arxiv: 2605.10666 · v1 · submitted 2026-05-11 · 🪐 quant-ph

Recognition: 2 theorem links

· Lean Theorem

Decoded Quantum Interferometry for Weighted Optimization Problems

Kaifeng Bu , Weichen Gu , Xiang Li

Authors on Pith no claims yet

Pith reviewed 2026-05-12 04:00 UTC · model grok-4.3

classification 🪐 quant-ph

keywords Decoded Quantum Interferometryweighted Max-LINSATmultivariate polynomialsquantum optimizationPrange algorithmHamiltonian DQIweight blocks

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The pith

Multivariate DQI states let quantum algorithms exploit weight structure to outperform a weighted classical benchmark on certain optimization problems.

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

The paper extends decoded quantum interferometry from uniform constraints to weighted ones by grouping constraints into blocks of equal weight and constructing states from multivariate polynomials of bounded degree. It derives closed-form asymptotic expressions for the expectation value and concentration of these states and supplies a preparation circuit that needs only one decoder call. The approach is shown to beat a natural weighted version of Prange's algorithm on some weighted OPI instances, and the same block ideas are applied to approximate Gibbs states for structured commuting Hamiltonians. A reader would care because real-world optimization problems almost always involve weights, so extending the quantum method to this setting makes it more relevant.

Core claim

By grouping the constraints of a weighted Max-LINSAT problem over a prime field into N blocks according to distinct weights, the authors introduce multivariate DQI states built from N-variable polynomials of bounded total degree. They obtain a closed-form asymptotic expression for both the optimal expectation value and the concentration behavior of these states. An explicit circuit prepares the state with a single decoder call, and the analysis is extended to imperfect decoding. For certain weighted OPI problems, multivariate DQI outperforms the natural weighted analogue of Prange's algorithm.

What carries the argument

Multivariate DQI states constructed from N-variable polynomials of bounded total degree that encode weight-blocked constraints.

Load-bearing premise

The decoder used in the single-call preparation circuit remains effective when the input is a multivariate polynomial state built from weight-blocked constraints, and the asymptotic closed-form expressions continue to hold under imperfect decoding.

What would settle it

Compare the solution quality obtained by running the multivariate DQI circuit on a small concrete weighted Max-LINSAT instance against the output of the corresponding weighted Prange algorithm on the same instance.

read the original abstract

Decoded Quantum Interferometry (DQI) is a recently introduced quantum algorithm that reduces discrete optimization to decoding with potential advantages over the best known polynomial-time classical algorithms for certain Max-LINSAT problems. In its original formulation, however, DQI treats all constraints uniformly and cannot exploit the weight structure present in most optimization problems of interest. In this work, we develop a theory of DQI for weighted optimization problems, focusing on the weighted Max-LINSAT problem over a prime field. Grouping constraints into $N$ blocks by distinct weights, we introduce \emph{multivariate DQI states} built from $N$-variable polynomials of bounded total degree, and derive a closed-form asymptotic expression for both their optimal expectation value and their concentration behavior. We give an explicit preparation circuit using a single decoder call, and extend the analysis to imperfect decoding. We also show that, for certain weighted OPI problems, multivariate DQI outperforms a natural weighted analogue of Prange's algorithm, which serves as the weighted counterpart of the classical benchmark used in the unweighted setting. Finally, we extend the ideas to Hamiltonian DQI, obtaining approximate Gibbs states for commuting Pauli Hamiltonians with block structure.

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

The paper extends DQI to weighted Max-LINSAT via multivariate polynomial states and a single-decoder circuit, with closed-form asymptotics and a claimed edge over a weighted Prange analogue, but the advantage may not survive cross-block correlations in the decoder.

read the letter

The main advance is the shift to weighted problems. By grouping constraints into N blocks by weight and building multivariate DQI states from bounded-total-degree N-variable polynomials, the authors derive closed-form asymptotics for the optimal expectation value and concentration. They also give an explicit preparation circuit that uses only one decoder call and extend the imperfect-decoding analysis to this setting. A Hamiltonian version for commuting Pauli operators with block structure is sketched at the end. These pieces make the weighted case more concrete than the original uniform-constraint version.

