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The Longer Term: Quantum Information Processing and Communication
Published in Simon Deleonibus, Electronic Device Architectures for the Nano-CMOS Era, 2019
In the mid-eighties, David Deutsch, from Oxford University, has pointed out that one of the most fundamental abstract models of what a computation is, the original, classical Turing machine designed in the thirties by Alan Turing, was entirely relying on the untold hypothesis that computations are performed by devices which obey the laws of classical physics. Deutsch developed a more abstract, but physically grounded view of what a computation is, namely the simulation of a physical system by another physical system. Based on that, he designed a quantum analogue of the Turing machine, with which he showed two major results, some ten years before the discovery of Shor’s and Grover’s algorithms: (i) the set of functions that can be computed by a quantum Turing machine is the same as the set of functions that can be computed by a classical Turing machine; and (ii) quantum computations can perform tasks that cannot be simulated classically (i.e. by a classical Turing machine), better than with an exponential complexity cost for the simulation. This means that the Turing machine, be it classical or quantum, sets the limits: in terms of computability, quantum computation and classical computation are proved equivalent. The promises of quantum computation are elsewhere: enlarge as far as possible the boundaries of what is reasonably computable.
Glossary of scientific and technical terms in bioengineering and biological engineering
Published in Megh R. Goyal, Scientific and Technical Terms in Bioengineering and Biological Engineering, 2018
Quantum computer (quantum supercomputer) is a computation device that makes direct use of quantum-mechanical phenomena, such as superposition and entanglement, to perform operations on data. Quantum computers are different from digital computers based on transistors. Whereas digital computers require data to be encoded into binary digits (bits), each of which is always in one of two definite states (0 or 1), quantum computation uses qubits (quantum bits). A theoretical model is the quantum Turing machine, also known as the universal quantum computer. Quantum computers share theoretical similarities with non-deterministic and probabilistic computers. As of today, quantum computing is still in its infancy but experiments have been carried out in which quantum computational operations were executed on a very small number of qubits. Both practical and theoretical research continues, and many national governments and military funding agencies support quantum computing research to develop quantum computers for both civilian and national security purposes, such as cryptanalysis.
Synthetic Nanostructures as Quantum Control Systems
Published in Günter Mahler, Volkhard May, Michael Schreiber, Molecular Electronics, 2020
In order to exploit entanglement, one will have to concentrate on unitary dynamics, by which, in principle, any superposition can be generated. General unitary transformations are, of course, extremely involved and likely to be beyond any external control. It has therefore been of considerable interest that D. Deutsch (6,27,28) could show that any such transformation can be composed from elementary types, called quantum gates (in analogy to the gates constituting a classical computer). The resulting (highly formal) architecture has been termed the quantum Turing machine. It is a variant of reversible computation.
Reflections on probabilistic compared to quantum computational devices
Published in International Journal of Parallel, Emergent and Distributed Systems, 2021
A quantum Turing machine (QTM) [9], on a finite set Q of states and the finite alphabet Γ, is given by a transition function assigning a so-called amplitude (or probability amplitude), a complex number, the absolute value of which is in the interval [0, 1], to each transition. Furthermore, for each configuration c0 and all its successor configurations c1, … , ck the following sentence must be true:
Quantum-computing with AI & blockchain: modelling, fault tolerance and capacity scheduling
Published in Mathematical and Computer Modelling of Dynamical Systems, 2019
In the future quantum cloud-computing and communication system (see, Figure 2 for a newly designed example), the traditional binary (zero or one) bit based data packets will be replaced by quantum data packets. Each of them will consist of user’s data payload and packet head that indicates the service requirements managed by system software called quantum blockchain in Dai [2] (see, Figure 4 for detail). The length of a quantum data packet is the number of qubits randomly walking over the Bloch sphere as shown in the lower-right graph of Figure 6. Note that, the random step size for each walk along a particular direction over the sphere may be greater than the unity. Furthermore, the packet length is also random from one quantum data packet to another one. However, no matter whether in a quantum computer or in a quantum communication channel, the service time and quality for a quantum data packet depends on the measurement of each single source qubit. Currently, there are numerous physical realizations of quantum computers, which are mainly based on four quantum computing models of practical importance besides the theoretical quantum Turing machine (see, e.g. Deutsch [3], Feynma [4], Nielsen and Chuang [6]). However, the error from the measurement or unitary operation is still the issue. In general, due to the non-cloning theorem (see, e.g. Niestegge [30], Wootters and Zurek [31]), unknown pure quantum states cannot be copied unless they are orthogonal. Nevertheless, according to Niestegge [30] and references therein, the approximate or imperfect cloning of quantum states is possible, e.g. via a generalized non-Gaussian mutual information formula (see, e.g. Dai [23]) by developing a quantum channel between quantum states and their measurements (or their received states) in a probabilistic way. Furthermore, the quantum Zeno effect or called Zeno’s paradox (i.e. the inhibition of transitions between quantum states by frequent measurements, see, e.g. Itano et al. [32], Misra and Sudarshan [33]) is the other concerned issue. Nevertheless, inside the recently realized IBM 50 qubit quantum computer, the quantum coherence time (the time gap to keep a channel stable (i.e. to keep the number of quantum states the same)) can last up to 90 μs to reduce the influence of Zeno effect, which is enough for the quantum computer to perform the required operation and realize one 20-qubit quantum entanglement in 187 ns (see, e.g. the latest announcement in Song et al. [34]). Therefore, with the hope to reduce the error, we develop a quantum channel method in performing the measurement and computation, which is evolved from the one currently being implemented in MIMO wireless channel (see e.g. Dai [2,24]). An example of such a quantum channel is presented in the lower graph of Figure 7 and illustrated via a comparison with an MIMO channel in the upper-left graph of the figure.