69-524: Education and Research Network ( ERNET ) is an autonomous scientific society of the Ministry of Electronics and Information Technology , Government of India . ERNET has made a significant contribution to the emergence of networking in the country. It practically brought the Internet to India and has built up national capabilities in the area of net-working, especially in protocol software engineering. It
138-530: A black box with a quantum state in superposition , sometimes referred to as quantum parallelism . Peter Shor built on these results with his 1994 algorithm for breaking the widely used RSA and Diffie–Hellman encryption protocols, which drew significant attention to the field of quantum computing. In 1996, Grover's algorithm established a quantum speedup for the widely applicable unstructured search problem. The same year, Seth Lloyd proved that quantum computers could simulate quantum systems without
207-407: A randomized algorithm , quantum mechanical notions like superposition and interference are largely irrelevant for program analysis . Quantum programs , in contrast, rely on precise control of coherent quantum systems. Physicists describe these systems mathematically using linear algebra . Complex numbers model probability amplitudes , vectors model quantum states , and matrices model
276-569: A 1984 paper, Charles Bennett and Gilles Brassard applied quantum theory to cryptography protocols and demonstrated that quantum key distribution could enhance information security . Quantum algorithms then emerged for solving oracle problems , such as Deutsch's algorithm in 1985, the Bernstein–Vazirani algorithm in 1993, and Simon's algorithm in 1994. These algorithms did not solve practical problems, but demonstrated mathematically that one could gain more information by querying
345-773: A 54-qubit machine, performing a computation that is impossible for any classical computer. However, the validity of this claim is still being actively researched. In December 2023, physicists, for the first time, reported the entanglement of individual molecules, which may have significant applications in quantum computing. Computer engineers typically describe a modern computer 's operation in terms of classical electrodynamics . Within these "classical" computers, some components (such as semiconductors and random number generators ) may rely on quantum behavior, but these components are not isolated from their environment, so any quantum information quickly decoheres . While programmers may depend on probability theory when designing
414-439: A classical bit; when both are nonzero, the qubit is in superposition. Such a quantum state vector acts similarly to a (classical) probability vector , with one key difference: unlike probabilities, probability amplitudes are not necessarily positive numbers. Negative amplitudes allow for destructive wave interference. When a qubit is measured in the standard basis , the result is a classical bit. The Born rule describes
483-411: A classical computer in any reasonable amount of time. This concept of extra ability has been called " quantum supremacy ". While such claims have drawn significant attention to the discipline, near-term practical use cases remain limited. For many years, the fields of quantum mechanics and computer science formed distinct academic communities. Modern quantum theory developed in the 1920s to explain
552-465: A computation, because the measurement at the end of the computation gives only one value. To be useful, a quantum algorithm must also incorporate some other conceptual ingredient. There are a number of models of computation for quantum computing, distinguished by the basic elements in which the computation is decomposed. A quantum gate array decomposes computation into a sequence of few-qubit quantum gates . A quantum computation can be described as
621-722: A mathematical consequence of this definition, CNOT | 00 ⟩ = | 00 ⟩ {\textstyle \operatorname {CNOT} |00\rangle =|00\rangle } , CNOT | 01 ⟩ = | 01 ⟩ {\textstyle \operatorname {CNOT} |01\rangle =|01\rangle } , CNOT | 10 ⟩ = | 11 ⟩ {\textstyle \operatorname {CNOT} |10\rangle =|11\rangle } , and CNOT | 11 ⟩ = | 10 ⟩ {\textstyle \operatorname {CNOT} |11\rangle =|10\rangle } . In other words,
690-471: A network of quantum logic gates and measurements. However, any measurement can be deferred to the end of quantum computation, though this deferment may come at a computational cost, so most quantum circuits depict a network consisting only of quantum logic gates and no measurements. Quantum parallelism is the heuristic that quantum computers can be thought of as evaluating a function for multiple input values simultaneously. This can be achieved by preparing
759-561: A network of quantum logic gates and measurements. However, any measurement can be deferred to the end of quantum computation, though this deferment may come at a computational cost, so most quantum circuits depict a network consisting only of quantum logic gates and no measurements. Any quantum computation (which is, in the above formalism, any unitary matrix of size 2 n × 2 n {\displaystyle 2^{n}\times 2^{n}} over n {\displaystyle n} qubits) can be represented as
