8 Search Results for "Slofstra, William"

Document
DOI: 10.4230/LIPIcs.STACS.2026.25
Homomorphism Indistinguishability, Multiplicity Automata Equivalence, and Polynomial Identity Testing

Authors: Marek Černý and Tim Seppelt

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
Two graphs G and H are homomorphism indistinguishable over a graph class ℱ if they admit the same number of homomorphisms from every graph F ∈ ℱ. Many graph isomorphism relaxations such as (quantum) isomorphism and cospectrality can be characterised as homomorphism indistinguishability over specific graph classes. Thereby, the problems HomInd(ℱ) of deciding homomorphism indistinguishability over ℱ subsume diverse graph isomorphism relaxations whose complexities range from logspace to undecidable. Establishing the first general result on the complexity of HomInd(ℱ), Seppelt (MFCS 2024) showed that HomInd(ℱ) is in randomised polynomial time for every graph class ℱ of bounded treewidth that can be defined in counting monadic second-order logic CMSO₂. We show that this algorithm is conditionally optimal, i.e. it cannot be derandomised unless polynomial identity testing is in P. For CMSO₂-definable graph classes ℱ of bounded pathwidth, we improve the previous complexity upper bound for HomInd(ℱ) from P to C_ = L and show that this is tight. Secondarily, we establish a connection between homomorphism indistinguishability and multiplicity automata equivalence which allows us to pinpoint the complexity of the latter problem as C_ = L-complete.
Cite as

Marek Černý and Tim Seppelt. Homomorphism Indistinguishability, Multiplicity Automata Equivalence, and Polynomial Identity Testing. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 25:1-25:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{cerny_et_al:LIPIcs.STACS.2026.25,
  author =	{\v{C}ern\'{y}, Marek and Seppelt, Tim},
  title =	{{Homomorphism Indistinguishability, Multiplicity Automata Equivalence, and Polynomial Identity Testing}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{25:1--25:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.25},
  URN =		{urn:nbn:de:0030-drops-255144},
  doi =		{10.4230/LIPIcs.STACS.2026.25},
  annote =	{Keywords: treewidth, Courcelle’s theorem, logspace, multiplicity automata, polynomial identity testing}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.83
The Pure-State Consistency of Local Density Matrices Problem: In PSPACE and Complete for a Class Between QMA and QMA(2)

Authors: Jonas Kamminga and Dorian Rudolph

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

Abstract
In this work we investigate the computational complexity of the pure consistency of local density matrices (PureCLDM) and pure N-representability (Pure-N-Representability; analog of PureCLDM for bosonic or fermionic systems) problems. In these problems the input is a set of reduced density matrices and the task is to determine whether there exists a global pure state consistent with these reduced density matrices. While mixed CLDM, i.e. where the global state can be mixed, was proven to be QMA-complete by Broadbent and Grilo [JoC 2022], almost nothing was known about the complexity of the pure version. Before our work the best upper and lower bounds were QMA(2) and QMA. Our contribution to the understanding of these problems is twofold. Firstly, we define a pure state analogue of the complexity class QMA^+ of Aharanov and Regev [FOCS 2003], which we call PureSuperQMA. We prove that both pure-N-Representability and PureCLDM are complete for this new class. Along the way we supplement Broadbent and Grilo by proving hardness for 2-qubit reduced density matrices and showing that mixed N-Representability is QMA-complete. Secondly, we improve the upper bound on PureCLDM. Using methods from algebraic geometry, we prove that PureSuperQMA ⊆ PSPACE. Our methods, and the PSPACE upper bound, are also valid for PureCLDM with exponential or even perfect precision, hence precisePureCLDM is not preciseQMA(2) = NEXP-complete, unless PSPACE = NEXP. We view this as evidence for a negative answer to the longstanding open question whether PureCLDM is QMA(2)-complete. The techniques we develop for our PSPACE upper bound are quite general. We are able to use them for various applications: from proving PSPACE upper bounds on other quantum problems to giving an efficient parallel (NC) algorithm for (non-convex) quadratically constrained quadratic programs with few constraints.
Cite as

