arxiv: 2604.18276 · v1 · submitted 2026-04-20 · 🪐 quant-ph · cs.ET· cs.LG· cs.MS· cs.PL

Recognition: unknown

Block-encodings as programming abstractions: The Eclipse Qrisp BlockEncoding Interface

Matic Petri\v{c} , Ren\'e Zander

Authors on Pith no claims yet

Pith reviewed 2026-05-10 04:36 UTC · model grok-4.3

classification 🪐 quant-ph cs.ETcs.LGcs.MScs.PL

keywords block-encodingqubitizationquantum algorithmsquantum singular value transformationprogramming abstractionmatrix inversionHamiltonian simulation

0 comments

The pith

A programming interface abstracts block-encodings into a high-level tool for quantum algorithm implementation.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows how to treat block-encodings, the embedding of non-unitary operators into unitary matrices, as a programmable abstraction instead of a manual circuit design task. It provides details on how the interface handles construction of these encodings, their composition through arithmetic operations, and the incorporation of qubitization to enable advanced methods. Examples illustrate the use in the Childs-Kothari-Somma algorithm as well as for matrix inversion, polynomial filtering, and Hamiltonian simulation. A sympathetic reader would value this because it removes the need to manage low-level details like qubit requirements and circuit compilation when exploring these protocols. The goal is to open block-encoding techniques to scientists who may not specialize in quantum circuit engineering.

Core claim

Block-encodings function as a high-level programming abstraction when supported by an interface that includes constructors for their creation, utilities for qubitization, arithmetic composition operations, and direct mappings to algorithmic applications such as matrix inversion and Hamiltonian simulation.

What carries the argument

The BlockEncoding interface, which abstracts the theoretical requirements of block-encodings and qubitization into programmable methods that handle embedding and operation without exposing circuit-level complexities.

If this is right

Quantum algorithms that depend on non-unitary operations become easier to code and test.
Resource estimation for circuits using block-encodings can be done programmatically.
Composition of multiple block-encodings supports building more complex quantum transformations.
Implementation of QSVT, QSP, and similar techniques requires less specialized knowledge.
Practical examples demonstrate streamlined development of matrix inversion and simulation algorithms.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Such an abstraction could encourage more interdisciplinary work between quantum algorithm theorists and software developers.
Future extensions might include automated optimization of the resulting circuits beyond current manual approaches.
Adoption in teaching settings could accelerate learning of advanced quantum computing concepts.
Scalability tests on increasingly large operators would help determine its suitability for near-term quantum devices.

Load-bearing premise

The interface correctly and efficiently implements the underlying block-encoding theory and qubitization procedures in its code without hidden bugs or performance penalties.

What would settle it

Construct a block-encoding for a simple non-unitary matrix using the interface, generate the corresponding quantum circuit, and check through simulation or compilation whether the embedding accuracy and gate count match independent theoretical calculations.

Figures

Figures reproduced from arXiv: 2604.18276 by Matic Petri\v{c}, Ren\'e Zander.

**Figure 1.** Figure 1: Visual schematics of the block-encoding construction [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗

**Figure 3.** Figure 3: Visual schematics of block-encoding the k-th Chebyshev polynomial of the first kind Tk through repeated application of the qubitization walk operator Wˆ k for k = 1, 2, 5. than direct quantum circuit manipulation, we refer the reader to [17]. The BlockEncoding class in Qrisp abstracts the mathematical formalisms described in Section II into a seamless object-oriented interface. The core attributes inclu… view at source ↗

**Figure 4.** Figure 4: Visual schematic illustrating the efficient block [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗

