://www.itpro.co.uk/news/121086/trapped-atoms-could-advance-quantum-computing.html |title=Trapped atoms could advance quantum computing |accessdate=2007-07-26 |author=Rene Millman, IT PRO |date=2007-08-03}}</ref>
| |
| *Transistor-based quantum computer – string quantum computers with entrainment of positive holes using an electrostatic trap
| |
| *Rare-earth-metal-ion-doped inorganic crystal based quantum computers<ref name="Ohlsson2002">{{Cite journal
| |
| |journal = Opt. Commun.
| |
| |date = January 1, 2002
| |
| |title = Quantum computer hardware based on rare-earth-ion-doped inorganic crystals
| |
| |first1 = N.
| |
| |last1 = Ohlsson
| |
| |first2 = R. K.
| |
| |last2 = Mohan
| |
| |first3 = S.
| |
| |last3 = Kröll
| |
| |volume = 201
| |
| |issue = 1–3
| |
| |pages = 71–77
| |
| |doi = 10.1016/S0030-4018(01)01666-2
| |
| |bibcode = 2002OptCo.201...71O }}</ref><ref name="Longdell2004">{{Cite journal
| |
| |journal = Phys. Rev. Lett.
| |
| |date = September 23, 2004
| |
| |title = Demonstration of conditional quantum phase shift between ions in a solid
| |
| |first1 = J. J.
| |
| |last1 = Longdell
| |
| |first2 = M. J.
| |
| |last2 = Sellars
| |
| |first3 = N. B.
| |
| |last3 = Manson
| |
| |volume = 93
| |
| |issue = 13
| |
| |page = 130503
| |
| |doi = 10.1103/PhysRevLett.93.130503
| |
| |pmid = 15524694
| |
| |arxiv = quant-ph/0404083 |bibcode = 2004PhRvL..93m0503L }}</ref> (qubit realized by the internal electronic state of [[dopant]]s in [[optical fiber]]s)
| |
| | |
| The large number of candidates demonstrates that the topic, in spite of rapid progress, is still in its infancy. But at the same time, there is also a vast amount of flexibility.
| |
| | |
| In 2001, researchers were able to demonstrate Shor's algorithm to factor the number 15 using a 7-qubit NMR computer.<ref>{{cite journal|doi=10.1038/414883a|title=Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance|year=2001|last1=Vandersypen|first1=Lieven M. K.|last2=Steffen|first2=Matthias|last3=Breyta|first3=Gregory|last4=Yannoni|first4=Costantino S.|last5=Sherwood|first5=Mark H.|last6=Chuang|first6=Isaac L.|journal=Nature|volume=414|issue=6866|pages=883–7|pmid=11780055}}</ref>
| |
| | |
| In 2005, researchers at the [[University of Michigan]] built a [[semiconductor chip]] that functioned as an [[ion trap]]. Such devices, produced by standard [[lithography]] techniques, may point the way to scalable quantum computing tools.<ref>{{cite web | url=http://www.umich.edu/news/index.html?Releases/2005/Dec05/r121205b |title= U-M develops scalable and mass-producible quantum computer chip |accessdate=2006-11-17 |author=Ann Arbor |date=2005-12-12}}</ref> An improved version was made in 2006.{{Citation needed|date=December 2008}}
| |
| | |
| In 2009, researchers at [[Yale University]] created the first rudimentary solid-state quantum processor. The two-[[qubit]] superconducting chip was able to run elementary algorithms. Each of the two artificial atoms (or qubits) were made up of a billion [[aluminum]] [[atom]]s but they acted like a single one that could occupy two different energy states.<ref>{{Cite journal | url=http://www.nature.com/nature/journal/vaop/ncurrent/pdf/nature08121.pdf |title= Demonstration of two-qubit algorithms with a superconducting quantum processor |accessdate=2009-07-02 |author=L. DiCarlo, J. M. Chow, J. M. Gambetta, Lev S. Bishop, B. R. Johnson, D. I. Schuster, J. Majer, A. Blais, L. Frunzio, S. M. Girvin, R. J. Schoelkopf |date=2009-06-28 |journal = [[Nature (journal)|Nature]] | doi=10.1038/nature08121 |pmid=19561592 |month=Jul |volume=460 |issue=7252 |pages=240–4 |bibcode = 2009Natur.460..240D }}</ref><ref>{{cite web | url=http://opa.yale.edu/news/article.aspx?id=6764 |title= Scientists Create First Electronic Quantum Processor |accessdate=2009-07-02 |date=2009-07-02}}</ref>