Jonas Kamminga and Dorian Rudolph. The Pure-State Consistency of Local Density Matrices Problem: In PSPACE and Complete for a Class Between QMA and QMA(2). In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 83:1-83:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{kamminga_et_al:LIPIcs.ITCS.2026.83,
  author =	{Kamminga, Jonas and Rudolph, Dorian},
  title =	{{The Pure-State Consistency of Local Density Matrices Problem: In PSPACE and Complete for a Class Between QMA and QMA(2)}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{83:1--83:23},
  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.2026.83},
  URN =		{urn:nbn:de:0030-drops-253701},
  doi =		{10.4230/LIPIcs.ITCS.2026.83},
  annote =	{Keywords: Quantum Complexity Theory, PSPACE, QMA(2), Consistency of Local Density Matrices, Polynomial Optimization}
}
Document
DOI: 10.4230/LIPIcs.TQC.2025.8
Self-Testing in the Compiled Setting via Tilted-CHSH Inequalities

Authors: Arthur Mehta, Connor Paddock, and Lewis Wooltorton

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

Abstract
This work investigates the family of extended tilted-CHSH inequalities in the single-prover cryptographic compiled setting. In particular, we show that a quantum polynomial-time prover can violate these Bell inequalities by at most negligibly more than the violation achieved by two non-communicating quantum provers. To obtain this result, we extend a sum-of-squares technique to monomials with arbitrarily high degree in the Bob operators and degree at most one in the Alice operators. We also introduce a notion of partial self-testing for the compiled setting, which resembles a weaker form of self-testing in the bipartite setting. As opposed to certifying the full model, partial self-testing attempts to certify the reduced states and measurements on separate subsystems. In the compiled setting, this is akin to the states after the first round of interaction and measurements made on that state. Lastly, we show that the extended tilted-CHSH inequalities satisfy this notion of a compiled self-test.
Cite as

Arthur Mehta, Connor Paddock, and Lewis Wooltorton. Self-Testing in the Compiled Setting via Tilted-CHSH Inequalities. In 20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 350, pp. 8:1-8:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{mehta_et_al:LIPIcs.TQC.2025.8,
  author =	{Mehta, Arthur and Paddock, Connor and Wooltorton, Lewis},
  title =	{{Self-Testing in the Compiled Setting via Tilted-CHSH Inequalities}},
  booktitle =	{20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025)},
  pages =	{8:1--8:19},
  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.2025.8},
  URN =		{urn:nbn:de:0030-drops-240577},
  doi =		{10.4230/LIPIcs.TQC.2025.8},
  annote =	{Keywords: Compiled Bell scenarios, self-testing}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.37
Satisfiability of Commutative vs. Non-Commutative CSPs

Authors: Andrei A. Bulatov and Stanislav Živný

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

Abstract
The Mermin-Peres magic square is a celebrated example of a system of Boolean linear equations that is not (classically) satisfiable but is satisfiable via linear operators on a Hilbert space of dimension four. A natural question is then, for what kind of problems such a phenomenon occurs? Atserias, Kolaitis, and Severini answered this question for all Boolean Constraint Satisfaction Problems (CSPs): For 0-Valid-SAT, 1-Valid-SAT, 2-SAT, Horn-SAT, and Dual Horn-SAT, classical satisfiability and operator satisfiability is the same and thus there is no gap; for all other Boolean CSPs, these notions differ as there are gaps, i.e., there are unsatisfiable instances that are satisfiable via operators on Hilbert spaces. We generalize their result to CSPs on arbitrary finite domains and give an almost complete classification: First, we show that NP-hard CSPs admit a separation between classical satisfiability and satisfiability via operators on finite- and infinite-dimensional Hilbert spaces. Second, we show that tractable CSPs of bounded width have no satisfiability gaps of any kind. Finally, we show that tractable CSPs of unbounded width can simulate, in a satisfiability-gap-preserving fashion, linear equations over an Abelian group of prime order p; for such CSPs, we obtain a separation of classical satisfiability and satisfiability via operators on infinite-dimensional Hilbert spaces. Furthermore, if p = 2, such CSPs also have gaps separating classical satisfiability and satisfiability via operators on finite- and infinite-dimensional Hilbert spaces.
Cite as

