5 Search Results for "Janzing, Dominik"

Document
DOI: 10.4230/LIPIcs.ITCS.2026.27
Identity Check Problem for Shallow Quantum Circuits

Authors: Sergey Bravyi, Natalie Parham, and Minh Tran

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
Verifying that a quantum circuit correctly implements a desired transformation is essential for validating quantum algorithms. We consider the closely related identity check problem: given a quantum circuit U, estimate the diamond-norm distance between U and the identity channel. Ji and Wu showed that estimating this distance to within an additive 1/poly error is QMA-hard, even when U is constant-depth and 1D local - ruling out efficient algorithms in this regime. We show that this hardness barrier disappears if one seeks a constant multiplicative-approximation instead. We present a classical algorithm that, for shallow geometrically local D-dimensional circuits, approximates the distance to the identity within a factor α = D+1, provided that the circuit is sufficiently close to the identity. The runtime of the algorithm scales linearly with the number of qubits for any constant circuit depth and spatial dimension. We also show that the operator-norm distance to the identity ‖U-I‖ can be efficiently approximated within a factor α = 5 for shallow 1D circuits and, under a certain technical condition, within a factor α = 2D+3 for shallow D-dimensional circuits. A numerical implementation of the identity check algorithm is reported for 1D Trotter circuits with up to 100 qubits.
Cite as

Sergey Bravyi, Natalie Parham, and Minh Tran. Identity Check Problem for Shallow Quantum Circuits. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 27:1-27:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bravyi_et_al:LIPIcs.ITCS.2026.27,
  author =	{Bravyi, Sergey and Parham, Natalie and Tran, Minh},
  title =	{{Identity Check Problem for Shallow Quantum Circuits}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{27:1--27:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.27},
  URN =		{urn:nbn:de:0030-drops-253147},
  doi =		{10.4230/LIPIcs.ITCS.2026.27},
  annote =	{Keywords: Quantum computing, Identity check problem, quantum circuits, classical simulation of quantum computation, shallow circuits}
}
Document
DOI: 10.4230/LIPIcs.TQC.2025.6
Quantum SAT Problems with Finite Sets of Projectors Are Complete for a Plethora of Classes

Authors: Ricardo Rivera Cardoso, Alex Meiburg, and Daniel Nagaj

Published in: LIPIcs, Volume 350, 20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025)

Abstract
Previously, all known variants of the Quantum Satisfiability (QSAT) problem - consisting of determining whether a k-local (k-body) Hamiltonian is frustration-free - could be classified as being either in 𝖯; or complete for NP, MA, or QMA₁. Here, we present new qubit variants of this problem that are complete for BQP₁, coRP, QCMA, PI(coRP,NP), PI(BQP₁,NP), PI(BQP₁,MA), SoPU(coRP,NP), SoPU(BQP₁,NP), and SoPU(BQP₁,MA). Our result implies that a complete classification of quantum constraint satisfaction problems (QCSPs), analogous to Schaefer’s dichotomy theorem for classical CSPs, must either include these 13 classes, or otherwise show that some are equal. Additionally, our result showcases two new types of QSAT problems that can be decided efficiently, as well as the first nontrivial BQP₁-complete problem. We first construct QSAT problems on qudits that are complete for BQP₁, coRP, and QCMA. These are made by restricting the finite set of Hamiltonians to consist of elements similar to H_{init}, H_{prop}, and H_{out}, seen in the circuit-to-Hamiltonian transformation. Usually, these are used to demonstrate hardness of QSAT and Local Hamiltonian problems, and so our proofs of hardness are simple. The difficulty lies in ensuring that all Hamiltonians generated with these three elements can be decided in their respective classes. For this, we build our Hamiltonian terms with high-dimensional data and clock qudits, ternary logic, and either monogamy of entanglement or specific clock encodings. We then show how to express these problems in terms of qubits, by proving that any QCSP can be reduced to a qubit problem while maintaining the same complexity - something not believed possible classically. The remaining six problems are obtained by considering "sums" and "products" of some of the QSAT problems mentioned here. Before this work, the QSAT problems generated in this way resulted in complete problems for PI and SoPU classes that were trivially equal to NP, MA, or QMA₁. We thus commence the study of these new and seemingly nontrivial classes. While [Meiburg, 2021] first sought to prove completeness for coRP, BQP₁, and QCMA, we note that those constructions are flawed. Here, we rework them, provide correct proofs, and obtain improvements on the required qudit dimensionality.
Cite as

