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:1906.00037 · Numerical Algebra Control and Optimization

Long-step path-following algorithm for quantum information theory: Some numerical aspects and applications

Leonid E. Faybusovich, Cunlu Zhou

Published Jun 4, 2021• 6 citations
arXivHTMLPDF

Abstract

We consider some important computational aspects of the long-step path-following algorithm developed in our previous work and show that a broad class of complicated optimization problems arising in quantum information theory can be solved using this approach. In particular, we consider one difficult optimization problem involving the quantum relative entropy in quantum key distribution and show that our method can solve problems of this type much faster in comparison with (very few) available options.

DOI
10.3934/naco.2021017

Related papers

On Implementation of Long-Step Path-Following Algorithms for Convex Optimization Problems in Quantum Information Theory

Leonid E. Faybusovich, Cunlu Zhou

•May 31, 2019•0 citations

Quantum key distribution rates from non-symmetric conic optimization

Andrés González Lorente, Pablo V. Parellada, Miguel Castillo-Celeita +1 more

Computing key rates in quantum key distribution (QKD) numerically is essential to unlock more powerful protocols, that use more sophisticated measurement bases or quantum systems of higher dimension. It is a difficult optimization problem, that depends on minimizing a convex non-linear function: the (quantum) relative entropy. Standard conic optimization techniques have for a long time been unable to handle the relative entropy cone, as it is a non-symmetric cone, and the standard algorithms can only handle symmetric ones. Recently, however, a practical algorithm has been discovered for optimizing over non-symmetric cones, including the relative entropy. Here we adapt this algorithm to the problem of computation of key rates, obtaining an efficient technique for lower bounding them. In comparison to previous techniques it has the advantages of flexibility, ease of use, and above all performance.

arXiv:2407.00152•Quantum•Mar 10, 2025•6 citations

Entropy, Optimization and Coding Theory

Cunlu Zhou

Entropy is a central concept in many different disciplines, and many important applications involving entropy can be viewed as entropy optimization problems. In this dissertation we study a class of symmetric (conic) programming problems with nonlinear convex objective functions in the context of Euclidean Jordan algebras, which includes the so-called quantum (von Neumann) entropy optimization as a special case. Quantum entropy optimization plays an important role in many areas such as quantum computing, quantum information theory, machine learning, etc. We develop a long-step path-following algorithm for such optimization problems. The theoretical framework is developed for functions compatible (in the sense of Nesterov and Nemirovski) with the standard barrier function - lndet(x). Complexity estimates similar to the case of a linear-quadratic objective function are established, and the theoretical scheme is implemented for the quantum entropy optimization problem. The Shannon entropy optimization problem can be viewed as a special case of the quantum entropy optimization problem with diagonal matrices. We briefly discuss one application of the Shannon entropy optimization in coding theory, namely evaluating the asymptotic pseudoweight enumerators for protograph-based low-density parity-check (LDPC) codes. In the end we also briefly discuss some future work related to quantum relative entropy optimization.

•Nov 16, 2022•1 citation

Progress and Prospects of Quantum Algorithms

Hang Yang, Bi Wu, Yongbo Xuan +2 more

Quantum computers are designed to outperform standard computers by running quantum algorithms. Fields in which quantum algorithms can be applied include cryptography, search and optimization, simulation of quantum systems and solving large systems of linear equations. Here we briefly survey some known quantum algorithms, with an emphasis on a broad overview of their applications rather than their technical details. We focus to introduce the development of entire field, and provide a comprehensive and accurate understanding concerning this field, which may be helpful for interested researchers in this area.

World Symposium on Software Engineering (WSSE)•Sep 28, 2022•2 citations

Interior Point Methods for Structured Quantum Relative Entropy Optimization Problems

Kerry He, James Saunderson, Hamza Fawzi

Abstract Quantum relative entropy optimization refers to a class of convex problems in which a linear functional is minimized over an affine section of the epigraph of the quantum relative entropy function. Recently, the self-concordance of a natural barrier function was proved for this set, and various implementations of interior-point methods have been made available to solve this class of optimization problems. In this paper, we show how common structures arising from applications in quantum information theory can be exploited to improve the efficiency of solving quantum relative entropy optimization problems using interior-point methods. First, we show that the natural barrier function for the epigraph of the quantum relative entropy composed with positive linear operators is self-concordant, even when these linear operators map to singular matrices. Compared to modeling problems using the full quantum relative entropy cone, this allows us to remove redundant log-determinant expressions from the barrier function and reduce the overall barrier parameter. Second, we show how certain slices of the quantum relative entropy cone exhibit useful properties which should be exploited whenever possible to perform certain key steps of interior-point methods more efficiently. We demonstrate how these methods can be applied to applications in quantum information theory, including quantifying quantum key rates, quantum rate-distortion functions, quantum channel capacities, and the ground state energy of Hamiltonians. Our numerical results show that these techniques improve computation times by up to several orders of magnitude, and allow previously intractable problems to be solved.

