A quantum computer is a computer that takes advantage of quantum mechanical phenomena. On small scales, physical matter exhibits properties of both particles and waves, and quantum computing leverages this behavior, specifically quantum superposition and entanglement, using specialized hardware that supports the preparation and manipulation of quantum states.

Classical physics cannot explain the operation of a quantum computer, and a scalable quantum computer, if it existed, could perform some calculations exponentially faster (with respect to input size scaling)^[2] than any current "classical" computer. A large-scale quantum computer could break widely used encryption schemes and aid physicists in performing physical simulations; however, the current state of the technology is largely experimental and impractical, with several obstacles to useful applications. Moreover, scalable quantum computers do not hold promise for many practical tasks, and for many important tasks quantum speedups are proven impossible.

The basic unit of information in quantum computing is the qubit, similar to the bit in traditional digital electronics. Unlike a classical bit, a qubit can exist in a superposition of its two "basis" states. When measuring a qubit, the result is a probabilistic output of a classical bit, therefore making quantum computers nondeterministic in general. If a quantum computer manipulates 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.

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. Paradoxically, perfectly isolating qubits is also undesirable because quantum computations typically need to initialize qubits, perform controlled qubit interactions, and measure the resulting quantum states. Each of those operations introduces errors and suffers from noise, and such inaccuracies accumulate.

In principle, a non-quantum (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 for carefully selected tasks require exponentially fewer computational steps than the best known non-quantum algorithms. Such tasks can in theory be solved on a large-scale quantum computer whereas classical computers would not finish computations in any reasonable amount of time. However, quantum speedup is not universal or even typical across computational tasks, since basic tasks such as sorting are proven to not allow any asymptotic quantum speedup. Claims of quantum supremacy have drawn significant attention to the discipline, but are demonstrated on contrived tasks, while near-term practical use cases remain limited.

History

For many years, the fields of quantum mechanics and computer science formed distinct academic communities.^[3] Modern quantum theory developed in the 1920s to explain the wave–particle duality observed at atomic scales,^[4] and digital computers emerged in the following decades to replace human computers for tedious calculations.^[5] Both disciplines had practical applications during World War II; computers played a major role in wartime cryptography,^[6] and quantum physics was essential for the nuclear physics used in the Manhattan Project.^[7]

As physicists applied quantum mechanical models to computational problems and swapped digital bits for qubits, 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.^[8] When digital computers became faster, physicists faced an exponential increase in overhead when simulating quantum dynamics,^[9] prompting Yuri Manin and Richard Feynman to independently suggest that hardware based on quantum phenomena might be more efficient for computer simulation.^[10][11][12] In a 1984 paper, Charles Bennett and Gilles Brassard applied quantum theory to cryptography protocols and demonstrated that quantum key distribution could enhance information security.^[13][14]

Quantum algorithms then emerged for solving oracle problems, such as Deutsch's algorithm in 1985,^[15] the Bernstein–Vazirani algorithm in 1993,^[16] and Simon's algorithm in 1994.^[17] These algorithms did not solve practical problems, but demonstrated mathematically that one could gain more information by querying a black box with a quantum state in superposition, sometimes referred to as quantum parallelism.^[18]

Peter Shor built on these results with his 1994 algorithms for breaking the widely used RSA and Diffie–Hellman encryption protocols,^[19] which drew significant attention to the field of quantum computing.^[20] In 1996, Grover's algorithm established a quantum speedup for the widely applicable unstructured search problem.^[21][22] The same year, Seth Lloyd proved that quantum computers could simulate quantum systems without the exponential overhead present in classical simulations,^[23] validating Feynman's 1982 conjecture.^[24]

Over the years, experimentalists have constructed small-scale quantum computers using trapped ions and superconductors.^[25] In 1998, a two-qubit quantum computer demonstrated the feasibility of the technology,^[26][27] and subsequent experiments have increased the number of qubits and reduced error rates.^[25]

