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arXiv:quant-ph/0205074

ALEPH-QP: Universal hybrid quantum processors

Alexander Yu. Vlasov

Published May 13, 2002• 2 citations
arXivHTMLPDF

Abstract

A quantum processor (the programmable gate array) is a quantum network with a fixed structure. A space of states is represented as tensor product of data and program registers. Different unitary operations with the data register correspond to "loaded" programs without any changing or "tuning" of network itself. Due to such property and undesirability of entanglement between program and data registers, universality of quantum processors is subject of rather strong restrictions. By different authors was developed universal "stochastic" quantum gate arrays. It was proved also, that "deterministic" quantum processors with finite-dimensional space of states may be universal only in approximate sense. In present paper is shown, that using hybrid system with continuous and discrete quantum variables, it is possible to suggest a design of strictly universal quantum processors. It is shown also that "deterministic" limit of specific programmable "stochastic" U(1) gates (probability of success becomes unit for infinite program register), discussed by other authors, may be essentially same kind of hybrid quantum systems used here.

DOI
10.48550/arxiv.quant-ph/0205074

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A quantum processor (the programmable gate array) is a quantum network with a fixed structure. A space of states is represented as tensor product of data and program registers. Different unitary operations with the data register correspond to "loaded" programs without any changing or "tuning" of network itself. Due to such property and undesirability of entanglement between program and data registers, universality of quantum processors is subject of rather strong restrictions. By different authors was developed universal "stochastic" quantum gate arrays. It was proved also, that "deterministic" quantum processors with finite-dimensional space of states may be universal only in approximate sense. In present paper is shown, that using hybrid system with continuous and discrete quantum variables, it is possible to suggest a design of strictly universal quantum processors. It is shown also that "deterministic" limit of specific programmable "stochastic" U(1) gates (probability of success becomes unit for infinite program register), discussed by other authors, may be essentially same kind of hybrid quantum systems used here.
A quantum processor (the programmable gate array) is a quantum network with a ˇxed structure. A space of states is represented as tensor product of data and program registers. Different unitary operations with the data register correspond to ®loaded ¯ programs without any changing or ®tuning¯ of network itself. Due to such property and undesirability of entanglement between program and data registers, universality of quantum processors is subject of rather strong restrictions. Universal ®stochastic¯ quantum gate arrays were developed by different authors. It was also proved, that ®deterministic¯ quantum processors with ˇnite-dimensional space of states may be universal only in approximate sense. In the present paper it is shown that, using hybrid system with continuous and discrete quantum variables, it is possible to suggest a design of strictly universal quantum processors. It is also shown that ®deterministic ¯ limit of speciˇc programmable ®stochastic ¯ U(1) gates (probability of success becomes unit for inˇnite program register), discussed by other authors, may be essentially the same kind of hybrid quantum systems used here.
Most modern classical processors support so-called von Neumann architecture with program and data registers. In present work is revisited similar approach to models of quantum processors. Deterministic programmable quantum gate arrays are considered as an example. They are also called von Neumann quantum processors here and use conditional quantum dynamics. Such devices have some problems with universality, but consideration of hybrid quantum processors, i.e., models with both continuous and discrete quantum variables resolves the problems. It is also discussed comparison of such a model of quantum processors with more traditional approach.
We present a probabilistic quantum processor for qubits. The processor itself is represented by a fixed array of gates. The input of the processor is constituted by two registers. In the program register the set of instructions (program) is encoded. This program is applied to the data register. The processor we present can perform any operation on a single qubit with a certain probability. If the operation is unitary, the probability is in general 1/4, but for more restricted sets of operators the probability can be higher.
Modern classical computing devices, except of simplest calculators, have von Neumann architecture, i.e., a part of the memory is used for the program and a part for the data. It is likely, that analogues of such architecture are also desirable for the future applications in quantum computing, communications and control. It is also interesting for the modern theoretical research in the quantum information science and raises challenging questions about an experimental assessment of such a programmable models. Together with some progress in the given direction, such ideas encounter specific problems arising from the very essence of quantum laws. Currently are known two different ways to overcome such problems, sometime denoted as a stochastic and deterministic approach. The presented paper is devoted to the second one, that is also may be called the programmable quantum networks with pure states. In the paper are discussed basic principles and theoretical models that can be used for the design of such nano-devices, e.g., the conditional quantum dynamics, the Nielsen-Chuang "no-programming theorem, the idea of deterministic and stochastic quantum gates arrays. Both programmable quantum networks with finite registers and hybrid models with continuous quantum variables are considered. As a basic model for the universal programmable quantum network with pure states and finite program register is chosen a "Control-Shift" quantum processor architecture with three buses introduced in earlier works. It is shown also, that quantum cellular automata approach to the construction of an universal programmable quantum computer often may be considered as the particular case of such design.
We show how to construct quantum gate arrays that can be programmed to perform different unitary operations on a data register, depending on the input to some program register. It is shown that a universal quantum gate array---a gate array which can be programmed to perform any unitary operation---exists only if one allows the gate array to operate in a probabilistic fashion. Thus it is not possible to build a fixed, general purpose quantum computer which can be programmed to perform an arbitrary quantum computation.
We present a probabilistic quantum processor for qudits on a single qudit of dimension N. The processor itself is represented by a fixed array of gates. The input of the processor consists of two registers. In the program register the set of instructions (program) is encoded. This program is applied to the data register. The processor can perform any operation on a single qudit of dimension N with a certain probability. For a general unitary operation, the probability is 1/N2,{1/N}^{2},1/N2, but for more restricted sets of operators the probability can be higher. In fact, this probability can be independent of the dimension of the qudit Hilbert space of the qudit under some conditions.