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:2111.07182 · Journal of Computational and Applied Mathematics

Density theorems with applications in quantum signal processing

Rahul Sarkar, Theodore J. Yoder

Published Apr 1, 2023• 1 citation
arXivHTMLPDF
DOI
10.1016/j.cam.2023.115243

Related papers

Quantum Windowed Fourier Transform and its Application to Quantum Signal Processing

Haiting Yin, Dayong Lu, Rui Zhang

International Journal of Theoretical Physics•Sep 15, 2021•12 citations

Density Operators and Other Tools of Quantum Statistics

W. Ebeling, Thorsten Pöschel

Lecture notes in physics•Jan 1, 2019•1 citation

A Solovay-Kitaev theorem for quantum signal processing

Zane M. Rossi

Quantum signal processing (QSP) studies quantum circuits interleaving known unitaries (the phases) and unknown unitaries encoding a hidden scalar (the signal). For a wide class of functions one can quickly compute the phases applying a desired function to the signal; surprisingly, this ability can be shown to unify many quantum algorithms. A separate, basic subfield in quantum computing is gate approximation: among its results, the Solovay-Kitaev theorem (SKT) establishes an equivalence between the universality of a gate set and its ability to efficiently approximate other gates. In this work we prove an 'SKT for QSP,' showing that the density of parameterized circuit ansätze in classes of functions implies the existence of short circuits approximating desired functions. This is quite distinct from a pointwise application of the usual SKT, and yields a suite of independently interesting 'lifted' variants of standard SKT proof techniques. Our method furnishes alternative, flexible proofs for results in QSP, extends simply to ansätze for which standard QSP proof methods fail, and establishes a formal intersection between QSP and gate approximation.

arXiv:2505.05468•May 8, 2025•0 citations

Parallel Quantum Signal Processing Via Polynomial Factorization

John M. Martyn, Zane M. Rossi, Kevin Z. Cheng +2 more

Quantum signal processing (QSP) is a methodology for constructing polynomial transformations of a linear operator encoded in a unitary. Applied to an encoding of a state ρ , QSP enables the evaluation of nonlinear functions of the form tr(P(ρ)) for a polynomial P(x) , which encompasses relevant properties like entropies and fidelity. However, QSP is a sequential algorithm: implementing a degree- d polynomial necessitates d queries to the encoding, equating to a query depth d . Here, we reduce the depth of these property estimation algorithms by developing Parallel Quantum Signal Processing. Our algorithm parallelizes the computation of tr(P(ρ)) over k systems and reduces the query depth to d/k , thus enabling a family of time-space tradeoffs for QSP. This furnishes a property estimation algorithm suitable for distributed quantum computers, and is realized at the expense of increasing the number of measurements by a factor O(poly(d)2O(k)) . We achieve this result by factorizing P(x) into a product of k smaller polynomials of degree O(d/k) , which are each implemented in parallel with QSP, and subsequently multiplied together with a swap test to reconstruct P(x) . We characterize the achievable class of polynomials by appealing to the fundamental theorem of algebra, and demonstrate application to canonical problems including entropy estimation and partition function evaluation.

arXiv:2409.19043•Quantum•Aug 27, 2025•2 citations

Quantum Information and Quantum Signal Processing

François Chapeau‐Blondeau

Springer eBooks•Jan 1, 2026•0 citations

Quantum Signal Processing in Strengthening Cyber Defense: A Comparative Study

Akindemowo Olayiwola Ayorinde

Aim: To examine the strengthening of cyber defense using Quantum Signal Processing. Significance of Study: There is need for the application of Quantum Signal Processing in cyber security due to the vulnerable attack. This paper addresses the relevant issues on the use of Quantum Signal Processing in strengthening cyber defense. Problem Statement: The development of cyber space and its inestimable contribution in information dissemination has led to its wide patronage and usage. Thus, third party are intruding to hijack and hack secretive information to suite their own purpose. Discussion: The concepts of Quantum Signal Processing (QSP) and cyber defense were examined. It was revealed that the measurement of Quantum Signal Processing is strongly involved in signal processing of algorithms design with significance to QSP framework such that in this framework, the processing of signals occur via the utilization of some Quantum Signal Processing measurement variables or subjecting them to a Quantum Signal Processing measurement. Also, the QSP framework is primarily assigned with the quantum physics constraints, QSP measurement design, a quantum measurement, borrowing from the principles, and axioms. Nonetheless, the measurement consistency principle, measurement concept and quantization of the measurement output principle were identified as the three interconnected fundamental principles of quantum mechanics in Quantum Signal Processing. The existing correlation between QSP framework and quantum physics together with relevant key results were also examined. was also discussed with major Considerations were given to modification of known algorithms, measurement parameters utilization, probabilistic mappings, imposition of inner product constraints and oblique projections as the algorithm design in quantum signal processing framework. Conclusion: In conclusion, Quantum Signal Processing is applicable in strengthening cyber defense.