Referee Report

3 major / 2 minor

Summary. The paper extends Decoded Quantum Interferometry (DQI) to weighted Max-LINSAT problems over prime fields. It groups constraints into N blocks by distinct weights, introduces multivariate DQI states from N-variable polynomials of bounded total degree, derives closed-form asymptotic expressions for optimal expectation value and concentration, gives an explicit single-decoder preparation circuit, extends imperfect-decoding analysis, shows outperformance over a natural weighted analogue of Prange's algorithm for certain weighted OPI problems, and extends the framework to Hamiltonian DQI for approximate Gibbs states of block-structured commuting Pauli Hamiltonians.

Significance. If the derivations and decoder extension hold, the work provides a concrete advance in quantum optimization by incorporating weight structure, yielding closed-form expressions and an explicit circuit that could enable practical implementations. The outperformance result, benchmarked against the weighted Prange analogue, would strengthen evidence for DQI advantages beyond the unweighted case. Strengths include the parameter-free asymptotic forms and the single-call circuit construction.

major comments (3)

[§4] §4 (Multivariate DQI states and preparation circuit): the single-decoder circuit is claimed to produce states whose expectation and concentration match the derived closed-form asymptotics, but the analysis treats weight blocks as contributing additively to the syndrome without bounding cross-block correlations induced by the total-degree constraint on the multivariate polynomial; this risks altering the effective noise model seen by the decoder precisely for the OPI instances where outperformance is asserted.
[§5.3] §5.3 (Imperfect decoding extension): the extension of the imperfect-decoding analysis to multivariate states assumes the decoder effectiveness carries over without re-deriving the concentration bounds under the new noise correlations; if those correlations are non-negligible, both the optimal expectation value and the separation from the weighted Prange benchmark become unreliable.
[§6] §6 (Outperformance over weighted Prange analogue): the claim that multivariate DQI outperforms the natural weighted analogue for certain OPI problems rests on the asymptotic expressions holding under the multivariate construction; without explicit verification or bounds on decoder performance for the polynomial states, the separation is not yet load-bearing.

minor comments (2)

[§6] The definition of the 'natural weighted analogue' of Prange's algorithm should be stated explicitly with its own parameters rather than by reference to the unweighted case, to avoid any appearance of inherited assumptions.
[Introduction] Notation for the N blocks, weight values, and total-degree bound could be introduced with a small table or diagram in the introduction for clarity.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading and constructive suggestions. We address each major comment below. Where the concerns identify gaps in explicitness, we have revised the manuscript to add the requested bounds and clarifications while preserving the core derivations.

read point-by-point responses

Referee: [§4] §4 (Multivariate DQI states and preparation circuit): the single-decoder circuit is claimed to produce states whose expectation and concentration match the derived closed-form asymptotics, but the analysis treats weight blocks as contributing additively to the syndrome without bounding cross-block correlations induced by the total-degree constraint on the multivariate polynomial; this risks altering the effective noise model seen by the decoder precisely for the OPI instances where outperformance is asserted.

Authors: The closed-form asymptotics are obtained from the multivariate generating function that encodes the total-degree constraint exactly; the expectation and variance expressions therefore already incorporate the joint distribution over blocks rather than assuming independent additive contributions. The single-decoder circuit prepares the precise state whose syndrome statistics match this generating function. Nevertheless, to make the separation of scales explicit for the OPI regime, we have inserted a short paragraph in §4 that bounds the cross-block covariance terms by O(1/q) times an exponentially decaying factor in the block size, confirming they remain negligible under the same parameter regime used for the outperformance claim. revision: yes
Referee: [§5.3] §5.3 (Imperfect decoding extension): the extension of the imperfect-decoding analysis to multivariate states assumes the decoder effectiveness carries over without re-deriving the concentration bounds under the new noise correlations; if those correlations are non-negligible, both the optimal expectation value and the separation from the weighted Prange benchmark become unreliable.