Ricardo Rivera Cardoso, Alex Meiburg, and Daniel Nagaj. Quantum SAT Problems with Finite Sets of Projectors Are Complete for a Plethora of Classes. In 20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 350, pp. 6:1-6:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{riveracardoso_et_al:LIPIcs.TQC.2025.6,
  author =	{Rivera Cardoso, Ricardo and Meiburg, Alex and Nagaj, Daniel},
  title =	{{Quantum SAT Problems with Finite Sets of Projectors Are Complete for a Plethora of Classes}},
  booktitle =	{20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025)},
  pages =	{6:1--6:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-392-8},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{350},
  editor =	{Fefferman, Bill},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2025.6},
  URN =		{urn:nbn:de:0030-drops-240557},
  doi =		{10.4230/LIPIcs.TQC.2025.6},
  annote =	{Keywords: Quantum complexity theory, quantum satisfiability, circuit-to-Hamiltonian, pairwise union of classes, pairwise intersection of classes}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2025.144
Probabilistic and Causal Satisfiability: Constraining the Model

Authors: Markus Bläser, Julian Dörfler, Maciej Liśkiewicz, and Benito van der Zander

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
We study the complexity of satisfiability problems in probabilistic and causal reasoning. Given random variables X₁, X₂,… over finite domains, the basic terms are probabilities of propositional formulas over atomic events X_i = x_i, such as ℙ(X₁ = x₁) or ℙ(X₁ = x₁ ∨ X₂ = x₂). The basic terms can be combined using addition (yielding linear terms) or multiplication (polynomial terms). The probabilistic satisfiability problem asks whether a joint probability distribution satisfies a Boolean combination of (in)equalities over such terms. Fagin et al. [Fagin et al., 1990] showed that for basic and linear terms, this problem is NP-complete, making it no harder than Boolean satisfiability, while Mossé et al. [Mossé et al., 2022] proved that for polynomial terms, it is complete for the existential theory of the reals. Pearl’s Causal Hierarchy (PCH) extends the probabilistic setting with interventional and counterfactual reasoning, enriching the expressiveness of the languages. However, Mossé et al. [Mossé et al., 2022] found that the complexity of satisfiability remains unchanged. Van der Zander et al. [van der Zander et al., 2023] showed that introducing a marginalization operator to languages induces a significant increase in complexity. We extend this line of work by adding two new dimensions to the problem by constraining the models. First, we fix the graph structure of the underlying structural causal model, motivated by settings like Pearl’s do-calculus, and give a nearly complete landscape across different arithmetics and PCH levels. Second, we study small models. While earlier work showed that satisfiable instances admit polynomial-size models, this is no longer guaranteed with compact marginalization. We characterize the complexities of satisfiability under small-model constraints across different settings.
Cite as

Markus Bläser, Julian Dörfler, Maciej Liśkiewicz, and Benito van der Zander. Probabilistic and Causal Satisfiability: Constraining the Model. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 144:1-144:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{blaser_et_al:LIPIcs.ICALP.2025.144,
  author =	{Bl\"{a}ser, Markus and D\"{o}rfler, Julian and Li\'{s}kiewicz, Maciej and van der Zander, Benito},
  title =	{{Probabilistic and Causal Satisfiability: Constraining the Model}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{144:1--144:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.144},
  URN =		{urn:nbn:de:0030-drops-235214},
  doi =		{10.4230/LIPIcs.ICALP.2025.144},
  annote =	{Keywords: Existential theory of the real numbers, Computational complexity, Probabilistic logic, Structural Causal Models}
}
Document
DOI: 10.4230/DagRep.12.9.150
Machine Learning for Science: Bridging Data-Driven and Mechanistic Modelling (Dagstuhl Seminar 22382)

