所谓“通用量子计算机”并非是一台基于量子物理的机器或仪器,应该像”图灵机”一样具有“通用性”或是“万能的”计算性能,即在经典算法意义上的通用计算机。
在算法和计算机理论中,“能行可计算性”是一个最基本的观念,这个观念表达了人类古老的算术演算与机器运算的等价性,著名的“丘奇-图灵论题”(The Church-Turing thesis)是这样表达的:the words "effectively calculable" will mean "produced by any intuitively ''effective'' means whatsoever" and "effectively computable" will mean "produced by a Turing-machine or equivalent mechanical device"(https://en.wikipedia.org/wiki/Church–Turing_thesis)。
所以,所谓“量子计算机”如果没有“能行可计算的”能力,不能在可接受的时间内得到一个确定性的结果,就只是一台普通的量子仪器而不能称为“量子计算机”或更一般的“通用量子计算机”。图灵机与符号表达的数学演绎(如丘奇的Lambda可定义函数)不同,图灵机是把算法中隐含的“实时性”(the actual time)机器化了,也就是以机器形式表现了人们对算法的直觉:计算的机械步骤。“图灵机可计算”已经成为了等价于“算法”被普遍接受的概念,丘奇-图灵论题不是由逻辑方法证明的,而是基于包括使用高级工具在内的所有人类智力活动的基本事实。
如何将一个问题表达为“量子算法”与“量子算法”如何在物理量子态上实现是性质不同的问题(虽然这两者密切难分),按照有关的解释,“量子算法”可以在物理量子态上实现“寄存器”(存貯)(利用量子傅叶变换),量子态的改变可以设计为逻辑门变换(按照矩阵力学的解释,矩阵变换在数学运算和量子态特征矩阵表达上是同一的),但这只是算法意义上的,远不能构成经典意义的“计算”步骤,目前的“量子计算”只对具体设计的“量子算法”才有意义(如“秀尔算法”等);而且,对量子态的测量(坍缩)得到一个量子算法所期望的结果是一个“概率”(amplitude)事件,这些都与经典意义的“计算”相去甚远。
“薛定鄂猫” 说量子世界拒绝经典世界的界入,我们只能以1/2的几率知道猫的死活,但如果”通用量子计算机”(像图灵机一样)是可以实现的,我们就能计算出任何时候猫的状态。这就是通用量子计算机是否可能的关键:确定性的经典方法能否操控不确定的量子现象?
由于外界并不能界入对纠缠态的控制操作,就是说,只有物理量子态在经典意义上(“特征矩阵”和“特征值”)设计为算法“寄存器”和“量子逻辑门”才是“通用”的,因此,设想“通用量子计算机”就意味着外界的操作必须侵入量子纠缠态,如果这是可以实现的,是不是“薛定鄂猫”也是可确定的? 或者相反地问,如果“薛定鄂猫”是不可确定的,则“通用量子计算机”也是不可能的。
对于另一个世界(并非宗教中的彼岸)所呈现给我们的量子现象,我们希望能够以我们人类能理解的方式来理解和掌握,但我不知道这是否合理或应该如此。
Schrodinger’s Cat vs. Universal Quantum Computer, a paradox? [1]
Zhou J.M.
The so-called universal quantum computer is not a machine or instrument based on quantum physics. It should have the capability of universal computing performance, such as the Turing Machine, namely a general computer in the sense of classical algorithm.
In the algorithm and the computer theory, "effective calculability" is the most basic concept, this concept expresses the equivalence of human’s ancient arithmetic and machine operation, the famous Church-Turing Thesis is expressed in this way: the words "effectively calculable" will mean "produced by any intuitively ''effective'' means whatsoever" and "effectively computable" will mean "produced by a Turing-machine or equivalent mechanical device" (https://en.wikipedia.org/wiki/Ch...).
Therefore, the so-called "quantum computer" without "effectively calculability" can not get a definitive result within an acceptable time, it is just an common quantum device or machine, which cannot be called a "quantum computer" or more generally "universal quantum computer". Unlike the mathematical deduction in symbols (such as Church''s lambda definable function), the Turing Machine mechanizes the "real time" implicated in the algorithm, namely, which represents in machine-form the people’s intuition about the algorithm: the mechanical steps of calculation. The “Turing Machine Computability" equivalent to "the algorithm" has become a common concept accepted widely by people. The Church-Turing Thesis is not logically proven, but it is based on the basic facts of human intellectual activity, including the use of advanced tools.
How to represent a problem as "Quantum Algorithm“ and how a quantum algorithm performs in physical quantum state (Quantum Computer) are two different things (although the two are closely related). According to the relevant explanation, the quantum algorithm can realize the register (storage) on physical quantum state (using quantum Fourier transformation), and a quantum state change can be designed as logic gate transform (according to the matrix mechanics explanation, matrix transformation in mathematics and representation of eigenmatrix is the same), but this is only in the sense of algorithm, far from the classical sense of “calculation steps". So, at present, a quantum computing is meaningful only to a specific design of "quantum algorithm" (such as Seoul’s algorithm etc.). Moreover, the expected result of a quantum algorithm by a measurement (collapse) to the quantum states is a probability (amplitude) event, these are far from the sense of classical computation.
"Schrodinger’s cat" says that the quantum world rejects the classical world, and we can only know the cat alive with probability 1/2, but if the "universal quantum computer” (like the Turing machine) can be realized, we can calculate the cat state at any moment. This is the key to the possibility of the universal quantum computer: whether the classical deterministic method can manipulate the uncertain quantum phenomena?
Because the outside world cannot enter the control operation to entangled state, that is to say, only the physical quantum state designed as quantum register and quantum logic gate are “universal” in classical sense (eigenmatrix and eigenvalue). Therefore, the supposition of universal quantum computer means that the outside world operations must trespass on quantum entanglement. If this can be done, the "Schrodinger’s cat" can also be determined? Or, conversely, if the "Schrödinger’s cat" is not certain, then the universal quantum computer is also impossible.
We hope to be able to understand and control in human’s way the quantum phenomena which is the other world (not the other side of religion) before us. But I do not know if this is reasonable or should be done.
Reference:
[1] https://zhoujm.quora.com/Schrodinger-s-Cat-vs-Universal-Quantum-Computer-a-paradox
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