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/9809055

An Optimization for Qubiter

Robert R. Tucci

Published Sep 17, 1998• 0 citations
arXivHTMLPDF

Abstract

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.
DOI
10.48550/arxiv.quant-ph/9809055

Related papers

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

Efficient Decomposition of Unitary Matrices in Quantum Circuit Compilers

Anna M. Krol, Aritra Sarkar, Imran Ashraf +2 more

Unitary decomposition is a widely used method to map quantum algorithms to an arbitrary set of quantum gates. Efficient implementation of this decomposition allows for the translation of bigger unitary gates into elementary quantum operations, which is key to executing these algorithms on existing quantum computers. The decomposition can be used as an aggressive optimization method for the whole circuit, as well as to test part of an algorithm on a quantum accelerator. For the selection and implementation of the decomposition algorithm, perfect qubits are assumed. We base our decomposition technique on Quantum Shannon Decomposition, which generates O(344n) controlled-not gates for an n-qubit input gate. In addition, we implement optimizations to take advantage of the potential underlying structure in the input or intermediate matrices, as well as to minimize the execution time of the decomposition. Comparing our implementation to Qubiter and the UniversalQCompiler (UQC), we show that our implementation generates circuits that are much shorter than those of Qubiter and not much longer than the UQC. At the same time, it is also up to 10 times as fast as Qubiter and about 500 times as fast as the UQC.

arXiv:2101.02993•Applied Sciences•Jan 12, 2022•54 citations

Qubiter Algorithm Modification, Expressing Unstructured Unitary Matrices with Fewer CNOTs

Robert R. Tucci

A quantum compiler is a software program for decomposing ("compiling") an arbitrary unitary matrix into a sequence of elementary operations (SEO). The author of this paper is also the author of a quantum compiler called Qubiter. Qubiter uses a matrix decomposition called the Cosine-Sine Decomposition (CSD) that is well known in the field of Computational Linear Algebra. One way of measuring the efficiency of a quantum compiler is to measure the number of CNOTs it uses to express an unstructured unitary matrix (a unitary matrix with no special symmetries). We will henceforth refer to this number as $ε$. In this paper, we show how to improve $ε$ for Qubiter so that it matches the current world record for $ε$, which is held by another quantum compiling algorithm based on CSD.

arXiv:quant-ph/0411027•Nov 3, 2004•6 citations

Efficient Decomposition of Quantum Gates

Juha J. Vartiainen, Mikko Möttönen, Martti M. Salomaa

Optimal implementation of quantum gates is crucial for designing a quantum computer. We consider the matrix representation of an arbitrary multiqubit gate. By ordering the basis vectors using the Gray code, we construct the quantum circuit which is optimal in the sense of fully controlled single-qubit gates and yet is equivalent with the multiqubit gate. In the second step of the optimization, superfluous control bits are eliminated, which eventually results in a smaller total number of the elementary gates. In our scheme the number of controlled NOT gates is O(4(n)) which coincides with the theoretical lower bound.

arXiv:quant-ph/0312218•Physical Review Letters•Apr 29, 2004•241 citations

Simplifying Quantum Circuits via Circuit Invariants and Dressed CNOTs

Robert R. Tucci

Quantum Compiling Algorithms decompose (exactly, without approximations) an arbitrary $2^\nb$ unitary matrix acting on $\nb$ qubits, into a sequence of elementary operations (SEO). There are many possible ways of decomposing a unitary matrix into a SEO, and some of these decompositions have shorter length (are more efficient) than others. Finding an optimum (shortest) decomposition is a very hard task, and is not our intention here. A less ambitious, more doable task is to find methods for optimizing small segments of a SEO. Call these methods piecewise optimizations. Piecewise optimizations involve replacing a small quantum circuit by an equivalent one with fewer CNOTs. Two circuits are said to be equivalent if one of them multiplied by some external local operations equals the other. This equivalence relation between circuits has its own class functions, which we call circuit invariants. Dressed CNOTs are a simple yet very useful generalization of standard CNOTs. After discussing circuit invariants and dressed CNOTs, we give some methods for simplifying 2-qubit and 3-qubit circuits. We include with this paper software (written in Octave/Matlab) that checks many of the algorithms proposed in the paper.