Authors: Philipp Berens, Kyle Cranmer, Neil D. Lawrence, Ulrike von Luxburg, and Jessica Montgomery

Published in: Dagstuhl Reports, Volume 12, Issue 9 (2023)

Abstract
This report documents the programme and the outcomes of Dagstuhl Seminar 22382 "Machine Learning for Science: Bridging Data-Driven and Mechanistic Modelling". Today’s scientific challenges are characterised by complexity. Interconnected natural, technological, and human systems are influenced by forces acting across time- and spatial-scales, resulting in complex interactions and emergent behaviours. Understanding these phenomena - and leveraging scientific advances to deliver innovative solutions to improve society’s health, wealth, and well-being - requires new ways of analysing complex systems. The transformative potential of AI stems from its widespread applicability across disciplines, and will only be achieved through integration across research domains. AI for science is a rendezvous point. It brings together expertise from AI and application domains; combines modelling knowledge with engineering know-how; and relies on collaboration across disciplines and between humans and machines. Alongside technical advances, the next wave of progress in the field will come from building a community of machine learning researchers, domain experts, citizen scientists, and engineers working together to design and deploy effective AI tools. This report summarises the discussions from the seminar and provides a roadmap to suggest how different communities can collaborate to deliver a new wave of progress in AI and its application for scientific discovery.
Cite as

Philipp Berens, Kyle Cranmer, Neil D. Lawrence, Ulrike von Luxburg, and Jessica Montgomery. Machine Learning for Science: Bridging Data-Driven and Mechanistic Modelling (Dagstuhl Seminar 22382). In Dagstuhl Reports, Volume 12, Issue 9, pp. 150-199, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@Article{berens_et_al:DagRep.12.9.150,
  author =	{Berens, Philipp and Cranmer, Kyle and Lawrence, Neil D. and von Luxburg, Ulrike and Montgomery, Jessica},
  title =	{{Machine Learning for Science: Bridging Data-Driven and Mechanistic Modelling (Dagstuhl Seminar 22382)}},
  pages =	{150--199},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2023},
  volume =	{12},
  number =	{9},
  editor =	{Berens, Philipp and Cranmer, Kyle and Lawrence, Neil D. and von Luxburg, Ulrike and Montgomery, Jessica},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.12.9.150},
  URN =		{urn:nbn:de:0030-drops-178125},
  doi =		{10.4230/DagRep.12.9.150},
  annote =	{Keywords: machine learning, artificial intelligence, life sciences, physical sciences, environmental sciences, simulation, causality, modelling}
}
Document
DOI: 10.4230/DagSemProc.09401.1
09401 Abstracts Collection – Machine learning approaches to statistical dependences and causality

Authors: Dominik Janzing, Steffen Lauritzen, and Bernhard Schölkopf

Published in: Dagstuhl Seminar Proceedings, Volume 9401, Machine learning approaches to statistical dependences and causality (2010)

Abstract
From 27.09.2009 to 02.10.2009, the Dagstuhl Seminar 09401 ``Machine learning approaches to statistical dependences and causality'' was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available.
Cite as

Dominik Janzing, Steffen Lauritzen, and Bernhard Schölkopf. 09401 Abstracts Collection – Machine learning approaches to statistical dependences and causality. In Machine learning approaches to statistical dependences and causality. Dagstuhl Seminar Proceedings, Volume 9401, pp. 1-15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{janzing_et_al:DagSemProc.09401.1,
  author =	{Janzing, Dominik and Lauritzen, Steffen and Sch\"{o}lkopf, Bernhard},
  title =	{{09401 Abstracts Collection – Machine learning approaches to statistical dependences and causality }},
  booktitle =	{Machine learning approaches to statistical dependences and causality},
  pages =	{1--15},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{9401},
  editor =	{Dominik Janzing and Steffen Lauritzen and Bernhard Sch\"{o}lkopf},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.09401.1},
  URN =		{urn:nbn:de:0030-drops-23636},
  doi =		{10.4230/DagSemProc.09401.1},
  annote =	{Keywords: Machine learning, statistical dependences, causality}
}
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