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Proceedings of the Royal Society of London A Mathematical and Physical Sciences

Quantum computational networks

David Deutsch

Published Sep 8, 1989• 1,270 citations
Publisher

Abstract

Abstract The theory of quantum computational networks is the quantum generalization of the theory of logic circuits used in classical computing machines. Quantum gates are the generalization of classical logic gates. A single type of gate, the universal quantum gate, together with quantum ‘unit wires’, is adequate for constructing networks with any possible quantum computational property.

DOI
10.1098/rspa.1989.0099

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Abstract The theory of quantum computational networks is the quantum generalization of the theory of logic circuits used in classical computing machines. Quantum gates are the generalization of classical logic gates. A single type of gate, the universal quantum gate, together with quantum ‘unit wires’, is adequate for constructing networks with any possible quantum computational property.
We show that in quantum computation almost every gate that operates on two or more bits is a universal gate. We discuss various physical considerations bearing on the proper definition of universality for computational components such as logic gates. Introduction It has been known for several years that the theory of quantum computers --- i.e. machines that rely on characteristically quantum phenomena to perform computations [1] --- is substantially different from the classical theory of computation, which is essentially the theory of the universal Turing machine. We may identify three important differences. Firstly, the properties of quantum computers are not postulated in abstracto but are deduced entirely from the laws of physics. Logically, this was already true of the classical theory, as Landauer [2] has pointed out, but the intuitive nature of the classically-available computational operations, and the millennia-long history of their study, allowed pioneers such as Turing, Chu...
Abstract Quantum computation is well known for its particular computational performance. In this paper, a novel quantum neuron model is constructed based on the universal quantum gates unit (i.e. phase-shift gate and controlled-NOT gate), which acts as the basic computational component, with this type of neuron a feed-forward network structure is also built. The simulation results show that the quantum neuron network is superior to classical BP and RBF network for two financial data analysis examples.
A quantum gate or quantum logic gate is an elementary quantum circuit working on a small number of qubits. It means that quantum gates can grasp two primary feature of quantum mechanics that are entirely out of reach for classical gates : superposition and entanglement. In simpler words quantum gates are reversible. In classical computing sets of logic gates are connected to construct digital circuits. Similarly, quantum logic gates operates on input states that are generally in superposition states to compute the output. In this paper the authors will discuss in detail what is single and multiple qubit gates and scope and challenges in quantum gates.
According to the statistical interpretation of quantum theory, quantum computers form a distinguished class of probabilistic machines (PMs) by encoding n qubits in 2n pbits (random binary variables). This raises the possibility of a large-scale quantum computing using PMs, especially with neural networks which have the innate capability for probabilistic information processing. Restricting ourselves to a particular model, we construct and numerically examine the performance of neural circuits implementing universal quantum gates. A discussion on the physiological plausibility of proposed coding scheme is also provided.
We proposed a new candidate for the construction of an universal quantum network, which are built from the elementary quantum gates to the elements of quantum circuit, again to quantum subnetworks and finally to a whole quantum network. The main advantages of our scheme are its simplicity and standardization in construction, facility and directness in assembly and scale, reusage and update in engineering, realizability and procedurization in an effective construction. Moreover our universal quantum networks are potentially programmable. It is proved that all the elementary quantum gates can be written as our quantum subnetwork. This implies that our scheme is compatible with the known quantum gate-assembly schemes, and so the known results from a quantum computation to a set of the elementary quantum gates can be directly inherited and used in our scheme. As the applications of our construction scheme, we obtain the whole quantum networks for Shor's algorithm, Grover's algorithm and simulating Schr\\"odinger equation in general. This means that our universal quantum network can generally describe the known main results in quantum computation.