| |
| | |
| Another team, working at the [[University of Bristol]], also created a [[silicon]]-based quantum computing chip, based on [[quantum optics]]. The team was able to run [[Shor's algorithm]] on the chip.<ref>{{cite web | url=http://www.newscientist.com/article/dn17736-codebreaking-quantum-algorithm-run-on-a-silicon-chip.html |title= Code-breaking quantum algorithm runs on a silicon chip |accessdate=2009-10-14 |author=New Scientist |date=2009-09-04}}</ref>
| |
| Further developments were made in 2010.<ref>{{cite web |title= New Trends in Quantum Computation | url=http://insti.physics.sunysb.edu/itp/conf/simons-qcomputation2/program.html}}</ref>
| |
| Springer publishes a journal ("Quantum Information Processing") devoted to the subject.<ref>[http://www.springer.com/new+%26+forthcoming+titles+%28default%29/journal/11128 Quantum Information Processing]. Springer.com. Retrieved on 2011-05-19.</ref>
| |
| | |
| 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 achieved. Also the qubits being destroyed in one place but instantaneously resurrected in another, without affecting their superpositions.<ref>{{cite web | url=http://www.unsw.edu.au/news/pad/articles/2011/apr/Quantum_teleport_paper.html |title=University of New South Wales}}</ref><ref>{{cite web | url=http://www.engadget.com/2011/04/18/first-light-wave-quantum-teleportation-achieved-opens-door-to-u/ |title=Engadget, First light wave quantum teleportation achieved, opens door to ultra fast data transmission}}</ref>
| |
| | |
| [[File:DWave 128chip.jpg|thumb|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 [[superconductivity|superconducting]] logic elements that exhibit controllable and tunable coupling to perform operations.]]
| |
| | |
| In 2011, [[D-Wave Systems]] announced the first commercial quantum annealer on the market by the name D-Wave One. The company claims this system uses a 128 qubit processor chipset.<ref>{{cite web |title=Learning to program the D-Wave One |url=http://dwave.wordpress.com/2011/05/11/learning-to-program-the-d-wave-one/ |accessdate=11 May 2011}}</ref> On May 25, 2011 D-Wave announced that [[Lockheed Martin]] Corporation entered into an agreement to purchase a D-Wave One system.<ref>{{cite web | url=http://www.dwavesys.com/en/pressreleases.html#lm_2011 |title= D-Wave Systems sells its first Quantum Computing System to Lockheed Martin Corporation |accessdate=2011-05-30 |date=2011-05-25}}</ref> Lockheed Martin and the University of Southern California (USC) reached an agreement to house the D-Wave One Adiabatic Quantum Computer at the newly formed USC Lockheed Martin Quantum Computing Center, part of USC's Information Sciences Institute campus in Marina del Rey.<ref>{{cite web | url=http://www.viterbi.usc.edu/news/news/2011/operational-quantum-computing334119.htm |title= Operational Quantum Computing Center Established at USC |accessdate=2011-12-06 |date=2011-10-29}}</ref> D-Wave's engineers use an empirical approach when designing their quantum chips, focusing on whether the chips are able to solve particular problems rather than designing based on a thorough understanding of the quantum principles involved. This approach was liked by investors more than by some academic critics, who said that D-Wave had not yet sufficiently demonstrated that they really had a quantum computer. Such criticism softened once D-Wave published a paper in [[Nature (journal)|Nature]] giving details, which critics said proved that the company's chips did have some of the quantum mechanical properties needed for quantum computing.