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Quantum Error Correction
Quantum error correction (QEC) is used in quantum computing to protect quantum information from errors due to decoherence and other quantum noise. Quantum error correction is theorised as essential to achieve fault tolerant quantum computing that can reduce the effects of noise on stored quantum information, faulty quantum gates, faulty quantum preparation, and faulty measurements. Classical error correction employs redundancy. The simplest albeit inefficient approach is the repetition code. The idea is to store the information multiple times, and—if these copies are later found to disagree—take a majority vote; e.g. suppose we copy a bit in the one state three times. Suppose further that a noisy error corrupts the three-bit state so that one of the copied bits is equal to zero but the other two are equal to one. Assuming that noisy errors are independent and occur with some sufficiently low probability ''p'', it is most likely that the error is a single-bit error and the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Computer
Quantum computing is a type of computation whose operations can harness the phenomena of quantum mechanics, such as superposition, interference, and entanglement. Devices that perform quantum computations are known as quantum computers. Though current quantum computers may be too small to outperform usual (classical) computers for practical applications, larger realizations are believed to be capable of solving certain computational problems, such as integer factorization (which underlies RSA encryption), substantially faster than classical computers. The study of quantum computing is a subfield of quantum information science. There are several models of quantum computation with the most widely used being quantum circuits. Other models include the quantum Turing machine, quantum annealing, and adiabatic quantum computation. Most models are based on the quantum bit, or " qubit", which is somewhat analogous to the bit in classical computation. A qubit can be in a 1 or 0 qu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Superposition
Quantum superposition is a fundamental principle of quantum mechanics. It states that, much like waves in classical physics, any two (or more) quantum states can be added together ("superposed") and the result will be another valid quantum state; and conversely, that every quantum state can be represented as a sum of two or more other distinct states. Mathematically, it refers to a property of solutions to the Schrödinger equation; since the Schrödinger equation is linear, any linear combination of solutions will also be a solution(s) . An example of a physically observable manifestation of the wave nature of quantum systems is the interference peaks from an electron beam in a double-slit experiment. The pattern is very similar to the one obtained by diffraction of classical waves. Another example is a quantum logical qubit state, as used in quantum information processing, which is a quantum superposition of the "basis states" , 0 \rangle and , 1 \rangle . Here ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fock State
In quantum mechanics, a Fock state or number state is a quantum state that is an element of a Fock space with a well-defined number of particles (or quanta). These states are named after the Soviet physicist Vladimir Fock. Fock states play an important role in the second quantization formulation of quantum mechanics. The particle representation was first treated in detail by Paul Dirac for bosons and by Pascual Jordan and Eugene Wigner for fermions. The Fock states of bosons and fermions obey useful relations with respect to the Fock space creation and annihilation operators. Definition One specifies a multiparticle state of N non-interacting identical particles by writing the state as a sum of tensor products of N one-particle states. Additionally, depending on the integrality of the particles' spin, the tensor products must be alternating (anti-symmetric) or symmetric products of the underlying one-particle Hilbert space. Specifically: * Fermions, having half-integer sp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Harmonic Oscillator
量子調和振動子 は、 古典調和振動子 の 量子力学 類似物です。任意の滑らかな ポテンシャル は通常、安定した 平衡点 の近くで 調和ポテンシャル として近似できるため、最も量子力学における重要なモデル系。さらに、これは正確な 解析解法が知られている数少ない量子力学系の1つである。 author=Griffiths, David J. , title=量子力学入門 , エディション=2nd , 出版社=プレンティス・ホール , 年=2004 , isbn=978-0-13-805326-0 , author-link=David Griffiths (物理学者) , URL アクセス = 登録 , url=https://archive.org/details/introductiontoel00grif_0 One-dimensional harmonic oscillator Hamiltonian and energy eigenstates 粒子の ハミルトニアン は次のとおりです。 \hat H = \frac + \frac k ^2 = \frac + \frac m \omega^2 ^2 \, , ここで、 は粒子の質量、 は力定数、\omega = \sqrt は ��動子の [角周波数 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Channel
In quantum information theory, a quantum channel is a communication channel which can transmit quantum information, as well as classical information. An example of quantum information is the state of a qubit. An example of classical information is a text document transmitted over the Internet. More formally, quantum channels are completely positive (CP) trace-preserving maps between spaces of operators. In other words, a quantum channel is just a quantum operation viewed not merely as the reduced dynamics of a system but as a pipeline intended to carry quantum information. (Some authors use the term "quantum operation" to also include trace-decreasing maps while reserving "quantum channel" for strictly trace-preserving maps.) Memoryless quantum channel We will assume for the moment that all state spaces of the systems considered, classical or quantum, are finite-dimensional. The memoryless in the section title carries the same meaning as in classical information theory: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shore Code
A shore or a shoreline is the fringe of land at the edge of a large body of water, such as an ocean, sea, or lake. In physical oceanography, a shore is the wider fringe that is geologically modified by the action of the body of water past and present, while the beach is at the edge of the shore, representing the intertidal zone where there is one. In contrast to a coast, a shore can border any body of water, while the coast must border an ocean or a sea. Therefore, in that sense, a coast is a type of shore. However, the word "coast" often refers to an area far wider than the shore, often stretching miles into the interior. Shores are influenced by the topography of the surrounding landscape, as well as by water induced erosion, such as Wind wave, waves. The geology, geological composition of Rock (geology), rock and soil dictates the type of shore which is created. Rivieras ''Riviera'' is an Italian word for "shoreline", ultimately derived from Latin ''ripa'' ("riverbank"). ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Error Correction Of Phase Flip Using Three Qubits