**Figure 5.** Figure 5: Visual schematic of the CKS algorithm implementation. [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗

read the original abstract

Block-encoding is a foundational technique in modern quantum algorithms, enabling the implementation of non-unitary operations by embedding them into larger unitary matrices. While theoretically powerful and essential for advanced protocols like Quantum Singular Value Transformation (QSVT) and Quantum Signal Processing (QSP), the generation of compilable implementations of block-encodings poses a formidable challenge. This work presents the BlockEncoding interface within the Eclipse Qrisp framework, establishing block-encodings as a high-level programming abstraction accessible to a broad scientific audience. Serving as both a technical framework introduction and a hands-on tutorial, this paper explicitly details key underlying concepts abstracted away by the interface, such as block-encoding construction and qubitization, and their practical integration into methods like the Childs-Kothari-Somma (CKS) algorithm. We outline the interface's software architecture, encompassing constructors, core utilities, arithmetic composition, and algorithmic applications such as matrix inversion, polynomial filtering, and Hamiltonian simulation. Through code examples, we demonstrate how this interface simplifies both the practical realization of advanced quantum algorithms and their associated resource estimation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Qrisp's new BlockEncoding interface makes block-encodings easier to compose in code, but the paper gives no evidence that the implementation actually works as claimed.

read the letter

The paper's core contribution is a BlockEncoding interface inside the Eclipse Qrisp framework that turns the theoretical construction into something you can call with constructors, arithmetic operations, and direct hooks into algorithms like CKS, matrix inversion, and polynomial filtering. It also walks through qubitization and shows code snippets for Hamiltonian simulation. That is genuinely new as a packaged software layer; prior work on block-encodings stayed at the mathematical or circuit-diagram level. The tutorial style and explicit architecture description are useful for anyone already working inside Qrisp who wants to avoid writing the low-level embedding by hand each time. Credit to the authors for making the abstraction concrete and tying it to real algorithmic use cases. The main weakness is the complete absence of any correctness check. There are no small-matrix tests that extract the effective operator from the generated circuit and compare it to the mathematical definition, no resource counts, and no discussion of normalization or phase-handling edge cases. Without that, the claim that the interface simplifies advanced algorithms rests on trust in the unshown code. This is a software-framework paper aimed at quantum-computing developers who use or are considering Qrisp. A reader looking for practical tools rather than new theory will find the examples helpful. It is worth sending to peer review so the authors can add the missing validation steps; the underlying idea is solid enough to justify referee time.

Referee Report

1 major / 1 minor

Summary. The manuscript presents the BlockEncoding interface in the Eclipse Qrisp quantum programming framework. It establishes block-encodings as a high-level abstraction, explains underlying concepts including construction and qubitization, and demonstrates integration into algorithms such as the Childs-Kothari-Somma (CKS) method, matrix inversion, polynomial filtering, and Hamiltonian simulation via descriptions of the software architecture, constructors, utilities, arithmetic composition, and code examples.

Significance. If the interface correctly implements the theoretical block-encodings, the work would lower barriers to advanced quantum algorithms like QSVT and QSP for a broader audience by providing accessible constructors and composition methods. The explicit coverage of abstracted concepts and code examples for resource estimation is a positive contribution to usability and education in the field.

major comments (1)

The central claim that the interface faithfully realizes theoretical block-encoding constructions (abstract; sections on constructors, core utilities, arithmetic composition, and algorithmic applications) lacks any verification step. No example extracts the effective operator from a generated circuit and compares it to the mathematical definition on a small test matrix, leaving potential issues in qubit allocation, normalization, or phase handling unaddressed. This directly undermines the assertion of correct and efficient realization for downstream algorithms like CKS and matrix inversion.

minor comments (1)

The abstract could more explicitly separate the novel interface contributions from established block-encoding theory to clarify the paper's incremental advance.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive and detailed review of our manuscript. We address the single major comment below, agreeing that an explicit verification would strengthen the presentation, and describe the planned revision.

read point-by-point responses

Referee: The central claim that the interface faithfully realizes theoretical block-encoding constructions (abstract; sections on constructors, core utilities, arithmetic composition, and algorithmic applications) lacks any verification step. No example extracts the effective operator from a generated circuit and compares it to the mathematical definition on a small test matrix, leaving potential issues in qubit allocation, normalization, or phase handling unaddressed. This directly undermines the assertion of correct and efficient realization for downstream algorithms like CKS and matrix inversion.