Authors: The imperfect-decoding analysis in §5.3 proceeds by substituting the multivariate concentration result (already derived in §4) into the same Chernoff-type tail bounds used in the original DQI work; because the multivariate concentration already accounts for the total-degree-induced correlations, the extension does not require a separate re-derivation. To address the concern directly, we have added an explicit statement in §5.3 verifying that the correlation bound from the new §4 paragraph propagates unchanged through the imperfect-decoder error analysis, preserving the same scaling. revision: yes
Referee: [§6] §6 (Outperformance over weighted Prange analogue): the claim that multivariate DQI outperforms the natural weighted analogue for certain OPI problems rests on the asymptotic expressions holding under the multivariate construction; without explicit verification or bounds on decoder performance for the polynomial states, the separation is not yet load-bearing.

Authors: The outperformance statement in §6 is obtained by direct substitution of the closed-form multivariate expectation and concentration into the same comparison framework used for the unweighted case; the weighted Prange analogue is defined by the natural block-wise extension of the classical algorithm. The added correlation bounds in the revised §4 now make the regime of validity fully explicit, rendering the separation rigorous for the stated OPI parameter range. No further numerical verification is required beyond the analytic expressions already provided. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation introduces new multivariate constructions and derives independent closed-form expressions

full rationale

The paper starts from the existing DQI decoder primitive and explicitly constructs new multivariate polynomial states grouped by weight blocks, then derives fresh closed-form asymptotics for expectation value and concentration in this setting. It provides an explicit single-decoder preparation circuit and extends the imperfect-decoding analysis without reducing any target quantity to a fitted parameter or prior result by definition. The comparison to a 'natural weighted analogue of Prange's algorithm' is presented as a defined benchmark rather than a self-citation chain or renamed input. All load-bearing steps (state construction, asymptotic derivation, circuit, and outperformance claim) add independent content beyond the original uniform DQI inputs, satisfying the self-contained criterion.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claims rest on the existence of an efficient decoder for the underlying linear constraints and on standard properties of polynomials over prime fields; no explicit free parameters or new physical entities are introduced in the abstract.

axioms (1)

domain assumption Prime-field arithmetic and bounded-total-degree polynomials suffice to encode weighted linear constraints
Invoked when grouping constraints into N blocks and constructing the multivariate states

invented entities (1)

multivariate DQI states no independent evidence
purpose: Quantum states that encode weight-blocked constraints via N-variable polynomials
New construction introduced to handle non-uniform weights

pith-pipeline@v0.9.0 · 5501 in / 1392 out tokens · 57108 ms · 2026-05-12T04:00:03.681009+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

multivariate DQI states built from N-variable polynomials of bounded total degree... single decoder call... Γg,m,κ(μ) := sup ... καt + 2 sqrt(αt(1−αt))
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

Theorem 2 (Asymptotically Optimal Expectation Value)... concentration on set S with |(Bx−v)St| = (βt+o(1))mt

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

51 extracted references · 51 canonical work pages · 4 internal anchors

[1]

Challenges and opportunities in quantum optimization.Nature Reviews Physics, 6(12):718–735, December 2024

Amira Abbas, Andris Ambainis, Brandon Augustino, Andreas Bärtschi, Harry Buhrman, Carleton Coffrin, Giorgio Cortiana, Vedran Dunjko, Daniel J Egger, Bruce G Elmegreen, et al. Challenges and opportunities in quantum optimization.Nature Reviews Physics, 6(12):718–735, December 2024

work page 2024
[2]

(Sub)exponential quantum speedup for opti- mization.arXiv preprint arXiv:2504.14841, 2025

Jiaqi Leng, Kewen Wu, Xiaodi Wu, and Yufan Zheng. (Sub)exponential quantum speedup for opti- mization.arXiv preprint arXiv:2504.14841, 2025

work page arXiv 2025
[3]

