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

Chinese Physics Letters

Construction of General Unitary Transformation for Conditional Quantum Dynamics and Realization of Quantum Controlled Gates

Xiaoguang Wang, YU Rong-jin, Jian-zheng Fu

Published Jun 1, 1998• 0 citations
Publisher

Abstract

By factorizing a general one-bit transformation matrix for one-bit gates in quantum computer, a general unitary transformation is constructed, which can serve as (controlled) m gate for the conditional quantum dynamics. When the quantized single-mode electromagnetic field containing n or no photons acts as the controlled bit, the quantum controlled-NOT gates and square root of the controlled-NOT gates in cavity-quantum electrodynamics are realized.

DOI
10.1088/0256-307x/15/6/003

Related papers

Unitary and Anti-Unitary Quantum Descriptions of the Classical Not Gate

Gianpiero Cattaneo, G. Conte, Roberto Leporini

Two possible quantum descriptions of the classical Not gate are investigated in the framework of the Hilbert space C2: the unitary and the anti-unitary operator realizations. The two cases are distinguished interpreting the unitary Not as a quantum realization of the classical gate which on a xed orthogonal pair of unit vectors, realizing once for all the classical bits 0 and 1, produces the required transformations 0 => 1 and 1 => 0 (i.e., logical quantum Not). The anti-unitary Not is a quantum realization of a gate which acts as a classical Not on any pair of mutually orthogonal vectors, each of which is a potential realization of the classical bits (i.e., universal quantum Not). Although the latter is not completely positive, one can give an approximated unitary realization of the gate by appending an ancilla. Finally, we consider the unitary and the anti-unitary operator realizations of two important genuine quantum gates that transform elements of the computational basis of C2 into its superpositions: the square root of the identity and the square root of the Not.

•Jan 1, 2010•0 citations

Quantum conditional operations

Alessandro Bisio, Michele Dall’Arno, Paolo Perinotti

An essential element of classical computation is the ``if-then'' construct, that accepts a control bit and an arbitrary gate, and provides conditional execution of the gate depending on the value of the controlling bit. On the other hand, quantum theory prevents the existence of an analogous universal construct accepting a control qubit and an arbitrary quantum gate as its input. Nevertheless, there are controllable sets of quantum gates for which such a construct exists. Here we provide a necessary and sufficient condition for a set of unitary transformations to be controllable, and we give a complete characterization of controllable sets in the two-dimensional case. This result reveals an interesting connection between the problem of controllability and the problem of extracting information from an unknown quantum gate while using it.

arXiv:1509.01062•Physical Review A•Aug 30, 2016•20 citations

Experimental realization of 7-qubit universal perfect controlled-NOT and controlled square-root NOT gates

Daxiu Wei, Xiaodong Yang, Jun Luo +4 more

The controlled-NOT gate and controlled square-root NOT gate play an important role in quantum algorithm. This article reports the experimental results of these two universal quantum logic gates (controlled square-root NOT gate and controlled-NOT gate) on a 7-qubit NMR quantum computer. Further, we propose a simple experimental method to measure and correct the error in the controlled phase-shift gate, which is helpful to construct a more perfect phase-shift gate experimentally and can also be used in more qubits discrete Fourier transformation.

arXiv:quant-ph/0109002•Sep 1, 2001•1 citation

Non-local quantum gates: A cavity-quantum-electrodynamics implementation

Mauro Paternostro, M. S. Kim, G. Massimo Palma

The problems related to the management of large quantum registers could be handled in the context of distributed quantum computation: unitary non-local transformations among spatially separated local processors are realized performing local unitary transformations and exchanging classical communication. In this paper, a scheme is proposed for the implementation of universal non-local quantum gates such as a controlled NOT (CNOT) and a controlled quantum phase gate (CQPG). The system chosen for their physical implementation is a cavity-quantum-electrodynamics (CQED) system formed by two spatially separated microwave cavities and two trapped Rydberg atoms. The procedures to follow for the realization of each step necessary to perform a specific non-local operation are described.

arXiv:quant-ph/0207043•Journal of Modern Optics•Jan 1, 2003•39 citations

Decompositions of general quantum gates

Mikko Möttönen, Juha J. Vartiainen

Quantum algorithms may be described by sequences of unitary transformations called quantum gates and measurements applied to the quantum register of n quantum bits, qubits. A collection of quantum gates is called universal if it can be used to construct any n-qubit gate. In 1995, the universality of the set of one-qubit gates and controlled NOT gate was shown by Barenco et al. using QR decomposition of unitary matrices. Almost ten years later the decomposition was improved to include essentially fewer elementary gates. In addition, the cosine-sine matrix decomposition was applied to efficiently implement decompositions of general quantum gates. In this chapter, we review the different types of general gate decompositions and slightly improve the best known gate count for the controlled NOT gates to (23/48)4^n in the leading order. In physical realizations, the interaction strength between the qubits can decrease strongly as a function of their distance. Therefore, we also discuss decompositions with the restriction to nearest-neighbor interactions in a linear chain of qubits.