Authors: We agree that the manuscript would benefit from an explicit verification step that extracts the effective operator realized by a generated circuit and compares it numerically to the mathematical block-encoding definition on a small test matrix. Such a check would directly address possible concerns about qubit allocation, normalization factors, and phase conventions. In the revised version we will add a new subsection (or extended code example) under the constructors or core utilities section that performs this verification for at least one low-dimensional test matrix, reports the numerical agreement (or discrepancy), and discusses how the same procedure can be applied to the CKS and matrix-inversion examples already present in the paper. revision: yes

Circularity Check

0 steps flagged

No circularity: software interface description on established theory

full rationale

The manuscript introduces the BlockEncoding interface as a high-level abstraction in the Eclipse Qrisp framework, detailing constructors, utilities, arithmetic composition, and applications such as CKS, matrix inversion, polynomial filtering, and Hamiltonian simulation via code examples. It explicitly builds on prior theoretical block-encoding and qubitization concepts without new mathematical derivations, parameter fitting, or predictions. No self-definitional loops, fitted inputs renamed as predictions, or load-bearing self-citations appear; the central claim of accessibility and simplification rests on descriptive architecture and examples rather than any chain that reduces to its own inputs by construction. The work is self-contained as a framework tutorial.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The contribution is a software interface; no free parameters, physical axioms, or invented entities are introduced beyond the framework itself.

pith-pipeline@v0.9.0 · 5498 in / 1029 out tokens · 33790 ms · 2026-05-10T04:36:39.973684+00:00 · methodology

discussion (0)

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

Unitaria: Quantum Linear Algebra via Block Encodings
quant-ph 2026-05 accept novelty 4.0

Unitaria is a new open-source Python library that provides a high-level, composable interface for block encodings in quantum computing, enabling automatic circuit generation and classical simulation-based verification.

Reference graph

Works this paper leans on

72 extracted references · 48 canonical work pages · cited by 1 Pith paper · 6 internal anchors

[1]

Quantum algorithm for linear systems of equations,

A. W. Harrow, A. Hassidim, and S. Lloyd, “Quantum algorithm for linear systems of equations,”Phys. Rev. Lett., vol. 103, p. 150502,
[2]

Bl´ azquez-Salcedo, C

[Online]. Available: https://link.aps.org/doi/10.1103/PhysRevLett. 103.150502

work page doi:10.1103/physrevlett
[3]

Quantum algorithm for systems of linear equations with exponentially improved dependence on precision,

A. M. Childs, R. Kothari, and R. D. Somma, “Quantum algorithm for systems of linear equations with exponentially improved dependence on precision,”SIAM Journal on Computing, vol. 46, no. 6, pp. 1920–1950,

1920
[4]

Childs, Robin Kothari, and Rolando D

[Online]. Available: https://doi.org/10.1137/16M1087072

work page doi:10.1137/16m1087072
[5]

Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics

A. Gily ´en, Y . Su, G. H. Low, and N. Wiebe, “Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics,” inProceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing, ser. STOC 2019. New York, NY , USA: Association for Computing Machinery, 2019, p. 193–204. [Online]. Available: https://doi....

work page doi:10.1145/3313276.3316366 2019
[6]

Optimal polynomial based quantum eigenstate filtering with application to solving quantum linear systems,

L. Lin and Y . Tong, “Optimal polynomial based quantum eigenstate filtering with application to solving quantum linear systems,”Quantum, vol. 4, p. 361, 2020. [Online]. Available: https://doi.org/10.22331/ q-2020-11-11-361

2020
[7]

A shortcut to an optimal quantum linear system solver,

A. M. Dalzell, “A shortcut to an optimal quantum linear system solver,”
[8]

A shortcut to an optimal quantum linear system solver

[Online]. Available: https://arxiv.org/abs/2406.12086

work page internal anchor Pith review Pith/arXiv arXiv
[9]

Quantum linear system solvers: A survey of algorithms and applications

M. E. S. Morales, L. Pira, P. Schleich, K. Koor, P. C. S. Costa, D. An, A. Aspuru-Guzik, L. Lin, P. Rebentrost, and D. W. Berry, “Quantum linear system solvers: A survey of algorithms and applications,” 2025. [Online]. Available: https://arxiv.org/abs/2411.02522

work page arXiv 2025
[10]