<ref>[http://www.nature.com/nature/journal/v473/n7346/full/nature10012.html Quantum annealing with manufactured spins] ''Nature'' 473, 194–198, 12 May 2011</ref><ref>[http://www.technologyreview.com/news/429429/the-cia-and-jeff-bezos-bet-on-quantum-computing/ The CIA and Jeff Bezos Bet on Quantum Computing] ''Technology Review'' October 4, 2012 by Tom Simonite</ref>
| |
| | |
| During the same year, researchers working at the [[University of Bristol]] created an all-bulk optics system able to run an iterative version of [[Shor's algorithm]]. They successfully managed to factorize 21.<ref>{{cite journal |title=Implementation of an iterative quantum order finding algorithm |author=Enrique Martin Lopez, Anthony Laing, Thomas Lawson, Roberto Alvarez, Xiao-Qi Zhou, Jeremy L. O'Brien |year=2011 |doi=10.1038/nphoton.2012.259 |journal=Nature Photonics |volume=6 |issue=11 |pages=773–776 | arxiv=1111.4147}}</ref>
| |
| | |
| In September 2011 researchers also proved that a quantum computer can be made with a [[Von Neumann architecture]] (separation of RAM).<ref>[http://arxiv.org/abs/1109.3743 Quantum computer with Von Neumann architecture]</ref>
| |
| | |
| In November 2011 researchers factorized 143 using 4 qubits.<ref>[http://arxiv.org/abs/1111.3726 Quantum Factorization of 143 on a Dipolar-Coupling NMR system]</ref>
| |
| | |
| In February 2012 [[IBM]] scientists said that they had made several breakthroughs in quantum computing with superconducting integrated circuits that put them "on the cusp of building systems that will take computing to a whole new level."<ref>[http://www.pcmag.com/article2/0,2817,2400930,00.asp IBM Says It's 'On the Cusp' of Building a Quantum Computer]</ref>
| |
| | |
| 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 crystal of diamond doped with some manner of impurity, that can easily be scaled up in size and functionality at room temperature. Two logical qubit directions of electron spin and nitrogen kernels spin were used. A system which formed an impulse of microwave radiation of certain duration and the form was developed for maintenance of protection against decoherence. By means of this computer Grover's algorithm for four variants of search has generated the right answer from the first try in 95% of cases.<ref>[http://www.futurity.org/science-technology/quantum-computer-built-inside-diamond/ Quantum computer built inside diamond]</ref>
| |
| | |
| 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 manufacture of its memory building blocks. A research team led by Australian engineers created the first working "quantum bit" based on a single atom in silicon, invoking the same technological platform that forms the building blocks of modern day computers, laptops and phones.<ref>{{cite web|title=Australian engineers write quantum computer 'qubit' in global breakthrough|url=http://www.theaustralian.com.au/australian-it/government/australian-engineers-write-quantum-computer-qubit-in-global-breakthrough/story-fn4htb9o-1226477592578|publisher=The Australian|accessdate=3 October 2012}}</ref>
| |
| <ref>{{cite web|title=Breakthrough in bid to create first quantum computer|url=http://newsroom.unsw.edu.au/news/technology/breakthrough-bid-create-first-quantum-computer|publisher=The University of New South Wales|accessdate=3 October 2012}}</ref>