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#1732779882639828-524: A network of quantum logic gates from a fairly small family of gates. A choice of gate family that enables this construction is known as a universal gate set , since a computer that can run such circuits is a universal quantum computer . One common such set includes all single-qubit gates as well as the CNOT gate from above. This means any quantum computation can be performed by executing a sequence of single-qubit gates together with CNOT gates. Though this gate set
897-495: A polynomial time algorithm for solving the dihedral hidden subgroup problem , which would break many lattice based cryptosystems, is a well-studied open problem. It has been proven that applying Grover's algorithm to break a symmetric (secret key) algorithm by brute force requires time equal to roughly 2 invocations of the underlying cryptographic algorithm, compared with roughly 2 in the classical case, meaning that symmetric key lengths are effectively halved: AES-256 would have
966-475: A quantum algorithm for integer factorization, could potentially break widely used public-key cryptography schemes like RSA, which rely on the difficulty of factoring large numbers. Post-quantum cryptography, which involves the development of cryptographic algorithms that are resistant to attacks by both classical and quantum computers, is an active area of research aimed at addressing this concern. Ongoing research in quantum cryptography and post-quantum cryptography
1035-426: A quantum system in a superposition of input states and applying a unitary transformation that encodes the function to be evaluated. The resulting state encodes the function's output values for all input values in the superposition, allowing for the computation of multiple outputs simultaneously. This property is key to the speedup of many quantum algorithms. However, "parallelism" in this sense is insufficient to speed up
1104-918: A sender and receiver exchange quantum states, they can guarantee that an adversary does not intercept the message, as any unauthorized eavesdropper would disturb the delicate quantum system and introduce a detectable change. With appropriate cryptographic protocols , the sender and receiver can thus establish shared private information resistant to eavesdropping. Modern fiber-optic cables can transmit quantum information over relatively short distances. Ongoing experimental research aims to develop more reliable hardware (such as quantum repeaters), hoping to scale this technology to long-distance quantum networks with end-to-end entanglement. Theoretically, this could enable novel technological applications, such as distributed quantum computing and enhanced quantum sensing . Progress in finding quantum algorithms typically focuses on this quantum circuit model, though exceptions like
1173-498: A single atomic particle using electromagnetic fields ). In principle, a classical computer can solve the same computational problems as a quantum computer, given enough time. Quantum advantage comes in the form of time complexity rather than computability , and quantum complexity theory shows that some quantum algorithms are exponentially more efficient than the best-known classical algorithms. A large-scale quantum computer could in theory solve computational problems unsolvable by
1242-642: A super-polynomial speedup, which is believed to be unlikely. Some quantum algorithms, like Grover's algorithm and amplitude amplification , give polynomial speedups over corresponding classical algorithms. Though these algorithms give comparably modest quadratic speedup, they are widely applicable and thus give speedups for a wide range of problems. Since chemistry and nanotechnology rely on understanding quantum systems, and such systems are impossible to simulate in an efficient manner classically, quantum simulation may be an important application of quantum computing. Quantum simulation could also be used to simulate
1311-461: A technique called quantum gate teleportation . An adiabatic quantum computer , based on quantum annealing , decomposes computation into a slow continuous transformation of an initial Hamiltonian into a final Hamiltonian, whose ground states contain the solution. Neuromorphic quantum computing (abbreviated as ‘n.quantum computing’) is an unconventional computing type of computing that uses neuromorphic computing to perform quantum operations. It
1380-475: A vector labeled ψ {\displaystyle \psi } . Because a qubit is a two-state system, any qubit state takes the form α | 0 ⟩ + β | 1 ⟩ {\displaystyle \alpha |0\rangle +\beta |1\rangle } , where | 0 ⟩ {\displaystyle |0\rangle } and | 1 ⟩ {\displaystyle |1\rangle } are
1449-416: Is 2 -dimensional, and this makes it challenging for a classical computer to simulate a quantum one: representing a 100-qubit system requires storing 2 classical values. The state of this one-qubit quantum memory can be manipulated by applying quantum logic gates , analogous to how classical memory can be manipulated with classical logic gates . One important gate for both classical and quantum computation
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#17327798826391518-459: Is an actively researched topic under the field of post-quantum cryptography . Some public-key algorithms are based on problems other than the integer factorization and discrete logarithm problems to which Shor's algorithm applies, like the McEliece cryptosystem based on a problem in coding theory . Lattice-based cryptosystems are also not known to be broken by quantum computers, and finding
