Volume
LIPIcs, Volume 350
20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025)
Publication Details
- published at: 2025-09-09
- Publisher: Schloss Dagstuhl – Leibniz-Zentrum für Informatik
- ISBN: 978-3-95977-392-8
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Complete Volume
LIPIcs, Volume 350, TQC 2025, Complete Volume
Abstract
LIPIcs, Volume 350, TQC 2025, Complete Volume
Cite as
20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 350, pp. 1-266, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@Proceedings{fefferman:LIPIcs.TQC.2025,
title = {{LIPIcs, Volume 350, TQC 2025, Complete Volume}},
booktitle = {20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025)},
pages = {1--266},
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},
URN = {urn:nbn:de:0030-drops-246614},
doi = {10.4230/LIPIcs.TQC.2025},
annote = {Keywords: LIPIcs, Volume 350, TQC 2025, Complete Volume}
}
Document
Front Matter
Front Matter, Table of Contents, Preface, Conference Organization
Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as
20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 350, pp. 0:i-0:xviii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{fefferman:LIPIcs.TQC.2025.0,
author = {Fefferman, Bill},
title = {{Front Matter, Table of Contents, Preface, Conference Organization}},
booktitle = {20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025)},
pages = {0:i--0:xviii},
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.2025.0},
URN = {urn:nbn:de:0030-drops-246604},
doi = {10.4230/LIPIcs.TQC.2025.0},
annote = {Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
Quantum Search with In-Place Queries
Abstract
Quantum query complexity is typically characterized in terms of xor queries |x,y⟩ ↦ |x,y⊕ f(x)⟩ or phase queries, which ensure that even queries to non-invertible functions are unitary. When querying a permutation, another natural model is unitary: in-place queries |x⟩↦ |f(x)⟩.
Some problems are known to require exponentially fewer in-place queries than xor queries, but no separation has been shown in the opposite direction. A candidate for such a separation was the problem of inverting a permutation over N elements. This task, equivalent to unstructured search in the context of permutations, is solvable with O(√N) xor queries but was conjectured to require Ω(N) in-place queries.
We refute this conjecture by designing a quantum algorithm for Permutation Inversion using O(√N) in-place queries. Our algorithm achieves the same speedup as Grover’s algorithm despite the inability to efficiently uncompute queries or perform straightforward oracle-controlled reflections.
Nonetheless, we show that there are indeed problems which require fewer xor queries than in-place queries. We introduce a subspace-conversion problem called Function Erasure that requires 1 xor query and Θ(√N) in-place queries. Then, we build on a recent extension of the quantum adversary method to characterize exact conditions for a decision problem to exhibit such a separation, and we propose a candidate problem.
Cite as
Blake Holman, Ronak Ramachandran, and Justin Yirka. Quantum Search with In-Place Queries. In 20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 350, pp. 1:1-1:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{holman_et_al:LIPIcs.TQC.2025.1,
author = {Holman, Blake and Ramachandran, Ronak and Yirka, Justin},
title = {{Quantum Search with In-Place Queries}},
booktitle = {20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025)},
pages = {1:1--1:18},
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.2025.1},
URN = {urn:nbn:de:0030-drops-240502},
doi = {10.4230/LIPIcs.TQC.2025.1},
annote = {Keywords: Quantum algorithms, query complexity, quantum complexity theory, quantum search, Grover’s algorithm, permutation inversion}
}
Document
A Quantum Cloning Game with Applications to Quantum Position Verification
Abstract
We introduce a quantum cloning game in which k separate collaborative parties receive a classical input, determining which of them has to share a maximally entangled state with an additional party (referee). We provide the optimal winning probability of such a game for every number of parties k, and show that it decays exponentially when the game is played n times in parallel. These results have applications to quantum cryptography, in particular in the topic of quantum position verification, where we show security of the routing protocol (played in parallel), and a variant of it, in the random oracle model.