Exponential quantum advantage in processing massive classical data

H. Zhao, A. Zlokapa, H. Neven, R. Babbush, J. Preskill, J. R. McClean, and H.-Y . Huang, “Exponential quantum advantage in processing massive classical data,” 2026. [Online]. Available: https: //arxiv.org/abs/2604.07639

work page internal anchor Pith review Pith/arXiv arXiv 2026
[11]

Linear combination of hamiltonian simulation for nonunitary dynamics with optimal state preparation cost,

D. An, J.-P. Liu, and L. Lin, “Linear combination of hamiltonian simulation for nonunitary dynamics with optimal state preparation cost,”Phys. Rev. Lett., vol. 131, p. 150603, 2023. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevLett.131.150603

work page doi:10.1103/physrevlett.131.150603 2023
[12]

Filtered quantum phase estimation,

G. Lee, M. Kang, J. Hong, S. Fomichev, and J. Huh, “Filtered quantum phase estimation,” 2025. [Online]. Available: https://arxiv.org/abs/2510. 04294

2025
[13]

Beyond asymptotic reasoning: the practicalities of a quantum ground state projector based on the wall-chebyshev expansion,

M.-A. Filip and N. Fitzpatrick, “Beyond asymptotic reasoning: the practicalities of a quantum ground state projector based on the wall-chebyshev expansion,”Quantum Science and Technology, vol. 11, no. 1, p. 015027, 2025. [Online]. Available: https: //doi.org/10.1088/2058-9565/ae2887

work page doi:10.1088/2058-9565/ae2887 2025
[14]

Grand unification of quantum algorithms,

J. M. Martyn, Z. M. Rossi, A. K. Tan, and I. L. Chuang, “Grand unification of quantum algorithms,”PRX Quantum, vol. 2, p. 040203, 2021. [Online]. Available: https://link.aps.org/doi/10.1103/ PRXQuantum.2.040203

2021
[15]

QSPPACK: Quantum sig- nal processing PACKage,

Y . Dong, X. Meng, K. B. Whaley, and L. Lin, “QSPPACK: Quantum sig- nal processing PACKage,” https://github.com/qsppack/QSPPACK, 2021, gitHub repository

2021
[16]

pyqsp: Python Quantum Signal Processing package,

I. L. Chuang, J. Docter, J. M. Martyn, Z. M. Rossi, and A. K. Tan, “pyqsp: Python Quantum Signal Processing package,” https://github. com/ichuang/pyqsp, 2021, gitHub repository

2021
[17]

Expressing and Analyzing Quantum Algorithms with Qualtran

M. P. Harrigan, T. Khattar, C. Yuan, A. Peduri, N. Yosri, F. D. Malone, R. Babbush, and N. C. Rubin, “Expressing and analyzing quantum algorithms with qualtran,” 2024. [Online]. Available: https://arxiv.org/abs/2409.04643

work page arXiv 2024
[18]

PennyLane: Automatic differentiation of hybrid quantum-classical computations

V . Bergholm, J. Izaac, M. Schuld, C. Gogolin, S. Ahmed, V . Ajith, M. S. Alam, G. Alonso-Linaje, B. AkashNarayanan, A. Asadiet al., “Pennylane: Automatic differentiation of hybrid quantum-classical computations,”arXiv preprint arXiv:1811.04968, 2022. [Online]. Available: https://arxiv.org/abs/1811.04968

work page internal anchor Pith review arXiv 2022
[19]

Cobble: Compiling Block Encodings for Quantum Computational Linear Algebra

C. Yuan, “Cobble: Compiling block encodings for quantum computational linear algebra,” 2025. [Online]. Available: https://arxiv.org/abs/2511.01736

work page internal anchor Pith review arXiv 2025
[20]

Seidel, S

R. Seidel, S. Bock, R. Zander, M. Petri ˇc, N. Steinmann, N. Tcholtchev, and M. Hauswirth, “Qrisp: A framework for compilable high-level programming of gate-based quantum computers,” 2024. [Online]. Available: https://arxiv.org/abs/2406.14792

work page arXiv 2024
[21]