1587-528: Is being enabled to support IPv6. The ERNET is supported by the following backbone sites which enable organizations located at different geographical locations to access various services. Ministry of Electronics and Information Technology (India) The Ministry of Electronics and Information Technology ( MEITy ) is an executive agency of the Union Government of the Republic of India . It
1656-410: 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). By comparison, a quantum computer could solve this problem exponentially faster 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
1725-575: Is crucial for ensuring the security of communication and data in the face of evolving quantum computing capabilities. Advances in these fields, such as the development of new QKD protocols, the improvement of QRNGs, and the standardization of post-quantum cryptographic algorithms, will play a key role in maintaining the integrity and confidentiality of information in the quantum era. Quantum cryptography enables new ways to transmit data securely; for example, quantum key distribution uses entangled quantum states to establish secure cryptographic keys . When
1794-672: Is in the quantum query model , which is a restricted model where lower bounds are much easier to prove and doesn't necessarily translate to speedups for practical problems. Other problems, including the simulation of quantum physical processes from chemistry and solid-state physics, the approximation of certain Jones polynomials , and the quantum algorithm for linear systems of equations have quantum algorithms appearing to give super-polynomial speedups and are BQP -complete. Because these problems are BQP-complete, an equally fast classical algorithm for them would imply that no quantum algorithm gives
1863-466: Is infinite, it can be replaced with a finite gate set by appealing to the Solovay-Kitaev theorem . Implementation of Boolean functions using the few-qubit quantum gates is presented here. A measurement-based quantum computer decomposes computation into a sequence of Bell state measurements and single-qubit quantum gates applied to a highly entangled initial state (a cluster state ), using
1932-465: Is known as a superposition of | 0 ⟩ {\displaystyle |0\rangle } and | 1 ⟩ {\displaystyle |1\rangle } . A two-dimensional vector mathematically represents a qubit state. Physicists typically use Dirac notation for quantum mechanical linear algebra , writing | ψ ⟩ {\displaystyle |\psi \rangle } ' ket psi ' for
2001-1134: Is simply to select a qubit and apply that gate to the target qubit while leaving the remainder of the memory unaffected. Another way is to apply the gate to its target only if another part of the memory is in a desired state. These two choices can be illustrated using another example. The possible states of a two-qubit quantum memory are | 00 ⟩ := ( 1 0 0 0 ) ; | 01 ⟩ := ( 0 1 0 0 ) ; | 10 ⟩ := ( 0 0 1 0 ) ; | 11 ⟩ := ( 0 0 0 1 ) . {\displaystyle |00\rangle :={\begin{pmatrix}1\\0\\0\\0\end{pmatrix}};\quad |01\rangle :={\begin{pmatrix}0\\1\\0\\0\end{pmatrix}};\quad |10\rangle :={\begin{pmatrix}0\\0\\1\\0\end{pmatrix}};\quad |11\rangle :={\begin{pmatrix}0\\0\\0\\1\end{pmatrix}}.} The controlled NOT (CNOT) gate can then be represented using
2070-531: Is the NOT gate, which can be represented by a matrix X := ( 0 1 1 0 ) . {\displaystyle X:={\begin{pmatrix}0&1\\1&0\end{pmatrix}}.} Mathematically, the application of such a logic gate to a quantum state vector is modelled with matrix multiplication . Thus The mathematics of single qubit gates can be extended to operate on multi-qubit quantum memories in two important ways. One way
2139-449: Is the first internet service in india. It has not only succeeded in building a large network that provides various facilities to the intellectual segment of Indian society—the research and education community, it has over the years become a trendsetter in the field of networking. ERNET is largest nationwide terrestrial and satellite network with point of presence located at the premiere educational and research institutions in major cities of
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2208-420: The dimension of the state space . As an example, the vector 1 / √2 |00⟩ + 1 / √2 |01⟩ represents a two-qubit state, a tensor product of the qubit |0⟩ with the qubit 1 / √2 |0⟩ + 1 / √2 |1⟩ . This vector inhabits a four-dimensional vector space spanned by
2277-416: The hidden subgroup problem for abelian finite groups. These algorithms depend on the primitive of the quantum Fourier transform . No mathematical proof has been found that shows that an equally fast classical algorithm cannot be discovered, but evidence suggests that this is unlikely. Certain oracle problems like Simon's problem and the Bernstein–Vazirani problem do give provable speedups, though this
2346-1036: The norm-squared correspondence between amplitudes and probabilities—when measuring a qubit α | 0 ⟩ + β | 1 ⟩ {\displaystyle \alpha |0\rangle +\beta |1\rangle } , the state collapses to | 0 ⟩ {\displaystyle |0\rangle } with probability | α | 2 {\displaystyle |\alpha |^{2}} , or to | 1 ⟩ {\displaystyle |1\rangle } with probability | β | 2 {\displaystyle |\beta |^{2}} . Any valid qubit state has coefficients α {\displaystyle \alpha } and β {\displaystyle \beta } such that | α | 2 + | β | 2 = 1 {\displaystyle |\alpha |^{2}+|\beta |^{2}=1} . As an example, measuring