| |
| | |
| In October 2012, [[Nobel Prizes]] were presented to [[David J. Wineland]] and [[Serge Haroche]] for their basic work on understanding the quantum world - work which may eventually help make ''quantum computing'' possible.<ref name="NYT-20121014">{{cite web |last=Frank |first=Adam |title=Cracking the Quantum Safe |url=http://www.nytimes.com/2012/10/14/opinion/sunday/the-possibilities-of-quantum-information.html |date=October 14, 2012 |publisher=[[New York Times]] |accessdate=October 14, 2012 }}</ref><ref name="NYT-20121009">{{cite web |last=Overbye |first=Dennis |title=A Nobel for Teasing Out the Secret Life of Atoms |url=http://www.nytimes.com/2012/10/10/science/french-and-us-scientists-win-nobel-physics-prize.html |date=October 9, 2012 |publisher=[[New York Times]] |accessdate=October 14, 2012 }}</ref>
| |
| | |
| In November 2012, the first [[quantum teleportation]] from one [[Macroscopic scale|macroscopic object]] to another was reported.<ref name="MIT-TR-20121115">{{cite web |author=The Physics arXiv Blog |title=First Teleportation from One Macroscopic Object to Another |url=http://www.technologyreview.com/view/507531/first-teleportation-from-one-macroscopic-object-to-another/ |date=November 15, 2012 |publisher=[[MIT Technology Review]] |accessdate=November 17, 2012 }}</ref><ref name="Arxiv-20121113">{{cite journal |last=Bao |first=Xiao-Hui |last2=Xu |first2=Xiao-Fan |last3=Li |first3=Che-Ming |last4=Yuan |first4=Zhen-Sheng |last5=Lu |first5=Chao-Yang |last6=Pan |first6=Jian-wei |title=Quantum teleportation between remote atomic-ensemble quantum memories |date=November 13, 2012 |journal=[[arXiv]] |arxiv=1211.2892 }}</ref>
| |
| | |
| 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 which may be good enough for practical problems. Science Feb 15, 2013
| |
| | |
| In May 2013, Google Inc announced that it was launching the Quantum Artificial Intelligence Lab, to be hosted by NASA’s Ames Research Center. The lab will house a 512-qubit quantum computer from D-Wave Systems, and the USRA (Universities Space Research Association) will invite researchers from around the world to share time on it. The goal being to study how quantum computing might advance machine learning<ref>{{cite web|title=Launching the Quantum Artificial Intelligence Lab|url=http://googleresearch.blogspot.co.uk/2013/05/launching-quantum-artificial.html|publisher=Research@Google Blog|accessdate=16 May 2013}}</ref>
| |
| | |
| ==Relation to computational complexity theory==
| |
| {{Main|Quantum complexity theory}}
| |
| | |
| [[File:BQP complexity class diagram.svg|thumb|The suspected relationship of BQP to other problem spaces.<ref>Nielsen, p. 42</ref>]]
| |
| 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 algorithm|probabilistic]] algorithms, so BQP on quantum computers is the counterpart of [[Bounded-error probabilistic polynomial|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.<ref>Nielsen, p. 41</ref> 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 ''[[Sharp-P|#P]]'' (or more precisely in the associated class of decision problems ''P<sup>#P</sup>''),<ref name=BernVazi>{{cite journal |last1=Bernstein |first1=Ethan |last2=Vazirani |first2=Umesh |doi=10.1137/S0097539796300921 |title=Quantum Complexity Theory |year=1997 |page=1411 |volume=26 |journal=SIAM Journal on Computing |url=http://www.cs.berkeley.edu/~vazirani/bv.ps |issue=5}}</ref> which is a subclass of [[PSPACE]].