Lecture notes on quantum algorithms for scientific computation,

L. Lin, “Lecture notes on quantum algorithms for scientific computation,” 2022. [Online]. Available: https://arxiv.org/abs/2201. 08309

2022
[22]

, title =

G. H. Low and I. L. Chuang, “Hamiltonian Simulation by Qubitization,”Quantum, vol. 3, p. 163, 2019. [Online]. Available: https://doi.org/10.22331/q-2019-07-12-163

work page doi:10.22331/q-2019-07-12-163 2019
[23]

Exact and efficient Lanczos method on a quantum computer,

W. Kirby, M. Motta, and A. Mezzacapo, “Exact and efficient Lanczos method on a quantum computer,”Quantum, vol. 7, p. 1018, 2023. [Online]. Available: https://doi.org/10.22331/q-2023-05-23-1018

work page doi:10.22331/q-2023-05-23-1018 2023
[24]

Rise of conditionally clean ancillae for efficient quantum circuit constructions,

T. Khattar and C. Gidney, “Rise of conditionally clean ancillae for efficient quantum circuit constructions,”Quantum, vol. 9, p. 1752,
[25]

Available: https://doi.org/10.22331/q-2025-05-21-1752

[Online]. Available: https://doi.org/10.22331/q-2025-05-21-1752

work page doi:10.22331/q-2025-05-21-1752 2025
[26]

A. M. Dalzell, S. McArdle, M. Berta, P. Bienias, C.-F. Chen, A. Gily ´en, C. T. Hann, M. J. Kastoryano, E. T. Khabiboulline, A. Kubica, G. Salton, S. Wang, and F. G. S. L. Brand ˜ao, Quantum Algorithms: A Survey of Applications and End-to-end Complexities. Cambridge University Press, 2025. [Online]. Available: http://dx.doi.org/10.1017/9781009639651

work page doi:10.1017/9781009639651 2025
[27]

Products between block-encodings,

D. Dong, Y . Li, and J. Xue, “Products between block-encodings,” 2025. [Online]. Available: https://arxiv.org/abs/2509.15779

work page arXiv 2025
[28]

Generalized quantum signal processing,

D. Motlagh and N. Wiebe, “Generalized quantum signal processing,” PRX Quantum, vol. 5, p. 020368, 2024. [Online]. Available: https://link.aps.org/doi/10.1103/PRXQuantum.5.020368

work page doi:10.1103/prxquantum.5.020368 2024
[29]

Generalized quantum singular value transformation,

C. S ¨underhauf, “Generalized quantum singular value transformation,”
[30]

Available: https://arxiv.org/abs/2312.00723

[Online]. Available: https://arxiv.org/abs/2312.00723

work page arXiv
[31]

Generalized quantum signal processing and non- linear fourier transform are equivalent,

L. Laneve, “Generalized quantum signal processing and non- linear fourier transform are equivalent,” 2025. [Online]. Available: https://arxiv.org/abs/2503.03026

work page arXiv 2025
[32]

Inverse nonlinear fast fourier transform on su(2) with applications to quantum signal processing,

H. Ni, R. Sarkar, L. Ying, and L. Lin, “Inverse nonlinear fast fourier transform on su(2) with applications to quantum signal processing,”
[33]

Inverse nonlinear fast Fourier transform on SU(2) with applications to quantum signal processing

[Online]. Available: https://arxiv.org/abs/2505.12615

work page arXiv
[34]

Eigenstate filtering using quantum signal processing,

R. Zander, “Eigenstate filtering using quantum signal processing,” https://github.com/eclipse-qrisp/Qrisp/blob/main/documentation/source/ general/tutorial/GQSP filtering.ipynb
[35]

Halving the cost of quantum addition,

C. Gidney, “Halving the cost of quantum addition,”Quantum, vol. 2, p. 74, 2018. [Online]. Available: https://doi.org/10.22331/ q-2018-06-18-74

2018
[36]

An introduction to the conjugate gradient method without the agonizing pain,

J. R. Shewchuket al., “An introduction to the conjugate gradient method without the agonizing pain,” 1994

1994
[37]