2415-428: The quantum adiabatic algorithm exist. Quantum algorithms can be roughly categorized by the type of speedup achieved over corresponding classical algorithms. Quantum algorithms that offer more than a polynomial speedup over the best-known classical algorithm include Shor's algorithm for factoring and the related quantum algorithms for computing discrete logarithms , solving Pell's equation , and more generally solving
2484-421: The qubit (or "quantum bit"), serves the same function as the bit in classical computing. However, unlike a classical bit, which can be in one of two states (a binary ), a qubit can exist in a superposition of its two "basis" states, which loosely means that it is in both states simultaneously. When measuring a qubit, the result is a probabilistic output of a classical bit. If a quantum computer manipulates
2553-569: The wave–particle duality observed at atomic scales, and digital computers emerged in the following decades to replace human computers for tedious calculations. Both disciplines had practical applications during World War II ; computers played a major role in wartime cryptography , and quantum physics was essential for nuclear physics used in the Manhattan Project . As physicists applied quantum mechanical models to computational problems and swapped digital bits for qubits ,
2622-532: The "Department of Information Technology", it was renamed as the Department of Electronics and Information Technology in 2012. On 19 July 2016, DeitY was made into full-fledged ministry, which henceforth is known as the Ministry of Electronics and Information Technology, bifurcating it from the Ministry of Communications and Information Technology. The following is a list of child agencies subordinated within
2691-461: The "Ministry of Electronics and Information Technology, Union Government of the Republic of India". To boost and leverage Quantum computing potential, ministry has done a partnership with Amazon Web Services (AWS). The initiative is said to boost researchers and scientists work on quantum computing and will provide access to Amazon’s Braket cloud-based quantum computing service. Ministry based on
2760-410: The CNOT applies a NOT gate ( X {\textstyle X} from before) to the second qubit if and only if the first qubit is in the state | 1 ⟩ {\textstyle |1\rangle } . If the first qubit is | 0 ⟩ {\textstyle |0\rangle } , nothing is done to either qubit. In summary, quantum computation can be described as
2829-468: The Department of Electronics (DoE), with funding support from the Government of India and United Nations Development Program (UNDP), involving eight premier institutions as participating agencies— NCST (National Centre for Software Technology) [Now CDAC ] Bombay, IISc (Indian Institute of Science) Bangalore, five IITs (Indian Institutes of Technology) at Delhi, Bombay, Kanpur, Kharagpur and Madras, and
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2898-564: The DoE, New Delhi. ERNET began as a multi protocol network with both the TCP/IP and the OSI -IP protocol stacks running over the leased-line portion of the backbone. Since 1995, however, almost all traffic is carried over TCP/IP. ERNET backbone is a sophisticated link of terrestrial and satellite-based wide area networks . The satellite WAN, using VSAT technology. The VSAT network acts as an overlay for
2967-417: The algorithm iterates is that of all possible answers. An example and possible application of this is a password cracker that attempts to guess a password. Breaking symmetric ciphers with this algorithm is of interest to government agencies. Quantum annealing relies on the adiabatic theorem to undertake calculations. A system is placed in the ground state for a simple Hamiltonian, which slowly evolves to
3036-434: The basis vectors |00⟩ , |01⟩ , |10⟩ , and |11⟩ . The Bell state 1 / √2 |00⟩ + 1 / √2 |11⟩ is impossible to decompose into the tensor product of two individual qubits—the two qubits are entangled because their probability amplitudes are correlated . In general, the vector space for an n -qubit system
3105-609: The behavior of atoms and particles at unusual conditions such as the reactions inside a collider . In June 2023, IBM computer scientists reported that a quantum computer produced better results for a physics problem than a conventional supercomputer. About 2% of the annual global energy output is used for nitrogen fixation to produce ammonia for the Haber process in the agricultural fertilizer industry (even though naturally occurring organisms also produce ammonia). Quantum simulations might be used to understand this process and increase
3174-597: The bit is the basic concept of classical information theory, the qubit is the fundamental unit of quantum information . The same term qubit is used to refer to an abstract mathematical model and to any physical system that is represented by that model. A classical bit, by definition, exists in either of two physical states, which can be denoted 0 and 1. A qubit is also described by a state, and two states often written | 0 ⟩ {\displaystyle |0\rangle } and | 1 ⟩ {\displaystyle |1\rangle } serve as
