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Magic State Distillation
Magic state distillation is a method for creating more accurate quantum states from multiple noisy ones, which is important for building fault tolerant quantum computers. It has also been linked to quantum contextuality, a concept thought to contribute to quantum computers' power. The technique was first proposed by Emanuel Knill in 2004, and further analyzed by Sergey Bravyi and Alexei Kitaev the same year. Thanks to the Gottesman–Knill theorem, it is known that some quantum operations (operations in the Clifford group) can be perfectly simulated in polynomial time on a classical computer. In order to achieve universal quantum computation, a quantum computer must be able to perform operations outside this set. Magic state distillation achieves this, in principle, by concentrating the usefulness of imperfect resources, represented by mixed states, into states that are conducive for performing operations that are difficult to simulate classically. A variety of qubit magic sta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Quantum State
In quantum physics, a quantum state is a mathematical entity that embodies the knowledge of a quantum system. Quantum mechanics specifies the construction, evolution, and measurement of a quantum state. The result is a prediction for the system represented by the state. Knowledge of the quantum state, and the rules for the system's evolution in time, exhausts all that can be known about a quantum system. Quantum states may be defined differently for different kinds of systems or problems. Two broad categories are * wave functions describing quantum systems using position or momentum variables and * the more abstract vector quantum states. Historical, educational, and application-focused problems typically feature wave functions; modern professional physics uses the abstract vector states. In both categories, quantum states divide into pure versus mixed states, or into coherent states and incoherent states. Categories with special properties include stationary states for tim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Fault Tolerant
Fault tolerance is the ability of a system to maintain proper operation despite failures or faults in one or more of its components. This capability is essential for high-availability, mission-critical, or even life-critical systems. Fault tolerance specifically refers to a system's capability to handle faults without any degradation or downtime. In the event of an error, end-users remain unaware of any issues. Conversely, a system that experiences errors with some interruption in service or graceful degradation of performance is termed 'resilient'. In resilience, the system adapts to the error, maintaining service but acknowledging a certain impact on performance. Typically, fault tolerance describes computer systems, ensuring the overall system remains functional despite hardware or software issues. Non-computing examples include structures that retain their integrity despite damage from fatigue, corrosion or impact. History The first known fault-tolerant computer was ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Quantum Contextuality
Quantum contextuality is a feature of the phenomenology of quantum mechanics whereby measurements of quantum observables cannot simply be thought of as revealing pre-existing values. Any attempt to do so in a realistic hidden-variable theory leads to values that are dependent upon the choice of the other (compatible) observables which are simultaneously measured (the measurement context). More formally, the measurement result (assumed pre-existing) of a quantum observable is dependent upon which other commuting observables are within the same measurement set. Contextuality was first demonstrated to be a feature of quantum phenomenology by the Bell–Kochen–Specker theorem. The study of contextuality has developed into a major topic of interest in quantum foundations as the phenomenon crystallises certain non-classical and counter-intuitive aspects of quantum theory. A number of powerful mathematical frameworks have been developed to study and better understand contextuality, fr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Emanuel Knill
{{disambiguation, geo, school ...
Emanuel may refer to: * Emanuel (name), a given name and surname (see there for a list of people with this name) * Emanuel School, Australia, Sydney, Australia * Emanuel School, Battersea, London, England * Emanuel (band), a five-piece rock band from Louisville, Kentucky, United States * Emanuel County, Georgia * ''Emanuel'' (film), a 2019 documentary film about the Charleston church shooting See also * Emmanuel (other) * Emanu-El (other) * Emmanuelle (other) * Immanuel (other) * Emmanouil (Εμμανουήλ), the modern Greek form of the name * Manuel (other) Manuel may refer to: People * Manuel (name), a given name and surname * Manuel (''Fawlty Towers''), a fictional character from the sitcom ''Fawlty Towers'' * Manuel I Komnenos, emperor of the Byzantine Empire * Manuel I of Portugal, king of Po ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Alexei Kitaev
Alexei Yurievich Kitaev (; born August 26, 1963) is a Russian-American theoretical physicist. He is currently a professor of theoretical physics and mathematics at the California Institute of Technology. Kitaev has received multiple awards for his contributions to the field of quantum mechanics, specifically quantum computing. Life Kitaev was educated in Russia, graduating from the Moscow Institute of Physics and Technology in 1986, and with a Ph.D. from the Landau Institute for Theoretical Physics under the supervision of Valery Pokrovsky in 1989. Kitaev worked as a research associate at the Landau Institute between 1989 and 1998. Between 1999 and 2001, he served as a researcher at Microsoft Research. Since 2002, Kitaev has been a professor at Caltech. In 2021, Kitaev was elected into the National Academy of Sciences. Research Toy models Kitaev has introduced many toy models in the fields of solid-state physics and quantum mechanics. In his words: Kitaev's toric ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Gottesman–Knill Theorem