arXiv:2407.00241•Mathematical Programming Computation•Nov 17, 2025•2 citations

Quantum algorithms: an overview

Ashley Montanaro

Abstract Quantum computers are designed to outperform standard computers by running quantum algorithms. Areas in which quantum algorithms can be applied include cryptography, search and optimisation, simulation of quantum systems and solving large systems of linear equations. Here we briefly survey some known quantum algorithms, with an emphasis on a broad overview of their applications rather than their technical details. We include a discussion of recent developments and near-term applications of quantum algorithms.

arXiv:1511.04206•npj Quantum Information•Jan 12, 2016•1,071 citations
We consider some important computational aspects of the long-step path-following algorithm developed in our previous work and show that a broad class of complicated optimization problems arising in quantum information theory can be solved using this approach. In particular, we consider one difficult optimization problem involving the quantum relative entropy in quantum key distribution and show that our method can solve problems of this type much faster in comparison with (very few) available options.
Computing key rates in quantum key distribution (QKD) numerically is essential to unlock more powerful protocols, that use more sophisticated measurement bases or quantum systems of higher dimension. It is a difficult optimization problem, that depends on minimizing a convex non-linear function: the (quantum) relative entropy. Standard conic optimization techniques have for a long time been unable to handle the relative entropy cone, as it is a non-symmetric cone, and the standard algorithms can only handle symmetric ones. Recently, however, a practical algorithm has been discovered for optimizing over non-symmetric cones, including the relative entropy. Here we adapt this algorithm to the problem of computation of key rates, obtaining an efficient technique for lower bounding them. In comparison to previous techniques it has the advantages of flexibility, ease of use, and above all performance.
Entropy is a central concept in many different disciplines, and many important applications involving entropy can be viewed as entropy optimization problems. In this dissertation we study a class of symmetric (conic) programming problems with nonlinear convex objective functions in the context of Euclidean Jordan algebras, which includes the so-called quantum (von Neumann) entropy optimization as a special case. Quantum entropy optimization plays an important role in many areas such as quantum computing, quantum information theory, machine learning, etc. We develop a long-step path-following algorithm for such optimization problems. The theoretical framework is developed for functions compatible (in the sense of Nesterov and Nemirovski) with the standard barrier function - lndet(x). Complexity estimates similar to the case of a linear-quadratic objective function are established, and the theoretical scheme is implemented for the quantum entropy optimization problem. The Shannon entropy optimization problem can be viewed as a special case of the quantum entropy optimization problem with diagonal matrices. We briefly discuss one application of the Shannon entropy optimization in coding theory, namely evaluating the asymptotic pseudoweight enumerators for protograph-based low-density parity-check (LDPC) codes. In the end we also briefly discuss some future work related to quantum relative entropy optimization.
Quantum computers are designed to outperform standard computers by running quantum algorithms. Fields in which quantum algorithms can be applied include cryptography, search and optimization, simulation of quantum systems and solving large systems of linear equations. Here we briefly survey some known quantum algorithms, with an emphasis on a broad overview of their applications rather than their technical details. We focus to introduce the development of entire field, and provide a comprehensive and accurate understanding concerning this field, which may be helpful for interested researchers in this area.
Abstract Quantum relative entropy optimization refers to a class of convex problems in which a linear functional is minimized over an affine section of the epigraph of the quantum relative entropy function. Recently, the self-concordance of a natural barrier function was proved for this set, and various implementations of interior-point methods have been made available to solve this class of optimization problems. In this paper, we show how common structures arising from applications in quantum information theory can be exploited to improve the efficiency of solving quantum relative entropy optimization problems using interior-point methods. First, we show that the natural barrier function for the epigraph of the quantum relative entropy composed with positive linear operators is self-concordant, even when these linear operators map to singular matrices. Compared to modeling problems using the full quantum relative entropy cone, this allows us to remove redundant log-determinant expressions from the barrier function and reduce the overall barrier parameter. Second, we show how certain slices of the quantum relative entropy cone exhibit useful properties which should be exploited whenever possible to perform certain key steps of interior-point methods more efficiently. We demonstrate how these methods can be applied to applications in quantum information theory, including quantifying quantum key rates, quantum rate-distortion functions, quantum channel capacities, and the ground state energy of Hamiltonians. Our numerical results show that these techniques improve computation times by up to several orders of magnitude, and allow previously intractable problems to be solved.
Abstract Quantum computers are designed to outperform standard computers by running quantum algorithms. Areas in which quantum algorithms can be applied include cryptography, search and optimisation, simulation of quantum systems and solving large systems of linear equations. Here we briefly survey some known quantum algorithms, with an emphasis on a broad overview of their applications rather than their technical details. We include a discussion of recent developments and near-term applications of quantum algorithms.