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/0605185

Single qubit, two qubit gates and no signalling principle

Indranil Chakrabarty

Published May 22, 2006• 0 citations
arXivHTMLPDF

Abstract

In this work we investigate that whether one can construct single and two qubit gates for arbitrary quantum states from the principle of no signalling. We considered the problem for Pauli gates, Hadamard gate, C-Not gate.
DOI
10.48550/arxiv.quant-ph/0605185

Related papers

Optimal Realization of an Arbitrary Two-Qubit Quantum Gate

Farrokh Vatan, Colin P. Williams

By an explicit construction, we show that an arbitrary two-qubit gate can be implemented by using at most 16 elementary one-qubit gates and 3 CNOT gates. We show that this construction is optimal; in the sense that these numbers of gates is the minimal possible ones. Moreover, we show that if the two-qubit gate belongs to SO(4), then we need only 12 elementary one-qubit gates and 2 CNOT gates. 1

•Aug 1, 2003•9 citations

Generators and Roots of Quantum Logic Gates

R. Muradian, Diego Frias

This is an exposition of some basic mathematical aspects of quantum logic gates. At first we established some general formulas for the case of arbitrary quantum gate A with unique restriction A^2=I. The explicit form of the generators and roots of matrix A have been found . Then we apply general results to the particular cases of one-qubit and multi-qubit quantum gates. Some interesting properties of square roots of basic Pauli and Hadamard gates are demonstrated.

arXiv:quant-ph/0511250•Nov 28, 2005•0 citations

Optimal quantum circuits for general two-qubit gates

Farrokh Vatan, Colin P. Williams

In order to demonstrate nontrivial quantum computations experimentally, such as the synthesis of arbitrary entangled states, it will be useful to understand how to decompose a desired quantum computation into the shortest possible sequence of one-qubit and two-qubit gates. We contribute to this effort by providing a method to construct an optimal quantum circuit for a general two-qubit gate that requires at most 3 controlled-NOT (CNOT) gates and 15 elementary one-qubit gates. Moreover, if the desired two-qubit gate corresponds to a purely real unitary transformation, we provide a construction that requries at most 2 CNOT and 12 one-qubit gates. We then prove that these constructions are optimal with respect to the family of CNOT, $y$-rotation, $z$-rotation, and phase gates.

arXiv:quant-ph/0308006•Physical Review A•Mar 22, 2004•442 citations

ON THE NON-EXISTENCE OF A UNIVERSAL HADAMARD GATE

Preeti Parashar

We establish the non-existence of a universal Hadamard gate for an arbitrary qubit, by considering two different principles; namely, no-superluminal signalling and non-increase of entanglement under LOCC. It is also shown that these principles are not violated if and only if the qubit states belong to the special ensemble obtained recently. We then extend the non-existence of the Hadamard operation to a multi-qubit system. In higher dimensions, the analog of the Hadamard gate is the quantum Fourier transform. We show that it is not possible to design this gate for an arbitrary qudit.

arXiv:quant-ph/0606231•International Journal of Quantum Information•Dec 1, 2007•2 citations

A Lecture on Quantum Logic Gates

Kazuyuki Fujii

In this note we make a short review of constructions of n-repeated controlled unitary gates in quantum logic gates.

arXiv:quant-ph/0101054•Jan 13, 2001•5 citations

Multiparty Quantum Telecommunication Using Quantum Fourier Transforms

Do Ngoc Diep

Consider the problem: Alice wishes to send the same key to $n-1$ users (Bob, Carol,. . . , Nathan), while preventing eavesdropper Eve from acquiring information without being detected. The problem has no solution in the classical cryptography but in quantum telecommunication there are some codes to solve the problem. In the paper \cite{zengetall}, Guo-Jyun Zeng, Kuan-Hung Chen, Zhe-Hua Chang, Yu-Shan Yang, and Yao-Hsin Chou from one side and Cabello in \cite{cabello} from other side, used Hadamard gates, Pauli gates in providing the quantum communication code for two-partity telecommunication with 3 persons and then generalized it to the case of arbitrary number of participants, indicating the position of measurements of participants. We remark that the Hadamard gate with precising the position of measurement is the same as Fourier transform for two qubits and hence use the general Fourier transform for $n$ entangled qubits, in place of Hadamard gates. The result is more natural for arbitrary $n$ qudits.

arXiv:1705.02608•May 7, 2017•4 citations
In order to demonstrate nontrivial quantum computations experimentally, such as the synthesis of arbitrary entangled states, it will be useful to understand how to decompose a desired quantum computation into the shortest possible sequence of one-qubit and two-qubit gates. We contribute to this effort by providing a method to construct an optimal quantum circuit for a general two-qubit gate that requires at most 3 controlled-NOT (CNOT) gates and 15 elementary one-qubit gates. Moreover, if the desired two-qubit gate corresponds to a purely real unitary transformation, we provide a construction that requries at most 2 CNOT and 12 one-qubit gates. We then prove that these constructions are optimal with respect to the family of CNOT, yyy-rotation, zzz-rotation, and phase gates.
We establish the non-existence of a universal Hadamard gate for an arbitrary qubit, by considering two different principles; namely, no-superluminal signalling and non-increase of entanglement under LOCC. It is also shown that these principles are not violated if and only if the qubit states belong to the special ensemble obtained recently. We then extend the non-existence of the Hadamard operation to a multi-qubit system. In higher dimensions, the analog of the Hadamard gate is the quantum Fourier transform. We show that it is not possible to design this gate for an arbitrary qudit.
Consider the problem: Alice wishes to send the same key to n−1n-1n−1 users (Bob, Carol,. . . , Nathan), while preventing eavesdropper Eve from acquiring information without being detected. The problem has no solution in the classical cryptography but in quantum telecommunication there are some codes to solve the problem. In the paper \cite{zengetall}, Guo-Jyun Zeng, Kuan-Hung Chen, Zhe-Hua Chang, Yu-Shan Yang, and Yao-Hsin Chou from one side and Cabello in \cite{cabello} from other side, used Hadamard gates, Pauli gates in providing the quantum communication code for two-partity telecommunication with 3 persons and then generalized it to the case of arbitrary number of participants, indicating the position of measurements of participants. We remark that the Hadamard gate with precising the position of measurement is the same as Fourier transform for two qubits and hence use the general Fourier transform for nnn entangled qubits, in place of Hadamard gates. The result is more natural for arbitrary nnn qudits.