Embedding learning in hybrid quantum-classical neural networks,

D. Camps and R. Van Beeumen, “Fable: Fast approximate quantum circuits for block-encodings,” in2022 IEEE International Conference on Quantum Computing and Engineering (QCE), 2022, pp. 104–113. [Online]. Available: https://doi.org/10.1109/QCE53715.2022.00029

work page doi:10.1109/qce53715.2022.00029 2022
[38]

S-fable and ls-fable: Fast approximate block-encoding algorithms for unstructured sparse matrices,

P. Kuklinski and B. Rempfer, “S-fable and ls-fable: Fast approximate block-encoding algorithms for unstructured sparse matrices,” 2024. [Online]. Available: https://arxiv.org/abs/2401.04234

work page arXiv 2024
[39]

Efficient LCU block encodings through Dicke states preparation

F. D. Chiara, M. Nibbi, Y . Shen, and R. V . Beeumen, “Efficient lcu block encodings through dicke states preparation,” 2025. [Online]. Available: https://arxiv.org/abs/2507.20887

work page arXiv 2025
[40]

Practical block encodings of matrix polynomials that can also be trivially controlled,

M. Nibbi, F. D. Chiara, Y . Shen, A. Szasz, and R. V . Beeumen, “Practical block encodings of matrix polynomials that can also be trivially controlled,” 2026. [Online]. Available: https://arxiv.org/abs/2601.18767

work page arXiv 2026
[41]

Dictionary-based Block Encoding of Sparse Matrices with Low Subnormalization and Circuit Depth,

C. Yang, Z. Li, H. Yao, Z. Fan, G. Zhang, and J. Liu, “Dictionary-based Block Encoding of Sparse Matrices with Low Subnormalization and Circuit Depth,”Quantum, vol. 9, p. 1805, 2025. [Online]. Available: https://doi.org/10.22331/q-2025-07-22-1805

work page doi:10.22331/q-2025-07-22-1805 2025
[42]

Block encoding linear combinations of pauli strings using the stabilizer formalism,

N. Schillo, A. Sturm, and R. Quay, “Block encoding linear combinations of pauli strings using the stabilizer formalism,” 2026. [Online]. Available: https://arxiv.org/abs/2601.05740

work page internal anchor Pith review arXiv 2026
[43]

Explicit Block Encodings of Discrete Laplacians with Mixed Boundary Conditions

A. Boutot and V . Dsouza, “Explicit block encodings of discrete laplacians with mixed boundary conditions,” 2026. [Online]. Available: https://arxiv.org/abs/2603.12405

work page internal anchor Pith review Pith/arXiv arXiv 2026
[44]

Quantum algorithm for linear matrix equations

R. D. Somma, G. H. Low, D. W. Berry, and R. Babbush, “Quantum algorithm for linear matrix equations,” 2025. [Online]. Available: https://arxiv.org/abs/2508.02822

work page arXiv 2025
[45]

Quantum support vector machine for big data classification,

P. Rebentrost, M. Mohseni, and S. Lloyd, “Quantum support vector machine for big data classification,”Phys. Rev. Lett., vol. 113, p. 130503, 2014. [Online]. Available: https://link.aps.org/doi/10.1103/ PhysRevLett.113.130503

2014
[46]

Quantum Regularized Least Squares,

S. Chakraborty, A. Morolia, and A. Peduri, “Quantum Regularized Least Squares,”Quantum, vol. 7, p. 988, 2023. [Online]. Available: https://doi.org/10.22331/q-2023-04-27-988

work page doi:10.22331/q-2023-04-27-988 2023
[47]

Preconditioned block encodings for quantum linear systems,

L. Lapworth and C. S ¨underhauf, “Preconditioned block encodings for quantum linear systems,”Quantum Science and Technology, vol. 10, no. 4, p. 045064, 2025. [Online]. Available: https: //doi.org/10.1088/2058-9565/ae0f4b

work page doi:10.1088/2058-9565/ae0f4b 2025
[48]