In 2019, Google AI and NASA announced that they had achieved quantum supremacy with a 54-qubit machine, performing a computation that is impossible for any classical computer.^[28][29][30] However, the validity of this claim is still being actively researched.^[31][32]

Finland completed its first quantum computer, a 5-qubit one, in 2021, and a 20- qubit one in 2023.^[33] Finland announced its efforts in quantum computing development in November 2020 with a total budget of EUR 20.7 million from the government to develop a 50-qubit quantum computer in 2024. In the coming years, the development will continue as the Finnish government has announced a total budget of EUR 70 million to scale up the quantum computer towards 300 qubits and quantum advantage.^[34]

The threshold theorem shows how increasing the number of qubits can mitigate errors,^[35] yet fully fault-tolerant quantum computing remains "a rather distant dream".^[36] According to some researchers, noisy intermediate-scale quantum (NISQ) machines may have specialized uses in the near future, but noise in quantum gates limits their reliability.^[36]

Investment in quantum computing research has increased in the public and private sectors.^[37][38] As one consulting firm summarized,^[39]

... investment dollars are pouring in, and quantum-computing start-ups are proliferating. ... While quantum computing promises to help businesses solve problems that are beyond the reach and speed of conventional high-performance computers, use cases are largely experimental and hypothetical at this early stage.

With focus on business management’s point of view, the potential applications of quantum computing into four major categories are cybersecurity, data analytics and artificial intelligence, optimization and simulation, and data management and searching.^[40]

In December 2023, physicists, for the first time, report the entanglement of individual molecules, which may have significant applications in quantum computing.^[41] Also in December 2023, 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.^[42][43] 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.^[44][45] Research efforts are ongoing to jumpstart quantum computing through topological and photonic approaches as well.^[46]

Quantum information processing

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 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 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,^[47]

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?"

Quantum information

Just as 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 ${\displaystyle |0\rangle }$ and ${\displaystyle |1\rangle }$ serve as the quantum counterparts of the classical states 0 and 1. However, the quantum states ${\displaystyle |0\rangle }$ and ${\displaystyle |1\rangle }$ 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 is known as a superposition of ${\displaystyle |0\rangle }$ and ${\displaystyle |1\rangle }$.^[48][49]

A two-dimensional vector mathematically represents a qubit state. Physicists typically use Dirac notation for quantum mechanical linear algebra, writing ${\displaystyle |\psi \rangle }$ 'ket psi' for a vector labeled ${\displaystyle \psi }$ . Because a qubit is a two-state system, any qubit state takes the form ${\displaystyle \alpha |0\rangle +\beta |1\rangle }$ , where ${\displaystyle |0\rangle }$ and ${\displaystyle |1\rangle }$ are the standard basis states,^[a] and ${\displaystyle \alpha }$ and ${\displaystyle \beta }$ are the probability amplitudes, which are in general complex numbers.^[49] If either ${\displaystyle \alpha }$ or ${\displaystyle \beta }$ is zero, the qubit is effectively 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.^[51] 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 the norm-squared correspondence between amplitudes and probabilities—when measuring a qubit ${\displaystyle \alpha |0\rangle +\beta |1\rangle }$, the state collapses to ${\displaystyle |0\rangle }$ with probability ${\displaystyle |\alpha |^{2}}$, or to ${\displaystyle |1\rangle }$ with probability ${\displaystyle |\beta |^{2}}$. Any valid qubit state has coefficients ${\displaystyle \alpha }$ and ${\displaystyle \beta }$ such that ${\displaystyle |\alpha |^{2}+|\beta |^{2}=1}$. As an example, measuring the qubit ${\displaystyle 1/{\sqrt {2}}|0\rangle +1/{\sqrt {2}}|1\rangle }$ would produce either ${\displaystyle |0\rangle }$ or ${\displaystyle |1⟩<!--\; ⟩\; -->}$Zdroj:https://en.wikipedia.org?pojem=Quantum_computers
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