Andrei A. Bulatov and Stanislav Živný. Satisfiability of Commutative vs. Non-Commutative CSPs. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 37:1-37:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bulatov_et_al:LIPIcs.ICALP.2025.37,
  author =	{Bulatov, Andrei A. and \v{Z}ivn\'{y}, Stanislav},
  title =	{{Satisfiability of Commutative vs. Non-Commutative CSPs}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{37:1--37:18},
  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.2025.37},
  URN =		{urn:nbn:de:0030-drops-234149},
  doi =		{10.4230/LIPIcs.ICALP.2025.37},
  annote =	{Keywords: constraint satisfaction, quantum CSP, operator CSP}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.76
A Quantum Unique Games Conjecture

Authors: Hamoon Mousavi and Taro Spirig

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract
After the NP-hardness of computational problems such as 3SAT and MaxCut was established, a natural next step was to explore whether these problems remain hard to approximate. While the quantum nonlocal games extensions of some of these problems are known to be hard - indeed undecidable - their inapproximability remains largely unresolved. In this work, we introduce definitions for the quantum extensions of Label-Cover and Unique-Label-Cover. We show that these problems play a similarly crucial role in studying the inapproximability of quantum constraint satisfaction problems as they do in the classical setting.
Cite as

Hamoon Mousavi and Taro Spirig. A Quantum Unique Games Conjecture. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 76:1-76:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{mousavi_et_al:LIPIcs.ITCS.2025.76,
  author =	{Mousavi, Hamoon and Spirig, Taro},
  title =	{{A Quantum Unique Games Conjecture}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{76:1--76:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.76},
  URN =		{urn:nbn:de:0030-drops-227047},
  doi =		{10.4230/LIPIcs.ITCS.2025.76},
  annote =	{Keywords: hardness of approximation, quantum computing, noncommutative constraint satisfaction problems, Fourier analysis}
}
Document
DOI: 10.4230/LIPIcs.TQC.2024.12
Quantum Delegation with an Off-The-Shelf Device

Authors: Anne Broadbent, Arthur Mehta, and Yuming Zhao

Published in: LIPIcs, Volume 310, 19th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2024)

Abstract
Given that reliable cloud quantum computers are becoming closer to reality, the concept of delegation of quantum computations and its verifiability is of central interest. Many models have been proposed, each with specific strengths and weaknesses. Here, we put forth a new model where the client trusts only its classical processing, makes no computational assumptions, and interacts with a quantum server in a single round. In addition, during a set-up phase, the client specifies the size n of the computation and receives an untrusted, off-the-shelf (OTS) quantum device that is used to report the outcome of a single measurement. We show how to delegate polynomial-time quantum computations in the OTS model. This also yields an interactive proof system for all of QMA, which, furthermore, we show can be accomplished in statistical zero-knowledge. This provides the first relativistic (one-round), two-prover zero-knowledge proof system for QMA. As a proof approach, we provide a new self-test for n EPR pairs using only constant-sized Pauli measurements, and show how it provides a new avenue for the use of simulatable codes for local Hamiltonian verification. Along the way, we also provide an enhanced version of a well-known stability result due to Gowers and Hatami and show how it completes a common argument used in self-testing.
Cite as

Anne Broadbent, Arthur Mehta, and Yuming Zhao. Quantum Delegation with an Off-The-Shelf Device. In 19th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 310, pp. 12:1-12:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{broadbent_et_al:LIPIcs.TQC.2024.12,
  author =	{Broadbent, Anne and Mehta, Arthur and Zhao, Yuming},
  title =	{{Quantum Delegation with an Off-The-Shelf Device}},
  booktitle =	{19th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2024)},
  pages =	{12:1--12:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-328-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{310},
  editor =	{Magniez, Fr\'{e}d\'{e}ric and Grilo, Alex Bredariol},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2024.12},
  URN =		{urn:nbn:de:0030-drops-206824},
  doi =		{10.4230/LIPIcs.TQC.2024.12},
  annote =	{Keywords: Delegated quantum computation, zero-knowledge proofs, device-independence}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2020.87
On the Complexity of Zero Gap MIP*