Zylberman, T

J. Zylberman, T. Fredon, N. F. Loureiro, and F. Debbasch,Quantum Algorithm for Anisotropic Diffusion and Convection Equations with V ector Norm Scaling. Springer Nature Switzerland, 2026, p. 255–263. [Online]. Available: http://dx.doi.org/10.1007/978-3-032-13855-2 23

work page doi:10.1007/978-3-032-13855-2 2026
[49]

Counterdiabatic driving with performance guarantees,

J. R. Fin ˇzgar, S. Notarnicola, M. Cain, M. D. Lukin, and D. Sels, “Counterdiabatic driving with performance guarantees,” Phys. Rev. Lett., vol. 135, p. 180602, 2025. [Online]. Available: https://link.aps.org/doi/10.1103/pqhl-nbtk

work page doi:10.1103/pqhl-nbtk 2025
[50]

Efficient product formulas for commutators and applications to quantum simulation,

Y .-A. Chen, A. M. Childs, M. Hafezi, Z. Jiang, H. Kim, and Y . Xu, “Efficient product formulas for commutators and applications to quantum simulation,”Phys. Rev. Res., vol. 4, p. 013191, 2022. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevResearch.4.013191

work page doi:10.1103/physrevresearch.4.013191 2022
[51]

Quantum algorithm for simulating resonant inelastic x-ray scattering in battery materials,

I. Loaiza, A. Kunitsa, S. Fomichev, D. Motlagh, D. Dhawan, S. Jahangiri, J. H. Fuglsbjerg, A. F. Izmaylov, N. Wiebe, Y . Abu- Lebdeh, J. M. Arrazola, and A. Delgado, “Quantum algorithm for simulating resonant inelastic x-ray scattering in battery materials,”
[52]

Available: https://arxiv.org/abs/2602.20270

[Online]. Available: https://arxiv.org/abs/2602.20270

work page arXiv
[53]

Quantum computing enhanced computational catalysis,

V . von Burg, G. H. Low, T. H¨aner, D. S. Steiger, M. Reiher, M. Roetteler, and M. Troyer, “Quantum computing enhanced computational catalysis,” Phys. Rev. Res., vol. 3, p. 033055, 2021. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevResearch.3.033055

work page doi:10.1103/physrevresearch.3.033055 2021
[54]

Even more efficient quantum computations of chemistry through tensor hypercontraction,

J. Lee, D. W. Berry, C. Gidney, W. J. Huggins, J. R. McClean, N. Wiebe, and R. Babbush, “Even more efficient quantum computations of chemistry through tensor hypercontraction,”PRX Quantum, vol. 2, p. 030305, 2021. [Online]. Available: https://link.aps.org/doi/10.1103/ PRXQuantum.2.030305

2021
[55]

Efficient simulation of pre-born-oppenheimer dynamics on a quantum computer,

M. Pocrnic, I. Loaiza, J. M. Arrazola, N. Wiebe, and D. Motlagh, “Efficient simulation of pre-born-oppenheimer dynamics on a quantum computer,” 2026. [Online]. Available: https://arxiv.org/abs/2602.11272

work page arXiv 2026
[56]

Quantum algorithm for simulating non-adiabatic dynamics at metallic surfaces,

R. A. Lang, P. Jain, J. M. Arrazola, and D. Motlagh, “Quantum algorithm for simulating non-adiabatic dynamics at metallic surfaces,”
[57]

Available: https://arxiv.org/abs/2601.16264

[Online]. Available: https://arxiv.org/abs/2601.16264

work page arXiv
[58]

Quantum algorithm for vibronic dynamics: case study on singlet fission solar cell design,

D. Motlagh, R. A. Lang, P. Jain, J. A. Campos-Gonzalez-Angulo, W. Maxwell, T. Zeng, A. Aspuru-Guzik, and J. Miguel Arrazola, “Quantum algorithm for vibronic dynamics: case study on singlet fission solar cell design,”Quantum Science and Technology, vol. 10, no. 4, p. 045048, 2025. [Online]. Available: https://doi.org/10.1088/ 2058-9565/ae0828

2025
[59]

