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Quantum computer - Wikipedia, the free encyclopedia
- A quantum computer is a device for computation that makes direct use of distinctively quantum mechanical phenomena, such as superposition and entanglement, to perform operations on data. In a classical (or conventional) computer, information is stored as bits; in a quantum computer, it is stored as qubits (quantum binary digits). The basic principle of quantum computation is that the quantum properties can be used to represent and structure data, and that quantum mechanisms can be devised and built to perform operations with these data.[1
- 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
- Quantum gates may be viewed as linear transformations. Daniel S. Abrams and Seth Lloyd have shown that if nonlinear transformations are permitted, then NP-complete problems could be solved in polynomial time. It could even do so for #P-complete problems. They do not believe that such a machine is possible.
- A Turing machine can simulate 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.
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Church–Turing thesis - Wikipedia, the free encyclopedia
- In computability theory the Church–Turing thesis (also known as Church's thesis, Church's conjecture and Turing's thesis) is a combined hypothesis about the nature of effectively calculable (computable) functions by recursion (Church's Thesis), by mechanical device equivalent to a Turing machine (Turing's Thesis) or by use of Church's λ-calculus:
- Every effectively calculable function (effectively decidable predicate) is general[1] recursive
- The three computational processes (recursion, λ-calculus, and Turing machine) were shown to be equivalent by Alonzo Church, Stephen Kleene and J.B. Rosser (1934-6)[2] and by Alan Turing (1936-7)[3]
- effectively calculable
- effectively computable
- Thus, as they stand, neither thesis can be proven
- Informally the Church–Turing thesis states that if an algorithm (a procedure that terminates) exists then there is an equivalent Turing machine or applicable λ-function[15] for that algorithm.
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Quantum entanglement - Wikipedia, the free encyclopedia
- Quantum entanglement （量子纠缠）is a quantum mechanical phenomenon in which the quantum states of two or more objects are linked together so that one object can no longer be adequately described without full mention of its counterpart — even though the individual objects may be spatially separated.
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Quantum superposition - Wikipedia, the free encyclopedia
- Quantum superposition （量子叠加）
- Quantum mechanics has the exact same rules for multiplying and adding numbers associated with events, except that the quantities are complex numbers called amplitudes instead of positive real numbers called probabilities
- The superposition principle says that the way to describe the world is to assign such a complex number to every possible situation, and that the way to describe how things change is to treat these numbers mathematically as if they were probabilities. Because these numbers can be positive or negative, quantum mechanics allows the counterintuitive phenomenon that sometimes when there are more ways for a thing to happen, the chance that it happens goes down. An event with a negative amplitude can cancel with an event with a positive amplitude.
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