We propose a concept of quantum computing which incorporates an additional kind of uncertainty, i.e. vagueness (fuzziness), in a natural way by introducing new entities, obscure qudits (e.g. obscure qubits), which are characterized simultaneously by a quantum probability and by a membership function. To achieve this, a membership amplitude for quantum states is introduced alongside the quantum amplitude. The Born rule is used for the quantum probability only, while the membership function can be computed from the membership amplitudes according to a chosen model. Two different versions of this approach are given here: the "product" obscure qubit, where the resulting amplitude is a product of the quantum amplitude and the membership amplitude, and the "Kronecker" obscure qubit, where quantum and vagueness computations are to be performed independently (i.e. quantum computation alongside truth evaluation). The latter is called a double obscure-quantum computation. In this case, the measurement becomes mixed in the quantum and obscure amplitudes, while the density matrix is not idempotent. The obscure-quantum gates act not in the tensor product of spaces, but in the direct product of quantum Hilbert space and so called membership space which are of different natures and properties. The concept of double (obscure-quantum) entanglement is introduced, and vector and scalar concurrences are proposed, with some examples being given.
翻译:我们提出了一个数量计算概念,它包含一种额外的不确定性,即模糊性(模糊性),以自然的方式,引入新的实体,模糊的夸度(例如模糊的夸比),其特征是量概率和会籍函数。为了实现这一点,在量度增量的同时引入了量度国家的会籍振幅。“起源规则”仅用于量概率,而会籍函数则根据所选模式从会籍振幅中计算。这里给出了两种不同的版本:“产品”模糊的夸比特,由此产生的振幅是量振幅和会籍振幅的产物,以及“克伦贝克尔”模糊的夸比特,为量度和模糊度计算法,而量值计算法则仅用于量度,而会籍函数函数的计算方法则由量度和模糊的振度计算法混合。这里给出两种不同的版本是“产品”的测量和模糊度,而密度矩阵表则由密度矩阵矩阵组成,而空间门的模糊性和交错性则由制成。