Cite as
Léo Colisson Palais, Llorenç Escolà-Farràs, and Florian Speelman. A Quantum Cloning Game with Applications to Quantum Position Verification. In 20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 350, pp. 2:1-2:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{colissonpalais_et_al:LIPIcs.TQC.2025.2,
author = {Colisson Palais, L\'{e}o and Escol\`{a}-Farr\`{a}s, Lloren\c{c} and Speelman, Florian},
title = {{A Quantum Cloning Game with Applications to Quantum Position Verification}},
booktitle = {20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025)},
pages = {2:1--2:17},
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.2025.2},
URN = {urn:nbn:de:0030-drops-240513},
doi = {10.4230/LIPIcs.TQC.2025.2},
annote = {Keywords: Quantum position verification, cloning game, random oracle, parallel repetition}
}
Document
Mixing Time of Quantum Gibbs Sampling for Random Sparse Hamiltonians
Abstract
Providing evidence that quantum computers can efficiently prepare low-energy or thermal states of physically relevant interacting quantum systems is a major challenge in quantum information science. A newly developed quantum Gibbs sampling algorithm [Chen et al., 2023] provides an efficient simulation of the detailed-balanced dissipative dynamics of non-commutative quantum systems. The running time of this algorithm depends on the mixing time of the corresponding quantum Markov chain, which has not been rigorously bounded except in the high-temperature regime. In this work, we establish a polylog(n) upper bound on its mixing time for various families of random n × n sparse Hamiltonians at any constant temperature. We further analyze how the choice of the jump operators for the algorithm and the spectral properties of these sparse Hamiltonians influence the mixing time. Our result places this method for Gibbs sampling on par with other efficient algorithms for preparing low-energy states of quantumly easy Hamiltonians.
Cite as
Akshar Ramkumar and Mehdi Soleimanifar. Mixing Time of Quantum Gibbs Sampling for Random Sparse Hamiltonians. In 20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 350, pp. 3:1-3:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{ramkumar_et_al:LIPIcs.TQC.2025.3,
author = {Ramkumar, Akshar and Soleimanifar, Mehdi},
title = {{Mixing Time of Quantum Gibbs Sampling for Random Sparse Hamiltonians}},
booktitle = {20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025)},
pages = {3:1--3:23},
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.2025.3},
URN = {urn:nbn:de:0030-drops-240520},
doi = {10.4230/LIPIcs.TQC.2025.3},
annote = {Keywords: Quantum algorithms, quantum Gibbs sampling, mixing time analysis}
}
Document
Optimal Locality and Parameter Tradeoffs for Subsystem Codes
Abstract
We study the tradeoffs between the locality and parameters of subsystem codes. We prove lower bounds on both the number and lengths of interactions in any D-dimensional embedding of a subsystem code. Specifically, we show that any embedding of a subsystem code with parameters [[n,k,d]] into R^D must have at least M^* interactions of length at least 𝓁^*, where
M^* = Ω(max(k,d)), and 𝓁^* = Ω(max(d/(n^((D-1)/D)), ((kd^(1/(D-1))/n))^((D-1)/D))).
We also give tradeoffs between the locality and parameters of commuting projector codes in D-dimensions, generalizing a result of Dai and Li [Dai and Li, 2025]. We provide explicit constructions of embedded codes that show our bounds are optimal in both the interaction count and interaction length.