arXiv:quant-ph/0606061•Jun 7, 2006•1 citation

Hardware-Efficient Decomposition of Qudit Gates

Sean P. Dougherty, Tanay Roy

Describes a decomposition technique to write a qudit unitary as a sequence of SU(2) rotations and outlines a scheme to map decompositions on to other decompositions.

•Aug 7, 2023•0 citations
Unitary decomposition is a widely used method to map quantum algorithms to an arbitrary set of quantum gates. Efficient implementation of this decomposition allows for the translation of bigger unitary gates into elementary quantum operations, which is key to executing these algorithms on existing quantum computers. The decomposition can be used as an aggressive optimization method for the whole circuit, as well as to test part of an algorithm on a quantum accelerator. For the selection and implementation of the decomposition algorithm, perfect qubits are assumed. We base our decomposition technique on Quantum Shannon Decomposition, which generates O(344n) controlled-not gates for an n-qubit input gate. In addition, we implement optimizations to take advantage of the potential underlying structure in the input or intermediate matrices, as well as to minimize the execution time of the decomposition. Comparing our implementation to Qubiter and the UniversalQCompiler (UQC), we show that our implementation generates circuits that are much shorter than those of Qubiter and not much longer than the UQC. At the same time, it is also up to 10 times as fast as Qubiter and about 500 times as fast as the UQC.
A quantum compiler is a software program for decomposing ("compiling") an arbitrary unitary matrix into a sequence of elementary operations (SEO). The author of this paper is also the author of a quantum compiler called Qubiter. Qubiter uses a matrix decomposition called the Cosine-Sine Decomposition (CSD) that is well known in the field of Computational Linear Algebra. One way of measuring the efficiency of a quantum compiler is to measure the number of CNOTs it uses to express an unstructured unitary matrix (a unitary matrix with no special symmetries). We will henceforth refer to this number as εεε. In this paper, we show how to improve εεε for Qubiter so that it matches the current world record for εεε, which is held by another quantum compiling algorithm based on CSD.
Optimal implementation of quantum gates is crucial for designing a quantum computer. We consider the matrix representation of an arbitrary multiqubit gate. By ordering the basis vectors using the Gray code, we construct the quantum circuit which is optimal in the sense of fully controlled single-qubit gates and yet is equivalent with the multiqubit gate. In the second step of the optimization, superfluous control bits are eliminated, which eventually results in a smaller total number of the elementary gates. In our scheme the number of controlled NOT gates is O(4(n)) which coincides with the theoretical lower bound.
Quantum Compiling Algorithms decompose (exactly, without approximations) an arbitrary $2^\nb$ unitary matrix acting on $\nb$ qubits, into a sequence of elementary operations (SEO). There are many possible ways of decomposing a unitary matrix into a SEO, and some of these decompositions have shorter length (are more efficient) than others. Finding an optimum (shortest) decomposition is a very hard task, and is not our intention here. A less ambitious, more doable task is to find methods for optimizing small segments of a SEO. Call these methods piecewise optimizations. Piecewise optimizations involve replacing a small quantum circuit by an equivalent one with fewer CNOTs. Two circuits are said to be equivalent if one of them multiplied by some external local operations equals the other. This equivalence relation between circuits has its own class functions, which we call circuit invariants. Dressed CNOTs are a simple yet very useful generalization of standard CNOTs. After discussing circuit invariants and dressed CNOTs, we give some methods for simplifying 2-qubit and 3-qubit circuits. We include with this paper software (written in Octave/Matlab) that checks many of the algorithms proposed in the paper.