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

Computing in Science & Engineering

Reducing quantum computations to elementary unitary operations

George V. Cybenko

Published Jan 1, 2001• 95 citations
Publisher

Abstract

Quantum computations are intimately connected with unitary operators. This article shows that standard techniques from numerical linear algebra can be used to represent quantum computations as sequences of simple quantum operations, called quantum Givens operators, on single quantum bits.
DOI
10.1109/5992.908999

Related papers

Quantum Computing

Michael F. Insana

Quantum computing (QC) is an exciting new technology that completes the text with an application that relies heavily on the mathematics of linear algebra. There is more to explain than the conversion of common matrix notation into Dirac bra-ket notation. There is also the bizarre world of quantum physics that is inspiring a range of quantum information technologies. Qubits and their entangled superposition states are introduced to show that the “quantum advantage” stems from qubits storing exponentially more information that can be processed at exponentially faster rates. The process of preparing, modifying, and measuring qubit states is explained. Linear algebra skills are exercised by representing QC coding through the application of unitary operators to qubit states. QC algorithms are designed by diagramming quantum circuits, casting those circuits into sequences of operators applied to qubit states, and converting the operators into matrix forms. These are the tools of QC. Several algorithms that demonstrate a range of computational tasks from simple arithmetic through quantum Fourier analysis complete the chapter.

Chapman & Hall/CRC eBooks•Sep 11, 2026•0 citations

An Optimization for Qubiter

Robert R. Tucci

In a previous paper, we described a computer program called Qubiter which can decompose an arbitrary unitary matrix into elementary operations of the type used in quantum computation. In this paper, we describe a method of reducing the number of elementary operations in such decompositions.

arXiv:quant-ph/9809055•Sep 17, 1998•0 citations

A Rudimentary Quantum Compiler

Robert R. Tucci

We present a new algorithm for reducing an arbitrary unitary matrix into a sequence of elementary operations (operations such as controlled-nots and qubit rotations). Such a sequence of operations can be used to manipulate an array of quantum bits (i.e., a quantum computer). We report on a C++ program called "Qubiter" that implements our algorithm. Qubiter source code is publicly available.

arXiv:quant-ph/9805015•May 7, 1998•48 citations

Quantum implementation of elementary arithmetic operations

Giuseppe Florio, DOMENICO PICCA

Quantum computation has received great attention in recent years for its possible application to difficult problem in classical calculation. Despite the experimental problems of implementing quantum devices, theoretical physicists have tried to conceive some implementations for quantum algorithms. We present here some explicit schemes for executing elementary arithmetic operations.

arXiv:quant-ph/0403048•Mar 5, 2004•14 citations

Operator Algebras in Quantum Computation

Mathys Rennela

In this master thesis, I discuss how the theory of operator algebras, also called operator theory, can be applied in quantum computer science.

arXiv:1510.06649•Oct 22, 2015•8 citations

A Rudimentary Quantum Compiler(2cnd Ed.)

Robert R. Tucci

We present a new algorithm for reducing an arbitrary unitary matrix U into a sequence of elementary operations (operations such as controlled-nots and qubit rotations). Such a sequence of operations can be used to manipulate an array of quantum bits (i.e., a quantum computer). Our algorithm applies recursively a mathematical technique called the CS Decomposition to build a binary tree of matrices whose product, in some order, equals the original matrix U. We show that the Fast Fourier Transform (FFT) algorithm is a special case of our algorithm. We report on a C++ program called "Qubiter" that implements the ideas of this paper. Qubiter(PATENT PENDING) source code is publicly available.

arXiv:quant-ph/9902062•Feb 18, 1999•30 citations
Quantum computing (QC) is an exciting new technology that completes the text with an application that relies heavily on the mathematics of linear algebra. There is more to explain than the conversion of common matrix notation into Dirac bra-ket notation. There is also the bizarre world of quantum physics that is inspiring a range of quantum information technologies. Qubits and their entangled superposition states are introduced to show that the “quantum advantage” stems from qubits storing exponentially more information that can be processed at exponentially faster rates. The process of preparing, modifying, and measuring qubit states is explained. Linear algebra skills are exercised by representing QC coding through the application of unitary operators to qubit states. QC algorithms are designed by diagramming quantum circuits, casting those circuits into sequences of operators applied to qubit states, and converting the operators into matrix forms. These are the tools of QC. Several algorithms that demonstrate a range of computational tasks from simple arithmetic through quantum Fourier analysis complete the chapter.
We present a new algorithm for reducing an arbitrary unitary matrix U into a sequence of elementary operations (operations such as controlled-nots and qubit rotations). Such a sequence of operations can be used to manipulate an array of quantum bits (i.e., a quantum computer). Our algorithm applies recursively a mathematical technique called the CS Decomposition to build a binary tree of matrices whose product, in some order, equals the original matrix U. We show that the Fast Fourier Transform (FFT) algorithm is a special case of our algorithm. We report on a C++ program called "Qubiter" that implements the ideas of this paper. Qubiter(PATENT PENDING) source code is publicly available.