In quantum computing, the Gottesman–Knill theorem is a theoretical result by Daniel Gottesman and Emanuel Knill that states that stabilizer circuits–circuits that only consist of gates from the normalizer of the qubit Pauli group, also called Clifford group–can be perfectly simulated in polynomial time on a probabilistic classical computer. The Clifford group can be generated solely by using the controlled NOT, Hadamard, and phase gates (CNOT, ''H'' and ''S''); and therefore stabilizer circuits can be constructed using only these gates. The reason for the speed up of quantum computers compared to classical ones is not yet fully understood. The Gottesman-Knill theorem proves that all quantum algorithms whose speed up relies on entanglement that can be achieved with CNOT and Hadamard gates do not achieve any computational advantage relative classical computers, due to the classical simulability of such algorithms (and the particular types of entangled states they ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Clifford Group
The Clifford group encompasses a set of quantum operations that map the set of ''n''-fold Pauli group products into itself. It is most famously studied for its use in quantum error correction. Definition The Pauli matrices, : \sigma_0=I=\begin 1 & 0 \\ 0 & 1 \end, \quad \sigma_1=X=\begin 0 & 1 \\ 1 & 0 \end, \quad \sigma_2=Y=\begin 0 & -i \\ i & 0 \end, \text \sigma_3=Z=\begin 1 & 0 \\ 0 & -1 \end provide a basis for the density operators of a single qubit, as well as for the unitaries that can be applied to them. For the n-qubit case, one can construct a group, known as the Pauli group, according to : \mathbf_n=\left\. The Clifford group is defined as the group of unitaries that normalize the Pauli group: \mathbf_n=\. Under this definition, \mathbf_n is infinite, since it contains all unitaries of the form e^I for a real number \theta and the identity matrix I. Any unitary in \mathbf_n is equivalent (up to a global phase factor) to a circuit generated using Hadamard, Ph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Polynomial Time
In theoretical computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by the algorithm, supposing that each elementary operation takes a fixed amount of time to perform. Thus, the amount of time taken and the number of elementary operations performed by the algorithm are taken to be related by a constant factor. Since an algorithm's running time may vary among different inputs of the same size, one commonly considers the worst-case time complexity, which is the maximum amount of time required for inputs of a given size. Less common, and usually specified explicitly, is the average-case complexity, which is the average of the time taken on inputs of a given size (this makes sense because there are only a finite number of possible inputs of a given size). In both cases, the time complexity is gener ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Mixed Quantum State
In quantum physics, a quantum state is a mathematical entity that embodies the knowledge of a quantum system. Quantum mechanics specifies the construction, evolution, and measurement of a quantum state. The result is a prediction for the system represented by the state. Knowledge of the quantum state, and the rules for the system's evolution in time, exhausts all that can be known about a quantum system. Quantum states may be defined differently for different kinds of systems or problems. Two broad categories are * wave functions describing quantum systems using position or momentum variables and * the more abstract vector quantum states. Historical, educational, and application-focused problems typically feature wave functions; modern professional physics uses the abstract vector states. In both categories, quantum states divide into pure versus mixed states, or into coherent states and incoherent states. Categories with special properties include stationary states for time ind ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Physical Review A
''Physical Review A'' (also known as PRA) is a monthly peer-reviewed scientific journal published by the American Physical Society covering atomic, molecular, and optical physics and quantum information. the editor was Jan M. Rost ( Max Planck Institute for the Physics of Complex Systems). History In 1893, the '' Physical Review'' was established at Cornell University. It was taken over by the American Physical Society (formed in 1899) in 1913. In 1970, ''Physical Review'' was subdivided into ''Physical Review A'', ''B'', ''C'', and ''D''. At that time, section ''A'' was subtitled ''Physical Review A: General Physics''. In 1990, a process was started to split this journal into two, resulting in the creation of '' Physical Review E'' in 1993. Hence, in 1993, ''Physical Review A'' changed its statement of scope to ''Atomic, Molecular and Optical Physics.'' In January 2007, the section of ''Physical Review E'' that published papers on classical optics was merged into ''Physical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
CNOT
In computer science, the controlled NOT gate (also C-NOT or CNOT), controlled-''X'' gate, controlled-bit-flip gate, Feynman gate or controlled Pauli-X is a quantum logic gate that is an essential component in the construction of a gate-based quantum computer. It can be used to entangle and disentangle Bell states. Any quantum circuit can be simulated to an arbitrary degree of accuracy using a combination of CNOT gates and single qubit rotations. The gate is sometimes named after Richard Feynman who developed an early notation for quantum gate diagrams in 1986. The CNOT can be expressed in the Pauli basis as: : \mbox = e^= e^. Being both unitary and Hermitian, CNOT has the property e^=(\cos \theta)I+(i\sin \theta) U and U =e^=e^, and is involutory. The CNOT gate can be further decomposed as products of rotation operator gates and exactly one two qubit interaction gate, for example : \mbox =e^R_(-\pi/2)R_(-\pi/2)R_(-\pi/2)R_(\pi/2)R_(\pi/2). In general, any sing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Quantum Logic Gate
In quantum computing and specifically the quantum circuit model of computation, a quantum logic gate (or simply quantum gate) is a basic quantum circuit operating on a small number of qubits. Quantum logic gates are the building blocks of quantum circuits, like classical logic gates are for conventional digital circuits. Unlike many classical logic gates, quantum logic gates are reversible. It is possible to perform classical computing using only reversible gates. For example, the reversible Toffoli gate can implement all Boolean functions, often at the cost of having to use ancilla bits. The Toffoli gate has a direct quantum equivalent, showing that quantum circuits can perform all operations performed by classical circuits. Quantum gates are unitary operators, and are described as unitary matrices relative to some orthonormal basis. Usually the ''computational basis'' is used, which unless comparing it with something, just means that for a ''d''-level quantum system ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