| |
| | |
| BQP is suspected to be disjoint from [[NP-complete]] and a strict superset of [[P (complexity)|P]], but that is not known. Both [[integer factorization]] and [[discrete logarithm problem|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.<ref name=BernVazi/>
| |
| | |
| 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.<ref name=Ozhigov1>{{cite journal |last1=Ozhigov |first1=Yuri |title=Quantum Computers Speed Up Classical with Probability Zero |year=1999 |pages=1707–1714 |volume=10 |journal=Chaos Solitons Fractals |arxiv=quant-ph/9803064 |bibcode = 1998quant.ph..3064O |doi=10.1016/S0960-0779(98)00226-4 |issue=10 }}</ref> A similar fact takes place for particular computational tasks, like the search problem, for which Grover's algorithm is optimal.<ref name=Ozhigov2>{{cite journal |last1=Ozhigov |first1=Yuri |title=Lower Bounds of Quantum Search for Extreme Point |year=1999 |pages=2165–2172 |volume=A455 |journal=Proceedings of the London Royal Society |arxiv=quant-ph/9806001 |bibcode = 1999RSPSA.455.2165O |doi = 10.1098/rspa.1999.0397 |issue=1986 }}</ref>
| |
| | |
| Although quantum computers may be faster than classical computers, those described above can't solve any problems that classical computers can't solve, given enough time and memory (however, those amounts might be practically infeasible). A [[Turing machine]] can simulate <!-- add mention about [[Quantum Virtual Machines]] which can simulate quantum computer on classical one -->these quantum computers, so such a quantum computer could never solve an [[undecidable problem]] like the [[halting problem]]. The existence of "standard" quantum computers does not disprove the [[Church–Turing thesis]].<ref>Nielsen, p. 126</ref> 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.<ref>[[Scott Aaronson]], ''[http://arxiv.org/abs/quant-ph/0502072 NP-complete Problems and Physical Reality]'', ACM [[SIGACT]] News, Vol. 36, No. 1. (March 2005), pp. 30–52, section 7 "Quantum Gravity": "[...] to anyone who wants
| |
| a test or benchmark for a favorite quantum gravity theory,[author's footnote: That is, one without all the bother of making numerical predictions and comparing them to observation] let me humbly propose the following: ''can you define Quantum Gravity Polynomial-Time?'' [...] until we can say what it means for a ‘user’ to specify an ‘input’ and
| |
| ‘later’ receive an ‘output’—''there is no such thing as computation, not even theoretically.''" (emphasis in original)</ref>
| |
| | |
| ==See also==
| |
| *[[Chemical computer]]
| |
| *[[DNA computer]]
| |
| *[[Electronic quantum holography]]
| |
| *[[List of emerging technologies]]
| |
| *[[Natural computing]]
| |
| *[[Normal mode]]
| |
| *[[Photonic computing]]
| |
| *[[Post-quantum cryptography]]
| |
| *[[Quantum annealing]]
| |
| *[[Quantum bus]]
| |
| *[[Quantum cognition]]
| |
| *[[Quantum gate]]
| |
| *[[Quantum threshold theorem]]
| |
| *[[Soliton]]
| |
| *[[Timeline of quantum computing]]
| |
| *[[Topological quantum computer]]
| |
| | |
| ==References==
| |
| {{Reflist|30em}}
| |
| | |
| ==Bibliography==
| |
| *{{Cite book | author= [[Michael Nielsen|Nielsen, Michael]] and [[Isaac L. Chuang|Chuang, Isaac]] |title=Quantum Computation and Quantum Information |publisher=Cambridge University Press |location=Cambridge |year=2000 |isbn=0-521-63503-9 |oclc= 174527496 |url=http://books.google.com/books?id=aai-P4V9GJ8C&printsec=frontcover}}
| |
| | |
| ===General references===
| |
| <!-- These need to be inlined -->
| |
| *{{Cite journal | author=[[Derek Abbott]], [[Charles R. Doering]], [[Carlton M. Caves]], [[Daniel Lidar|Daniel M. Lidar]], [[Howard Brandt|Howard E. Brandt]], [[Alexander R. Hamilton]], [[David K. Ferry]], [[Julio Gea-Banacloche]], [[Sergey M. Bezrukov]], and [[Laszlo B. Kish]] |title=Dreams versus Reality: Plenary Debate Session on Quantum Computing |journal=Quantum Information Processing |year=2003 |volume=2 |issue=6 |pages=449–472 |doi=10.1023/B:QINP.0000042203.24782.9a | arxiv=quant-ph/0310130 |id={{hdl|2027.42/45526}}}}
| |
| *David P. DiVincenzo (2000). "The Physical Implementation of Quantum Computation". ''Experimental Proposals for Quantum Computation''. {{arxiv|quant-ph/0002077}}
| |
| *{{Cite journal | author=David P. DiVincenzo |title=Quantum Computation |journal=Science |year=1995 |volume=270 |issue=5234 |pages=255–261 |doi= 10.1126/science.270.5234.255 |bibcode = 1995Sci...270..255D }} Table 1 lists switching and dephasing times for various systems.