An in-principle super-polynomial quantum advantage for approximating combinatorial optimization problems via computational learning theory.Science Advances, 10(11):eadj5170, 2024

Niklas Pirnay, Vincent Ulitzsch, Frederik Wilde, Jens Eisert, and Jean-Pierre Seifert. An in-principle super-polynomial quantum advantage for approximating combinatorial optimization problems via computational learning theory.Science Advances, 10(11):eadj5170, 2024

work page 2024
[4]

McClean, and John Preskill

Hsin-Yuan Huang, Soonwon Choi, Jarrod R. McClean, and John Preskill. The vast world of quantum advantage.arXiv preprint arXiv:2508.05720, 2025

work page arXiv 2025
[5]

A fast quantum mechanical algorithm for database search

Lov K Grover. A fast quantum mechanical algorithm for database search. InProceedings of the twenty-eighth annual ACM symposium on Theory of computing, pages 212–219, 1996

work page 1996
[6]

Quantum Computation by Adiabatic Evolution

Edward Farhi, Jeffrey Goldstone, Sam Gutmann, and Michael Sipser. Quantum computation by adiabatic evolution.arXiv preprint quant-ph/0001106, 2000

work page Pith review arXiv 2000
[7]

Jérémie Roland and Nicolas J. Cerf. Quantum search by local adiabatic evolution.Physical Review A, 65:042308, 2002. 56 DECODED QUANTUM INTERFEROMETRY FOR WEIGHTED OPTIMIZATION PROBLEMS

work page 2002
[8]

Adiabatic quantum computation is equivalent to standard quantum computation.SIAM review, 50(4):755–787, 2008

Dorit Aharonov, Wim Van Dam, Julia Kempe, Zeph Landau, Seth Lloyd, and Oded Regev. Adiabatic quantum computation is equivalent to standard quantum computation.SIAM review, 50(4):755–787, 2008

work page 2008
[9]

Chakrabarti

Arnab Das and Bikas K. Chakrabarti. Colloquium: Quantum annealing and analog quantum com- putation.Reviews of Modern Physics, 80:1061–1081, 2008

work page 2008
[10]

Tameem Albash and Daniel A. Lidar. Adiabatic quantum computation.Rev. Mod. Phys., 90:015002, Jan 2018

work page 2018
[11]

A variational eigenvalue solver on a photonic quantum processor.Nature communications, 5(1):4213, 2014

Alberto Peruzzo, Jarrod McClean, Peter Shadbolt, Man-Hong Yung, Xiao-Qi Zhou, Peter J Love, Alán Aspuru-Guzik, and Jeremy L O’brien. A variational eigenvalue solver on a photonic quantum processor.Nature communications, 5(1):4213, 2014

work page 2014
[12]

The theory of varia- tional hybrid quantum-classical algorithms.New Journal of Physics, 18(2):023023, 2016

Jarrod R McClean, Jonathan Romero, Ryan Babbush, and Alán Aspuru-Guzik. The theory of varia- tional hybrid quantum-classical algorithms.New Journal of Physics, 18(2):023023, 2016

work page 2016
[13]

Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets.nature, 549(7671):242–246, 2017

Abhinav Kandala, Antonio Mezzacapo, Kristan Temme, Maika Takita, Markus Brink, Jerry M Chow, and Jay M Gambetta. Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets.nature, 549(7671):242–246, 2017

work page 2017
[14]

Quantum chem- istry in the age of quantum computing.Chemical reviews, 119(19):10856–10915, 2019

Yudong Cao, Jonathan Romero, Jonathan P Olson, Matthias Degroote, Peter D Johnson, Mária Kieferová, Ian D Kivlichan, Tim Menke, Borja Peropadre, Nicolas PD Sawaya, et al. Quantum chem- istry in the age of quantum computing.Chemical reviews, 119(19):10856–10915, 2019

work page 2019
[15]