3243-401: The country. Focus of ERNET is not limited to just providing connectivity, but to meet the entire needs of the educational and research institutions by hosting and providing relevant information to their users. Research and Development and Training are integral parts of ERNET activities. The activities at ERNET India are organised around five technology focus areas: ERNET was initiated in 1986 by
3312-718: The database, quadratically fewer than the Ω ( n ) {\displaystyle \Omega (n)} queries required for 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. Many examples of provable quantum speedups for query problems are based on Grover's algorithm, including Brassard, Høyer, and Tapp's algorithm for finding collisions in two-to-one functions, and Farhi, Goldstone, and Gutmann's algorithm for evaluating NAND trees. Problems that can be efficiently addressed with Grover's algorithm have
3381-497: The energy efficiency of production. It is expected that an early use of quantum computing will be modeling that improves the efficiency of the Haber–Bosch process by the mid-2020s although some have predicted it will take longer. A notable application of quantum computation is for attacks on cryptographic systems that are currently in use. Integer factorization , which underpins the security of public key cryptographic systems,
3450-494: The exponential overhead present in classical simulations, validating Feynman's 1982 conjecture. Over the years, experimentalists have constructed small-scale quantum computers using trapped ions and superconductors. In 1998, a two-qubit quantum computer demonstrated the feasibility of the technology, and subsequent experiments have increased the number of qubits and reduced error rates. In 2019, Google AI and NASA announced that they had achieved quantum supremacy with
3519-638: The fields of cryptography and cybersecurity. Quantum cryptography, which relies on the principles of quantum mechanics, offers the possibility of secure communication channels that are resistant to eavesdropping. Quantum key distribution (QKD) protocols, such as BB84, enable the secure exchange of cryptographic keys between parties, ensuring the confidentiality and integrity of communication. Moreover, quantum random number generators (QRNGs) can produce high-quality random numbers, which are essential for secure encryption. However, quantum computing also poses challenges to traditional cryptographic systems. Shor's algorithm,
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#17327798826393588-494: The fields of quantum mechanics and computer science began to converge. In 1980, Paul Benioff introduced the quantum Turing machine , which uses quantum theory to describe a simplified computer. When digital computers became faster, physicists faced an exponential increase in overhead when simulating quantum dynamics , prompting Yuri Manin and Richard Feynman to independently suggest that hardware based on quantum phenomena might be more efficient for computer simulation. In
3657-400: The following matrix: CNOT := ( 1 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 ) . {\displaystyle \operatorname {CNOT} :={\begin{pmatrix}1&0&0&0\\0&1&0&0\\0&0&0&1\\0&0&1&0\end{pmatrix}}.} As
3726-415: The following properties: For problems with all these properties, the running time of Grover's algorithm on a quantum computer scales 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 is a Boolean satisfiability problem , where the database through which
3795-561: The near future, but noise in quantum gates limits their reliability. Scientists at Harvard University successfully created "quantum circuits" that correct errors more efficiently than alternative methods, which may potentially remove a major obstacle to practical quantum computers. The Harvard research team was supported by MIT , QuEra Computing , Caltech , and Princeton University and funded by DARPA 's Optimization with Noisy Intermediate-Scale Quantum devices (ONISQ) program. Quantum computing has significant potential applications in
3864-499: The operation of these quantum devices, and a scalable quantum computer could perform some calculations exponentially faster than any modern "classical" computer. Theoretically a large-scale quantum computer could break some widely used encryption schemes and aid physicists in performing physical simulations ; however, the current state of the art is largely experimental and impractical, with several obstacles to useful applications. The basic unit of information in quantum computing,
3933-572: The operations that can be performed on these states. Programming a quantum computer is then a matter of composing operations in such a way that the resulting program computes a useful result in theory and is implementable in practice. As physicist Charlie Bennett describes the relationship between quantum and classical computers, A classical computer is a quantum computer ... so we shouldn't be asking about "where do quantum speedups come from?" We should say, "well, all computers are quantum. ... Where do classical slowdowns come from?" Just as
