Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/9703032 · Physical Review Letters

Programmable Quantum Gate Arrays

Michael A. Nielsen, Isaac L. Chuang

Published Jul 14, 1997• 378 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.79.321

Related papers

Programmable Quantum Gate Arrays

Mark S. Hillery, Vladimír Bužek, Mário Ziman

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.

Fortschritte der Physik•Oct 1, 2001•16 citations

Probabilistic implementation of universal quantum processors

Mark S. Hillery, Vladimír Bužek, Mário Ziman

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 ${1/N}^{2},$ 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.

arXiv:quant-ph/0106088•Physical Review A•Jan 3, 2002•79 citations

Classical programmability is enough for quantum circuits universality in approximate sense

Alexander Yu. Vlasov

It was shown by M.A. Nielsen and I.L. Chuang 1997, that it is impossible to build strictly universal programmable quantum gate array, that could perform any unitary operation precisely and it was suggested to use probabilistic gate arrays instead. In present work is shown, that if to use more physical and weak condition of universality (suggested already in earliest work by D.Deutsch 1985) and to talk about simulation with arbitrary, but finite precision, then it is possible to build universal programmable gate array. But now the same no-go theorem by Nielsen and Chuang will have new interesting consequence --- controlling programs for the gate arrays can be considered as pure classical. More detailed design of such deterministic quantum gate arrays universal ``in approximate sense'' is considered in the paper.

arXiv:quant-ph/0103119•Mar 20, 2001•10 citations

UNIVERSAL HYBRID QUANTUM PROCESSORS

Alexander Yu. Vlasov

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.

•Jan 1, 2003•6 citations

ALEPH-QP: Universal hybrid quantum processors

Alexander Yu. Vlasov

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.

arXiv:quant-ph/0205074•May 13, 2002•2 citations

Quantum gate arrays can be programmed to evaluate the expectation value of any operator

Juan Pablo Paz, Augusto J. Roncaglia

A programmable gate array is a circuit whose action is controlled by input data. In this paper we describe a special-purpose quantum circuit that can be programmed to evaluate the expectation value of any operator O acting on a space of states of N dimensions. The circuit has a program register whose state $|\ensuremath{\Psi}(O){〉}_{P}$ encodes the operator O whose expectation value is to be evaluated. The method requires knowledge of the expansion of O in a basis of the space of operators. We discuss some applications of this circuit and its relation to known instances of quantum state tomography.

arXiv:quant-ph/0306143•Physical Review A•Nov 21, 2003•42 citations
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 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.
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.
It was shown by M.A. Nielsen and I.L. Chuang 1997, that it is impossible to build strictly universal programmable quantum gate array, that could perform any unitary operation precisely and it was suggested to use probabilistic gate arrays instead. In present work is shown, that if to use more physical and weak condition of universality (suggested already in earliest work by D.Deutsch 1985) and to talk about simulation with arbitrary, but finite precision, then it is possible to build universal programmable gate array. But now the same no-go theorem by Nielsen and Chuang will have new interesting consequence --- controlling programs for the gate arrays can be considered as pure classical. More detailed design of such deterministic quantum gate arrays universal ``in approximate sense'' is considered in the paper.
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.
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 programmable gate array is a circuit whose action is controlled by input data. In this paper we describe a special-purpose quantum circuit that can be programmed to evaluate the expectation value of any operator O acting on a space of states of N dimensions. The circuit has a program register whose state $|\ensuremath{\Psi}(O){〉}_{P}$ encodes the operator O whose expectation value is to be evaluated. The method requires knowledge of the expansion of O in a basis of the space of operators. We discuss some applications of this circuit and its relation to known instances of quantum state tomography.