Authors: Hamoon Mousavi, Seyed Sajjad Nezhadi, and Henry Yuen

Published in: LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

Abstract
The class MIP^* is the set of languages decidable by multiprover interactive proofs with quantum entangled provers. It was recently shown by Ji, Natarajan, Vidick, Wright and Yuen that MIP^* is equal to RE, the set of recursively enumerable languages. In particular this shows that the complexity of approximating the quantum value of a non-local game G is equivalent to the complexity of the Halting problem. In this paper we investigate the complexity of deciding whether the quantum value of a non-local game G is exactly 1. This problem corresponds to a complexity class that we call zero gap MIP^*, denoted by MIP₀^*, where there is no promise gap between the verifier’s acceptance probabilities in the YES and NO cases. We prove that MIP₀^* extends beyond the first level of the arithmetical hierarchy (which includes RE and its complement coRE), and in fact is equal to Π₂⁰, the class of languages that can be decided by quantified formulas of the form ∀ y ∃ z R(x,y,z). Combined with the previously known result that MIP₀^{co} (the commuting operator variant of MIP₀^*) is equal to coRE, our result further highlights the fascinating connection between various models of quantum multiprover interactive proofs and different classes in computability theory.
Cite as

Hamoon Mousavi, Seyed Sajjad Nezhadi, and Henry Yuen. On the Complexity of Zero Gap MIP*. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 87:1-87:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{mousavi_et_al:LIPIcs.ICALP.2020.87,
  author =	{Mousavi, Hamoon and Nezhadi, Seyed Sajjad and Yuen, Henry},
  title =	{{On the Complexity of Zero Gap MIP*}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{87:1--87:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.87},
  URN =		{urn:nbn:de:0030-drops-124940},
  doi =		{10.4230/LIPIcs.ICALP.2020.87},
  annote =	{Keywords: Quantum Complexity, Multiprover Interactive Proofs, Computability Theory}
}
Document
DOI: 10.4230/LIPIcs.CCC.2019.25
Complexity Lower Bounds for Computing the Approximately-Commuting Operator Value of Non-Local Games to High Precision

Authors: Matthew Coudron and William Slofstra

Published in: LIPIcs, Volume 137, 34th Computational Complexity Conference (CCC 2019)

Abstract
We study the problem of approximating the commuting-operator value of a two-player non-local game. It is well-known that it is NP-complete to decide whether the classical value of a non-local game is 1 or 1- epsilon, promised that one of the two is the case. Furthermore, as long as epsilon is small enough, this result does not depend on the gap epsilon. In contrast, a recent result of Fitzsimons, Ji, Vidick, and Yuen shows that the complexity of computing the quantum value grows without bound as the gap epsilon decreases. In this paper, we show that this also holds for the commuting-operator value of a game. Specifically, in the language of multi-prover interactive proofs, we show that the power of MIP^{co}(2,1,1,s) (proofs with two provers, one round, completeness probability 1, soundness probability s, and commuting-operator strategies) can increase without bound as the gap 1-s gets arbitrarily small. Our results also extend naturally in two ways, to perfect zero-knowledge protocols, and to lower bounds on the complexity of computing the approximately-commuting value of a game. Thus we get lower bounds on the complexity class PZK-MIP^{co}_{delta}(2,1,1,s) of perfect zero-knowledge multi-prover proofs with approximately-commuting operator strategies, as the gap 1-s gets arbitrarily small. While we do not know any computable time upper bound on the class MIP^{co}, a result of the first author and Vidick shows that for s = 1-1/poly(f(n)) and delta = 1/poly(f(n)), the class MIP^{co}_delta(2,1,1,s), with constant communication from the provers, is contained in TIME(exp(poly(f(n)))). We give a lower bound of coNTIME(f(n)) (ignoring constants inside the function) for this class, which is tight up to polynomial factors assuming the exponential time hypothesis.
Cite as

Matthew Coudron and William Slofstra. Complexity Lower Bounds for Computing the Approximately-Commuting Operator Value of Non-Local Games to High Precision. In 34th Computational Complexity Conference (CCC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 137, pp. 25:1-25:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{coudron_et_al:LIPIcs.CCC.2019.25,
  author =	{Coudron, Matthew and Slofstra, William},
  title =	{{Complexity Lower Bounds for Computing the Approximately-Commuting Operator Value of Non-Local Games to High Precision}},
  booktitle =	{34th Computational Complexity Conference (CCC 2019)},
  pages =	{25:1--25:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-116-0},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{137},
  editor =	{Shpilka, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2019.25},
  URN =		{urn:nbn:de:0030-drops-108478},
  doi =		{10.4230/LIPIcs.CCC.2019.25},
  annote =	{Keywords: Quantum complexity theory, Non-local game, Multi-prover interactive proof, Entanglement}
}
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