4002-598: The physical problem at hand and then leverage their respective physics properties of the system to seek the “minimum”. Neuromorphic quantum computing and quantum computing share similar physical properties during computation. A topological quantum computer decomposes computation into the braiding of anyons in a 2D lattice. A quantum Turing machine is the quantum analog of a Turing machine . All of these models of computation—quantum circuits, one-way quantum computation , adiabatic quantum computation, and topological quantum computation —have been shown to be equivalent to
4071-516: The proposal received and vetted by a steering committee will approve and sanction the set-up of the lab to bolster the quantum computing capability in India. Quantum computing A quantum computer is a computer that exploits quantum mechanical phenomena. On small scales, physical matter exhibits properties of both particles and waves , and quantum computing leverages this behavior using specialized hardware. Classical physics cannot explain
4140-570: The quantum Turing machine; given a perfect implementation of one such quantum computer, it can simulate all the others with no more than polynomial overhead. This equivalence need not hold for practical quantum computers, since the overhead of simulation may be too large to be practical. The threshold theorem shows how increasing the number of qubits can mitigate errors, yet fully fault-tolerant quantum computing remains "a rather distant dream". According to some researchers, noisy intermediate-scale quantum ( NISQ ) machines may have specialized uses in
4209-406: The quantum counterparts of the classical states 0 and 1. However, the quantum states | 0 ⟩ {\displaystyle |0\rangle } and | 1 ⟩ {\displaystyle |1\rangle } belong to a vector space , meaning that they can be multiplied by constants and added together, and the result is again a valid quantum state. Such a combination
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#17327798826394278-443: The qubit 1 / 2 | 0 ⟩ + 1 / 2 | 1 ⟩ {\displaystyle 1/{\sqrt {2}}|0\rangle +1/{\sqrt {2}}|1\rangle } would produce either | 0 ⟩ {\displaystyle |0\rangle } or | 1 ⟩ {\displaystyle |1\rangle } with equal probability. Each additional qubit doubles
4347-837: The qubit in a particular way, wave interference effects can amplify the desired measurement results. The design of quantum algorithms involves creating procedures that allow a quantum computer to perform calculations efficiently and quickly. Quantum computers are not yet practical for real work. Physically engineering high-quality qubits has proven challenging. If a physical qubit is not sufficiently isolated from its environment, it suffers from quantum decoherence , introducing noise into calculations. National governments have invested heavily in experimental research that aims to develop scalable qubits with longer coherence times and lower error rates. Example implementations include superconductors (which isolate an electrical current by eliminating electrical resistance ) and ion traps (which confine
4416-509: The same security against an attack using Grover's algorithm that AES-128 has against classical brute-force search (see Key size ). The most well-known example of a problem that allows for a polynomial quantum speedup is unstructured search , which involves finding a marked item out of a list of n {\displaystyle n} items in a database. This can be solved by Grover's algorithm using O ( n ) {\displaystyle O({\sqrt {n}})} queries to
4485-735: 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. Identifying cryptographic systems that may be secure against quantum algorithms
4554-399: The standard basis states , and α {\displaystyle \alpha } and β {\displaystyle \beta } are the probability amplitudes , which are in general complex numbers . If either α {\displaystyle \alpha } or β {\displaystyle \beta } is zero, the qubit is effectively
4623-482: The terrestrial WAN by providing backup links between the backbone sites. International connectivity is achieved through gateways at New Delhi , Mumbai , Bangalore and Kolkata , with a total capacity of 6.64 Mb. Daily traffic over ERNET exceeds 200 GB. ERNET architecture is based on industry standard TCP/IP protocol. This network had undergone a major upgrade during year 2000–2001 in association with CMC Ltd. (A Govt. of India Undertaking, then). ERNET backbone
4692-607: Was carved out of the Ministry of Communications and Information Technology on 19 July 2016 as a standalone ministerial agency responsible for IT policy, strategy and development of the electronics industry . Under the sponsorship of the Ministry of Electronics and Information Technology , the "Northeast Heritage" Web, owned by the Government of India , publishes information on Northeast India , in 5 Indian languages , Assamese , Meitei ( Manipuri ), Bodo , Khasi and Mizo, in addition to Hindi and English . Previously known as
4761-434: Was suggested that quantum algorithms, which are algorithms that run on a realistic model of quantum computation, can be computed equally efficiently with neuromorphic quantum computing. Both, traditional quantum computing and neuromorphic quantum computing are physics-based unconventional computing approaches to computations and do not follow the von Neumann architecture . They both construct a system (a circuit) that represents
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