In physics, a quantum (plural quanta) is the minimum amount of any physical entity (physical property) involved in an fundamental interaction, interaction. The fundamental notion that a physical property can be "quantized" is referred to as "the hypothesis of quantization (physics), quantization". This means that the magnitude of the physical property can take on only Wiktionary:discrete, discrete values consisting of integer multiples of one quantum. For example, a photon is a single quantum of light (or of any other form of electromagnetic radiation). Similarly, the energy of an electron bound within an atom is quantized and can exist only in certain discrete values. (Atoms and matter in general are stable because electrons can exist only at discrete energy levels within an atom.) Quantization is one of the foundations of the much broader physics of quantum mechanics. Quantization of energy and its influence on how energy and matter interact (quantum electrodynamics) is part of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fidelity Of Quantum States
In quantum mechanics, notably in quantum information theory, fidelity is a measure of the "closeness" of two quantum states. It expresses the probability that one state will pass a test to identify as the other. The fidelity is not a metric on the space of density matrices, but it can be used to define the Bures metric on this space. Given two density operators \rho and \sigma, the fidelity is generally defined as the quantity F(\rho, \sigma) = \left(\operatorname \sqrt\right)^2. In the special case where \rho and \sigma represent pure quantum states, namely, \rho=, \psi_\rho\rangle\!\langle\psi_\rho, and \sigma=, \psi_\sigma\rangle\!\langle\psi_\sigma, , the definition reduces to the squared overlap between the states: F(\rho, \sigma)=, \langle\psi_\rho, \psi_\sigma\rangle, ^2. While not obvious from the general definition, the fidelity is symmetric: F(\rho,\sigma)=F(\sigma,\rho). Motivation Given two random variables X,Y with values (1, ..., n) ( categorical random varia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fidelity Error Correction Bit Flips
Fidelity is the quality of faithfulness or loyalty. Its original meaning regarded duty in a broader sense than the related concept of ''fealty''. Both derive from the Latin word ''fidēlis'', meaning "faithful or loyal". In the City of London financial markets it has traditionally been used in the sense encompassed in the motto "My word is my bond". Audio and electronics In audio, "fidelity" denotes how accurately a copy reproduces its source. In the 1950s, the terms " high fidelity" or "hi-fi" were popularized for equipment and recordings which exhibited more accurate sound reproduction. For example, a worn gramophone record will have a lower fidelity than one in good condition, and a recording made by a low budget record company in the early 20th century is likely to have significantly less audio fidelity than a good modern recording. Similarly in electronics, fidelity refers to the correspondence of the output signal to the input signal, rather than sound quality, as in the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isaac L
Isaac; grc, Ἰσαάκ, Isaák; ar, إسحٰق/إسحاق, Isḥāq; am, ይስሐቅ is one of the three patriarchs of the Israelites and an important figure in the Abrahamic religions, including Judaism, Christianity, and Islam. He was the son of Abraham and Sarah, the father of Jacob and Esau, and the grandfather of the twelve tribes of Israel. Isaac's name means "he will laugh", reflecting the laughter, in disbelief, of Abraham and Sarah, when told by God that they would have a child., He is the only patriarch whose name was not changed, and the only one who did not move out of Canaan. According to the narrative, he died aged 180, the longest-lived of the three patriarchs. Etymology The anglicized name "Isaac" is a transliteration of the Hebrew name () which literally means "He laughs/will laugh." Ugaritic texts dating from the 13th century BCE refer to the benevolent smile of the Canaanite deity El. Genesis, however, ascribes the laughter to Isaac's parents, Abrah ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michael A
Michael may refer to: People * Michael (given name), a given name * Michael (surname), including a list of people with the surname Michael Given name "Michael" * Michael (archangel), ''first'' of God's archangels in the Jewish, Christian and Islamic religions * Michael (bishop elect), English 13th-century Bishop of Hereford elect * Michael (Khoroshy) (1885–1977), cleric of the Ukrainian Orthodox Church of Canada * Michael Donnellan (1915–1985), Irish-born London fashion designer, often referred to simply as "Michael" * Michael (footballer, born 1982), Brazilian footballer * Michael (footballer, born 1983), Brazilian footballer * Michael (footballer, born 1993), Brazilian footballer * Michael (footballer, born February 1996), Brazilian footballer * Michael (footballer, born March 1996), Brazilian footballer * Michael (footballer, born 1999), Brazilian footballer Rulers =Byzantine emperors= *Michael I Rangabe (d. 844), married the daughter of Emperor Nikephoros I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ancilla Bit
Ancilla bits are some extra bits being used to achieve some specific goals in computation (e.g. reversible computation). In classical computation, any memory bit can be turned on or off at will, requiring no prior knowledge or extra complexity. However, this is not the case in quantum computing or classical reversible computing. In these models of computing, all operations on computer memory must be reversible, and toggling a bit on or off would lose the information about the initial value of that bit. For this reason, in a quantum algorithm there is no way to deterministically put bits in a specific prescribed state unless one is given access to bits whose original state is known in advance. Such bits, whose values are known ''a priori'', are known as ancilla bits in a quantum or reversible computing task. A trivial use for ancilla bits is downgrading complicated quantum gates into simple gates. For example, by placing controls on ancilla bits, a Toffoli gate can be u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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