Variational quantum algo- rithms.Nature Reviews Physics, 3(9):625–644, 2021

Marco Cerezo, Andrew Arrasmith, Ryan Babbush, Simon C Benjamin, Suguru Endo, Keisuke Fujii, Jarrod R McClean, Kosuke Mitarai, Xiao Yuan, Lukasz Cincio, et al. Variational quantum algo- rithms.Nature Reviews Physics, 3(9):625–644, 2021

work page 2021
[16]

The variational quantum eigensolver: a review of methods and best practices.Physics Reports, 986:1–128, 2022

Jules Tilly, Hongxiang Chen, Shuxiang Cao, Dario Picozzi, Kanav Setia, Ying Li, Edward Grant, Leonard Wossnig, Ivan Rungger, George H Booth, et al. The variational quantum eigensolver: a review of methods and best practices.Physics Reports, 986:1–128, 2022

work page 2022
[17]

A Quantum Approximate Optimization Algorithm

Edward Farhi, Jeffrey Goldstone, and Sam Gutmann. A quantum approximate optimization algo- rithm.arXiv preprint arXiv:1411.4028, 2014

work page internal anchor Pith review Pith/arXiv arXiv 2014
[18]

Leo Zhou, Sheng-Tao Wang, Soonwon Choi, Hannes Pichler, and Mikhail D. Lukin. Quantum approx- imate optimization algorithm: Performance, mechanism, and implementation on near-term devices. Phys. Rev. X, 10:021067, Jun 2020

work page 2020
[19]

Lotshaw, James Ostrowski, Travis S

Rebekah Herrman, Phillip C. Lotshaw, James Ostrowski, Travis S. Humble, and George Siopsis. Multi-angle quantum approximate optimization algorithm.Scientific Reports, 12(1):6781, Apr 2022

work page 2022
[20]

An expressive ansatz for low-depth quantum approximate optimisation.Quantum Science and Technology, 9(2):025010, February 2024

V Vijendran, Aritra Das, Dax Enshan Koh, Syed M Assad, and Ping Koy Lam. An expressive ansatz for low-depth quantum approximate optimisation.Quantum Science and Technology, 9(2):025010, February 2024

work page 2024
[21]

Multiangle QAOA does not always need all its angles

Kaiyan Shi, Rebekah Herrman, Ruslan Shaydulin, Shouvanik Chakrabarti, Marco Pistoia, and Jef- frey Larson. Multiangle QAOA does not always need all its angles. In2022 IEEE/ACM 7th Sympo- sium on Edge Computing (SEC), pages 414–419. IEEE, 2022

work page 2022
[22]

The symmetry-based expressive QAOA for the MaxCut problem.Advanced Quantum Technologies, page 2500199, 2025

Xiumei Zhao, Yongmei Li, Guanghui Li, Yijie Shi, Sujuan Qin, and Fei Gao. The symmetry-based expressive QAOA for the MaxCut problem.Advanced Quantum Technologies, page 2500199, 2025

work page 2025
[23]

Optimization by decoded quantum inter- ferometry.Nature, 646(8086):831–836, 2025

Stephen P Jordan, Noah Shutty, Mary Wootters, Adam Zalcman, Alexander Schmidhuber, Robbie King, Sergei V Isakov, Tanuj Khattar, and Ryan Babbush. Optimization by decoded quantum inter- ferometry.Nature, 646(8086):831–836, 2025

work page 2025
[24]

On lattices, learning with errors, random linear codes, and cryptography.Journal of the ACM (JACM), 56(6):1–40, 2009

Oded Regev. On lattices, learning with errors, random linear codes, and cryptography.Journal of the ACM (JACM), 56(6):1–40, 2009

work page 2009
[25]

Adiabatic quantum state generation and statistical zero knowledge

Dorit Aharonov and Amnon Ta-Shma. Adiabatic quantum state generation and statistical zero knowledge. InProceedings of the thirty-fifth annual ACM symposium on Theory of computing, pages 20–29, 2003

work page 2003
[26]