| |
| *{{Cite journal | author=[[Richard Feynman]] |title=Simulating physics with computers |journal=International Journal of Theoretical Physics |volume=21 |page=467 |year=1982 |doi = 10.1007/BF02650179 |bibcode = 1982IJTP...21..467F | issue=6–7 }}
| |
| *{{Cite book | author=Gregg Jaeger |title=Quantum Information: An Overview |publisher=Springer |location=Berlin |year=2006 |isbn=0-387-35725-4 |oclc=255569451}}
| |
| *{{Cite book | author= Stephanie Frank Singer |title=Linearity, Symmetry, and Prediction in the Hydrogen Atom |publisher=Springer |location=New York |year=2005 |isbn=0-387-24637-1 |oclc= 253709076}}
| |
| *{{Cite book | author= Giuliano Benenti |title=Principles of Quantum Computation and Information Volume 1 | publisher=World Scientific |location=New Jersey |year=2004 |isbn=981-238-830-3 |oclc= 179950736}}
| |
| *Sam Lomonaco [http://www.csee.umbc.edu/~lomonaco/Lectures.html#OxfordLectures Four Lectures on Quantum Computing given at Oxford University in July 2006]
| |
| *C. Adami, N.J. Cerf. (1998). "Quantum computation with linear optics". {{arxiv|quant-ph/9806048v1}}.
| |
| | |
| *<cite id=Joachim>{{Cite book
| |
| |author = Joachim Stolze,
| |
| |coauthors = Dieter Suter,
| |
| |year = 2004
| |
| |title = Quantum Computing
| |
| |publisher = Wiley-VCH
| |
| |isbn = 3-527-40438-4
| |
| }}</cite>
| |
| | |
| *<cite id=Ian>{{cite web
| |
| |author = Ian Mitchell,
| |
| |year = 1998
| |
| |title = Computing Power into the 21st Century: Moore's Law and Beyond
| |
| |url = http://citeseer.ist.psu.edu/mitchell98computing.html
| |
| }}</cite>
| |
| | |
| *<cite id=Rolf>{{cite web
| |
| |author = [[Rolf Landauer]],
| |
| |year = 1961
| |
| |title = Irreversibility and heat generation in the computing process
| |
| |url = http://www.research.ibm.com/journal/rd/053/ibmrd0503C.pdf
| |
| }}</cite>
| |
| | |
| *<cite id=Moore>{{Cite book
| |
| |author = [[Gordon E. Moore]]
| |
| |year = 1965
| |
| |title = Cramming more components onto integrated circuits
| |
| |journal = Electronics Magazine
| |
| }}</cite>
| |
| | |
| *<cite id=R.w.>{{Cite book
| |
| |author = R.W. Keyes,
| |
| |year = 1988
| |
| |title = Miniaturization of electronics and its limits
| |
| |journal = "IBM Journal of Research and Development"
| |
| }}</cite>
| |
| | |
| *<cite id=M.>{{cite web
| |
| |author = [[Michael Nielsen|M. A. Nielsen]],
| |
| |coauthors = E. Knill, ; [[Raymond Laflamme|R. Laflamme]],
| |
| |year =
| |
| |title = Complete Quantum Teleportation By Nuclear Magnetic Resonance
| |
| |url = http://citeseer.ist.psu.edu/595490.html
| |
| }}</cite>
| |
| | |
| *<cite id=Lieven>{{Cite book
| |
| |author = Lieven M.K. Vandersypen,
| |
| |coauthors = Constantino S. Yannoni, ; Isaac L. Chuang,
| |
| |year = 2000
| |
| |title = Liquid state NMR Quantum Computing
| |
| }}</cite>
| |
| | |
| *<cite id=Imai>{{Cite book
| |
| |author = Imai Hiroshi,
| |
| |coauthors = Hayashi Masahito,
| |
| |year = 2006
| |
| |title = Quantum Computation and Information
| |
| |publisher = Springer
| |
| |isbn = 3-540-33132-8
| |
| |location = Berlin
| |
| }}</cite>
| |
| | |
| *<cite id=Andre>{{cite web
| |
| |author = Andre Berthiaume,
| |
| |year = 1997
| |
| |title = Quantum Computation
| |
| |url = http://citeseer.ist.psu.edu/article/berthiaume97quantum.html