arXiv:quant-ph/0504100•Apr 14, 2005•86 citations

Mathematical models of contemporary elementary quantum computing devices

Guannan Chen, Dawson Church, Berthold‐Georg Englert +1 more

Computations with a future quantum computer will be implemented through the operations by elementary quantum gates.It is now well known that the collection of 1-bit and 2-bit quantum gates are universal for quantum computation, i.e., any n-bit unitary operation can be carried out by concatenations of 1-bit and 2-bit elementary quantum gates.Three contemporary quantum devices-cavity QED, ion traps and quantum dots-have been widely regarded as perhaps the most promising candidates for the construction of elementary quantum gates.In this paper, we describe the physical properties of these devices, and show the mathematical derivations based on the interaction of the laser field as control with atoms, ions or electron spins, leading to the following:(i) the 1-bit unitary rotation gates; and(ii) the 2-bit quantum phase gates and the controlled-not gate.This paper is aimed at providing a sufficiently self-contained survey account of analytical nature for mathematicians, physicists and computer scientists to aid interdisciplinary understanding in the research of quantum computation.

arXiv:quant-ph/0303163•CRM proceedings & lecture notes•Dec 17, 2003•15 citations
By factorizing a general one-bit transformation matrix for one-bit gates in quantum computer, a general unitary transformation is constructed, which can serve as (controlled) m gate for the conditional quantum dynamics. When the quantized single-mode electromagnetic field containing n or no photons acts as the controlled bit, the quantum controlled-NOT gates and square root of the controlled-NOT gates in cavity-quantum electrodynamics are realized.
Two possible quantum descriptions of the classical Not gate are investigated in the framework of the Hilbert space C2: the unitary and the anti-unitary operator realizations. The two cases are distinguished interpreting the unitary Not as a quantum realization of the classical gate which on a xed orthogonal pair of unit vectors, realizing once for all the classical bits 0 and 1, produces the required transformations 0 => 1 and 1 => 0 (i.e., logical quantum Not). The anti-unitary Not is a quantum realization of a gate which acts as a classical Not on any pair of mutually orthogonal vectors, each of which is a potential realization of the classical bits (i.e., universal quantum Not). Although the latter is not completely positive, one can give an approximated unitary realization of the gate by appending an ancilla. Finally, we consider the unitary and the anti-unitary operator realizations of two important genuine quantum gates that transform elements of the computational basis of C2 into its superpositions: the square root of the identity and the square root of the Not.
An essential element of classical computation is the ``if-then'' construct, that accepts a control bit and an arbitrary gate, and provides conditional execution of the gate depending on the value of the controlling bit. On the other hand, quantum theory prevents the existence of an analogous universal construct accepting a control qubit and an arbitrary quantum gate as its input. Nevertheless, there are controllable sets of quantum gates for which such a construct exists. Here we provide a necessary and sufficient condition for a set of unitary transformations to be controllable, and we give a complete characterization of controllable sets in the two-dimensional case. This result reveals an interesting connection between the problem of controllability and the problem of extracting information from an unknown quantum gate while using it.
The controlled-NOT gate and controlled square-root NOT gate play an important role in quantum algorithm. This article reports the experimental results of these two universal quantum logic gates (controlled square-root NOT gate and controlled-NOT gate) on a 7-qubit NMR quantum computer. Further, we propose a simple experimental method to measure and correct the error in the controlled phase-shift gate, which is helpful to construct a more perfect phase-shift gate experimentally and can also be used in more qubits discrete Fourier transformation.
The problems related to the management of large quantum registers could be handled in the context of distributed quantum computation: unitary non-local transformations among spatially separated local processors are realized performing local unitary transformations and exchanging classical communication. In this paper, a scheme is proposed for the implementation of universal non-local quantum gates such as a controlled NOT (CNOT) and a controlled quantum phase gate (CQPG). The system chosen for their physical implementation is a cavity-quantum-electrodynamics (CQED) system formed by two spatially separated microwave cavities and two trapped Rydberg atoms. The procedures to follow for the realization of each step necessary to perform a specific non-local operation are described.
Quantum algorithms may be described by sequences of unitary transformations called quantum gates and measurements applied to the quantum register of n quantum bits, qubits. A collection of quantum gates is called universal if it can be used to construct any n-qubit gate. In 1995, the universality of the set of one-qubit gates and controlled NOT gate was shown by Barenco et al. using QR decomposition of unitary matrices. Almost ten years later the decomposition was improved to include essentially fewer elementary gates. In addition, the cosine-sine matrix decomposition was applied to efficiently implement decompositions of general quantum gates. In this chapter, we review the different types of general gate decompositions and slightly improve the best known gate count for the controlled NOT gates to (23/48)4^n in the leading order. In physical realizations, the interaction strength between the qubits can decrease strongly as a function of their distance. Therefore, we also discuss decompositions with the restriction to nearest-neighbor interactions in a linear chain of qubits.
Computations with a future quantum computer will be implemented through the operations by elementary quantum gates.It is now well known that the collection of 1-bit and 2-bit quantum gates are universal for quantum computation, i.e., any n-bit unitary operation can be carried out by concatenations of 1-bit and 2-bit elementary quantum gates.Three contemporary quantum devices-cavity QED, ion traps and quantum dots-have been widely regarded as perhaps the most promising candidates for the construction of elementary quantum gates.In this paper, we describe the physical properties of these devices, and show the mathematical derivations based on the interaction of the laser field as control with atoms, ions or electron spins, leading to the following:(i) the 1-bit unitary rotation gates; and(ii) the 2-bit quantum phase gates and the controlled-not gate.This paper is aimed at providing a sufficiently self-contained survey account of analytical nature for mathematicians, physicists and computer scientists to aid interdisciplinary understanding in the research of quantum computation.