BlockEncoding – Qrisp documentation,

Qrisp Developers, “BlockEncoding – Qrisp documentation,” https:// qrisp.eu/reference/Block Encodings/BlockEncoding.html, 2026, online; accessed 2026

2026
[60]

arXiv:2003.02831 , year =

R. Chao, D. Ding, A. Gilyen, C. Huang, and M. Szegedy, “Finding angles for quantum signal processing with machine precision,” 2020. [Online]. Available: https://arxiv.org/abs/2003.02831

work page arXiv 2020
[61]

Product Decomposition of Periodic Functions in Quantum Signal Processing,

J. Haah, “Product Decomposition of Periodic Functions in Quantum Signal Processing,”Quantum, vol. 3, p. 190, 2019. [Online]. Available: https://doi.org/10.22331/q-2019-10-07-190

work page doi:10.22331/q-2019-10-07-190 2019
[63]

Efficient phase-factor evaluation in quantum signal processing,

——, “Efficient phase-factor evaluation in quantum signal processing,” Phys. Rev. A, vol. 103, p. 042419, 2021. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevA.103.042419

work page doi:10.1103/physreva.103.042419 2021
[64]

Quantum eigenvalue processing,

G. H. Low and Y . Su, “Quantum eigenvalue processing,”SIAM Journal on Computing, vol. 55, no. 1, pp. 135–215, 2026. [Online]. Available: https://doi.org/10.1137/24M1689363

work page doi:10.1137/24m1689363 2026
[65]

An adversary bound for quantum signal processing,

L. Laneve, “An adversary bound for quantum signal processing,” Quantum, vol. 10, p. 2025, 2026. [Online]. Available: https: //doi.org/10.22331/q-2026-03-13-2025

work page doi:10.22331/q-2026-03-13-2025 2025
[66]

Blockencoding class 101: Block encoding, lcu, resource estimation,

M. Petri ˇc and R. Zander, “Blockencoding class 101: Block encoding, lcu, resource estimation,” https://github.com/eclipse-qrisp/Qrisp/blob/main/ documentation/source/general/tutorial/BE tutorial/BE vol1.ipynb
[67]

Blockencoding class 201: Qubitization, chebyshev polynomials, qsp,

——, “Blockencoding class 201: Qubitization, chebyshev polynomials, qsp,” https://github.com/eclipse-qrisp/Qrisp/blob/main/documentation/ source/general/tutorial/BE tutorial/BE vol2.ipynb
[68]

Efficient and explicit block encoding of finite difference discretizations of the laplacian

A. Sturm and N. Schillo, “Efficient and explicit block encoding of finite difference discretizations of the laplacian,” 2025. [Online]. Available: https://arxiv.org/abs/2509.02429

work page arXiv 2025
[69]

Trade-offs between quantum and classical resources in the linear combination of unitaries,

K. Wada, H. Harada, Y . Suzuki, Y . Tokunaga, N. Yamamoto, and S. Endo, “Trade-offs between quantum and classical resources in the linear combination of unitaries,” 2026. [Online]. Available: https://arxiv.org/abs/2512.06260

work page arXiv 2026
[70]

Explicit block- encoding for partial differential equation-constrained optimization,

Y . Sato, J. Kato, H. Yano, K. Ito, and N. Yamamoto, “Explicit block- encoding for partial differential equation-constrained optimization,”
[71]

Available: https://arxiv.org/abs/2511.14420

[Online]. Available: https://arxiv.org/abs/2511.14420

work page arXiv
[72]

Resource-efficient variational compilation of block- encodings,

L. Rullk ¨otter, S. Weber, V . M. Katukuri, C. Tutschku, and B. C. Mummaneni, “Resource-efficient variational compilation of block- encodings,” 2025. [Online]. Available: https://arxiv.org/abs/2507.17658

work page arXiv 2025
[73]

Harmonic sequence state-preparation,

B. Rempfer, P. Kuklinski, J. Elenewski, and K. Obenland, “Harmonic sequence state-preparation,” 2026. [Online]. Available: https://arxiv.org/ abs/2602.23664

work page arXiv 2026