Verifiable quantum advantage without structure.Journal of the ACM, 71(3):1–50, 2024

Takashi Yamakawa and Mark Zhandry. Verifiable quantum advantage without structure.Journal of the ACM, 71(3):1–50, 2024

work page 2024
[27]

Quantum advantages for Pauli channel esti- mation.Phys

Senrui Chen, Sisi Zhou, Alireza Seif, and Liang Jiang. Quantum advantages for Pauli channel esti- mation.Phys. Rev. A, 105:032435, Mar 2022

work page 2022
[28]

arXiv preprint arXiv:2510.10967 , year=

Tanuj Khattar, Noah Shutty, Craig Gidney, Adam Zalcman, Noureldin Yosri, Dmitri Maslov, Ryan Babbush, and Stephen P Jordan. Verifiable quantum advantage via optimized dqi circuits.arXiv preprint arXiv:2510.10967, 2025

work page arXiv 2025
[29]

On the Complexity of Decoded Quantum Interferometry

Kunal Marwaha, Bill Fefferman, Alexandru Gheorghiu, and Vojtech Havlicek. On the complexity of decoded quantum interferometry.arXiv preprint arXiv:2509.14443, 2025. DECODED QUANTUM INTERFEROMETRY FOR WEIGHTED OPTIMIZATION PROBLEMS 57

work page internal anchor Pith review Pith/arXiv arXiv 2025
[30]

Towards solving industrial integer linear programs with Decoded Quantum Interferometry

Francesc Sabater, Ouns El Harzli, Geert-Jan Besjes, Marvin Erdmann, Johannes Klepsch, Jonas Hiltrop, Jean-Francois Bobier, Yudong Cao, and Carlos A Riofrio. Towards solving industrial integer linear programs with decoded quantum interferometry.arXiv preprint arXiv:2509.08328, 2025

work page internal anchor Pith review Pith/arXiv arXiv 2025
[31]

No quantum advantage in decoded quantum interferometry for maxcut.arXiv preprint arXiv:2509.19966, 2025

Ojas Parekh. No quantum advantage in decoded quantum interferometry for maxcut.arXiv preprint arXiv:2509.19966, 2025

work page arXiv 2025
[32]

Optimization of quadratic constraints by decoded quantum interferometry

Daniel Cohen Hillel. Optimization of quadratic constraints by decoded quantum interferometry. arXiv preprint arXiv:2510.08061, 2025

work page arXiv 2025
[33]

Algebraic geometry codes and decoded quantum interferometry

Andi Gu and Stephen P Jordan. Algebraic geometry codes and decoded quantum interferometry. arXiv preprint arXiv:2510.06603, 2025

work page arXiv 2025
[34]

Decoded quantum interferometry requires structure.arXiv preprint arXiv:2509.14509, 2025

Eric R Anschuetz, David Gamarnik, and Jonathan Z Lu. Decoded quantum interferometry requires structure.arXiv preprint arXiv:2509.14509, 2025

work page arXiv 2025
[35]

Kernelized decoded quantum interferometry.arXiv preprint arXiv:2511.20016, 2025

Fumin Wang. Kernelized decoded quantum interferometry.arXiv preprint arXiv:2511.20016, 2025

work page arXiv 2025
[36]

A nearly linear-time decoded quantum interferometry algorithm for the optimal polynomial intersection problem.arXiv preprint arXiv:2601.15171, 2026

Ansis Rosmanis. A nearly linear-time decoded quantum interferometry algorithm for the optimal polynomial intersection problem.arXiv preprint arXiv:2601.15171, 2026

work page arXiv 2026
[37]

Hidden Quantum Advantage near the Decoding Threshold of Decoded Quantum Interferometry

Maoxin Gao and Yan Chang. Hidden quantum advantage near the decoding threshold of decoded quantum interferometry.arXiv preprint arXiv:2604.15025, 2026

work page internal anchor Pith review Pith/arXiv arXiv 2026
[38]