| |
| }}</cite>
| |
| | |
| *<cite id=David>{{cite web
| |
| |author = Daniel R. Simon,
| |
| |year = 1994
| |
| |title = On the Power of Quantum Computation
| |
| |publisher = Institute of Electrical and Electronic Engineers Computer Society Press
| |
| |url = http://citeseer.ist.psu.edu/simon94power.html
| |
| }}</cite>
| |
| | |
| *<cite id=rub>{{cite web
| |
| |title = Seminar Post Quantum Cryptology
| |
| |publisher = Chair for communication security at the Ruhr-University Bochum
| |
| |url = http://www.crypto.rub.de/its_seminar_ss08.html
| |
| }}</cite>
| |
| | |
| *<cite id=Sanders>{{cite web
| |
| |author = Laura Sanders,
| |
| |year = 2009
| |
| |title = First programmable quantum computer created
| |
| |url = http://www.sciencenews.org/view/generic/id/49951/title/First_programmable_quantum_computer_created
| |
| }}</cite>
| |
| *<cite id=sb>{{cite web
| |
| |title = New trends in quantum computation
| |
| |url = http://insti.physics.sunysb.edu/itp/conf/simons-qcomputation2/
| |
| }}
| |
| </cite>
| |
| | |
| ==External links==
| |
| {{Commons|Quantum computer}}
| |
| *[[Stanford Encyclopedia of Philosophy]]: "[http://plato.stanford.edu/entries/qt-quantcomp/ Quantum Computing]" by Amit Hagar.
| |
| *[http://www.quantiki.org/ Quantiki] – Wiki and portal with free-content related to quantum information science.
| |
| *[http://www.scottaaronson.com/blog/ Scott Aaronson's blog]<!--Comes highly recommended by Tim Gowers-->, which features informative and critical commentary on developments in the field<!--and which delivers regular smackdowns of D-Wave rubbish-->
| |
| *[http://arxiv.org/pdf/1310.1339.pdf Quantum Annealing and Computation: A Brief Documentary Note, A. Ghosh and S. Mukherjee]
| |
| *[http://www.lps.umd.edu/Quantum%20Computing%20Group/QuantumComputingIndex.html Maryland University Laboratory for Physical Sciences]: conducts researches for the quantum computer-based project led by the NSA, named 'Penetrating Hard Target'.
| |
| | |
| ;Lectures
| |
| *[https://www.coursera.org/course/qcomp Quantum Mechanics and Quantum Computation] — [[Coursera]] course by [[Umesh Vazirani]]
| |
| *[http://www.youtube.com/playlist?list=PL1826E60FD05B44E4 Quantum computing for the determined] — 22 video lectures by [[Michael Nielsen]]
| |
| *[http://www.quiprocone.org/Protected/DD_lectures.htm Video Lectures] by [[David Deutsch]]
| |
| *[http://www.quantware.ups-tlse.fr/IHP2006/ Lectures at the Institut Henri Poincaré (slides and videos)]
| |
| *[http://nanohub.org/resources/4778 Online lecture on An Introduction to Quantum Computing, Edward Gerjuoy (2008)]
| |
| *[http://www.youtube.com/watch?v=dWcT_qrBN_w Quantum Computing research by Mikko Möttönen at Aalto University (video)]
| |
| | |
| {{Quantum computing}}
| |
| {{Emerging technologies}}
| |
| {{Computer science}}
| |
| | |
| {{DEFAULTSORT:Quantum Computer}}
| |
| [[Category:Quantum information science| ]]
| |
| [[Category:Models of computation]]
| |
| [[Category:Quantum cryptography]]
| |
| [[Category:Information theory]]
| |
| [[Category:Computational complexity theory]]
| |
| [[Category:Classes of computers]]
| |
| [[Category:Theoretical computer science]]
| |
| [[Category:Open problems]]
| |
| [[Category:1980 introductions]]
| |