Current Journal of Applied Science and Technology•Jun 18, 2024•0 citations
Quantum signal processing (QSP) studies quantum circuits interleaving known unitaries (the phases) and unknown unitaries encoding a hidden scalar (the signal). For a wide class of functions one can quickly compute the phases applying a desired function to the signal; surprisingly, this ability can be shown to unify many quantum algorithms. A separate, basic subfield in quantum computing is gate approximation: among its results, the Solovay-Kitaev theorem (SKT) establishes an equivalence between the universality of a gate set and its ability to efficiently approximate other gates. In this work we prove an 'SKT for QSP,' showing that the density of parameterized circuit ansätze in classes of functions implies the existence of short circuits approximating desired functions. This is quite distinct from a pointwise application of the usual SKT, and yields a suite of independently interesting 'lifted' variants of standard SKT proof techniques. Our method furnishes alternative, flexible proofs for results in QSP, extends simply to ansätze for which standard QSP proof methods fail, and establishes a formal intersection between QSP and gate approximation.
Quantum signal processing (QSP) is a methodology for constructing polynomial transformations of a linear operator encoded in a unitary. Applied to an encoding of a state ρ , QSP enables the evaluation of nonlinear functions of the form tr(P(ρ)) for a polynomial P(x) , which encompasses relevant properties like entropies and fidelity. However, QSP is a sequential algorithm: implementing a degree- d polynomial necessitates d queries to the encoding, equating to a query depth d . Here, we reduce the depth of these property estimation algorithms by developing Parallel Quantum Signal Processing. Our algorithm parallelizes the computation of tr(P(ρ)) over k systems and reduces the query depth to d/k , thus enabling a family of time-space tradeoffs for QSP. This furnishes a property estimation algorithm suitable for distributed quantum computers, and is realized at the expense of increasing the number of measurements by a factor O(poly(d)2O(k)) . We achieve this result by factorizing P(x) into a product of k smaller polynomials of degree O(d/k) , which are each implemented in parallel with QSP, and subsequently multiplied together with a swap test to reconstruct P(x) . We characterize the achievable class of polynomials by appealing to the fundamental theorem of algebra, and demonstrate application to canonical problems including entropy estimation and partition function evaluation.
Aim: To examine the strengthening of cyber defense using Quantum Signal Processing. Significance of Study: There is need for the application of Quantum Signal Processing in cyber security due to the vulnerable attack. This paper addresses the relevant issues on the use of Quantum Signal Processing in strengthening cyber defense. Problem Statement: The development of cyber space and its inestimable contribution in information dissemination has led to its wide patronage and usage. Thus, third party are intruding to hijack and hack secretive information to suite their own purpose. Discussion: The concepts of Quantum Signal Processing (QSP) and cyber defense were examined. It was revealed that the measurement of Quantum Signal Processing is strongly involved in signal processing of algorithms design with significance to QSP framework such that in this framework, the processing of signals occur via the utilization of some Quantum Signal Processing measurement variables or subjecting them to a Quantum Signal Processing measurement. Also, the QSP framework is primarily assigned with the quantum physics constraints, QSP measurement design, a quantum measurement, borrowing from the principles, and axioms. Nonetheless, the measurement consistency principle, measurement concept and quantization of the measurement output principle were identified as the three interconnected fundamental principles of quantum mechanics in Quantum Signal Processing. The existing correlation between QSP framework and quantum physics together with relevant key results were also examined. was also discussed with major Considerations were given to modification of known algorithms, measurement parameters utilization, probabilistic mappings, imposition of inner product constraints and oblique projections as the algorithm design in quantum signal processing framework. Conclusion: In conclusion, Quantum Signal Processing is applicable in strengthening cyber defense.