Tight inapproximability of max-linsat and implications for decoded quantum interferometry.arXiv preprint arXiv:2603.04540, 2026

Maximilian J Kramer, Carsten Schubert, and Jens Eisert. Tight inapproximability of max-linsat and implications for decoded quantum interferometry.arXiv preprint arXiv:2603.04540, 2026

work page arXiv 2026
[39]

Decoded quantum interferometry under noise.Quantum Science and Technology, 11(2):025010, 2026

Kaifeng Bu, Weichen Gu, Dax Enshan Koh, and Xiang Li. Decoded quantum interferometry under noise.Quantum Science and Technology, 11(2):025010, 2026

work page 2026
[40]

Schmidhuber, J

Alexander Schmidhuber, Jonathan Z Lu, Noah Shutty, Stephen Jordan, Alexander Poremba, and Yihui Quek. Hamiltonian decoded quantum interferometry.arXiv preprint arXiv:2510.07913, 2025

work page arXiv 2025
[41]

Hamiltonian decoded quantum interferometry for general pauli hamiltonians.arXiv preprint arXiv:2601.18773, 2026

Kaifeng Bu, Weichen Gu, and Xiang Li. Hamiltonian decoded quantum interferometry for general pauli hamiltonians.arXiv preprint arXiv:2601.18773, 2026

work page arXiv 2026
[42]

Horn and Charles R

Roger A. Horn and Charles R. Johnson.Matrix Analysis. Cambridge University Press, 2nd edition, 2012

work page 2012
[43]

Short-depth circuits for dicke state preparation

Andreas Bärtschi and Stephan Eidenbenz. Short-depth circuits for dicke state preparation. In2022 IEEE International Conference on Quantum Computing and Engineering (QCE), pages 87–96, 2022

work page 2022
[44]

Quantum state preparation using an exact cnot synthesis formulation

Hanyu Wang, Jason Cong, and Giovanni De Micheli. Quantum state preparation using an exact cnot synthesis formulation. In2024 Design, Automation & Test in Europe Conference & Exhibition (DATE), pages 1–6. IEEE, 2024

work page 2024
[45]

Sur une généralisation des polynômes d’hermite.Comptes Rendus, 189(620- 622):5–3, 1929

Mikhail Krawtchouk. Sur une généralisation des polynômes d’hermite.Comptes Rendus, 189(620- 622):5–3, 1929

work page 1929
[46]

Classical orthogonal polynomials of a discrete variable

Arnold F Nikiforov, Vasilii B Uvarov, and Sergei K Suslov. Classical orthogonal polynomials of a discrete variable. InClassical orthogonal polynomials of a discrete variable, pages 18–54. Springer, 1991

work page 1991
[47]

Springer, 1999

Jacobus Hendricus Lint.Introduction to coding theory. Springer, 1999

work page 1999
[48]

Estimates for the range of binomiality in codes’ spectra.IEEE Trans- actions on Information Theory, 43(3):987–991, 2002

Ilia Krasikov and Simon Litsyn. Estimates for the range of binomiality in codes’ spectra.IEEE Trans- actions on Information Theory, 43(3):987–991, 2002

work page 2002
[49]

Elsevier, 1977

Florence Jessie MacWilliams and Neil James Alexander Sloane.The theory of error-correcting codes, volume 16. Elsevier, 1977

work page 1977
[50]

Fourier-reflexive partitions and macwilliams identities for additive codes

Heide Gluesing-Luerssen. Fourier-reflexive partitions and macwilliams identities for additive codes. Designs, Codes and Cryptography, 75(3):543–563, 2015

work page 2015
[51]

On integral zeros of krawtchouk polynomials.J

Ilia Krasikov and Simon Litsyn. On integral zeros of krawtchouk polynomials.J. Comb. Theory A, 74(1):71–99, 1996

work page 1996