Cite as
Samuel Dai, Ray Li, and Eugene Tang. Optimal Locality and Parameter Tradeoffs for Subsystem Codes. In 20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 350, pp. 4:1-4:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{dai_et_al:LIPIcs.TQC.2025.4,
author = {Dai, Samuel and Li, Ray and Tang, Eugene},
title = {{Optimal Locality and Parameter Tradeoffs for Subsystem Codes}},
booktitle = {20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025)},
pages = {4:1--4:22},
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.2025.4},
URN = {urn:nbn:de:0030-drops-240539},
doi = {10.4230/LIPIcs.TQC.2025.4},
annote = {Keywords: Quantum Error Correcting Code, Locality, Subsystem Code, Commuting Projector Code}
}
Document
Towards a Complexity-Theoretic Dichotomy for TQFT Invariants
Abstract
We show that for any fixed (2+1)-dimensional TQFT over ℂ of either Turaev-Viro-Barrett-Westbury or Reshetikhin-Turaev type, the problem of (exactly) computing its invariants on closed 3-manifolds is either solvable in polynomial time, or else it is #𝖯-hard to (exactly) contract certain tensors that are built from the TQFT’s fusion category. Our proof is an application of a dichotomy result of Cai and Chen [J. ACM, 2017] concerning weighted constraint satisfaction problems over ℂ. We leave for future work the issue of reinterpreting the conditions of Cai and Chen that distinguish between the two cases (i.e. #𝖯-hard tensor contractions vs. polynomial time invariants) in terms of fusion categories. We expect that with more effort, our reduction can be improved so that one gets a dichotomy directly for TQFTs' invariants of 3-manifolds rather than more general tensors built from TQFTs' fusion categories.
Cite as
Nicolas Bridges and Eric Samperton. Towards a Complexity-Theoretic Dichotomy for TQFT Invariants. In 20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 350, pp. 5:1-5:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{bridges_et_al:LIPIcs.TQC.2025.5,
author = {Bridges, Nicolas and Samperton, Eric},
title = {{Towards a Complexity-Theoretic Dichotomy for TQFT Invariants}},
booktitle = {20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025)},
pages = {5:1--5:21},
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.2025.5},
URN = {urn:nbn:de:0030-drops-240548},
doi = {10.4230/LIPIcs.TQC.2025.5},
annote = {Keywords: Complexity, topological quantum field theory, dichotomy theorems, constraint satisfaction problems, tensor categories}
}
Document
Quantum SAT Problems with Finite Sets of Projectors Are Complete for a Plethora of Classes
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
Uniformity Testing When You Have the Source Code
Abstract
We study quantum algorithms for verifying properties of the output probability distribution of a classical or quantum circuit, given access to the source code that generates the distribution. We consider the basic task of uniformity testing, which is to decide if the output distribution is uniform on [d] or ε-far from uniform in total variation distance. More generally, we consider identity testing, which is the task of deciding if the output distribution equals a known hypothesis distribution, or is ε-far from it. For both problems, the previous best known upper bound was O(min{d^{1/3}/ε²,d^{1/2}/ε}). Here we improve the upper bound to O(min{d^{1/3}/ε^{4/3}, d^{1/2}/ε}), which we conjecture is optimal.
Cite as
Clément L. Canonne, Robin Kothari, and Ryan O'Donnell. Uniformity Testing When You Have the Source Code. In 20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 350, pp. 7:1-7:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{canonne_et_al:LIPIcs.TQC.2025.7,
author = {Canonne, Cl\'{e}ment L. and Kothari, Robin and O'Donnell, Ryan},
title = {{Uniformity Testing When You Have the Source Code}},
booktitle = {20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025)},
pages = {7:1--7:20},
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.2025.7},
URN = {urn:nbn:de:0030-drops-240561},
doi = {10.4230/LIPIcs.TQC.2025.7},
annote = {Keywords: distribution testing, uniformity testing, quantum algorithms}
}
Document
Self-Testing in the Compiled Setting via Tilted-CHSH Inequalities
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
Efficient Quantum Pseudorandomness from Hamiltonian Phase States
Abstract
Quantum pseudorandomness has found applications in many areas of quantum information, ranging from entanglement theory, to models of scrambling phenomena in chaotic quantum systems, and, more recently, in the foundations of quantum cryptography. Kretschmer (TQC '21) showed that both pseudorandom states and pseudorandom unitaries exist even in a world without classical one-way functions. To this day, however, all known constructions require classical cryptographic building blocks which are themselves synonymous with the existence of one-way functions, and which are also challenging to implement on realistic quantum hardware.
In this work, we seek to make progress on both of these fronts simultaneously - by decoupling quantum pseudorandomness from classical cryptography altogether. We introduce a quantum hardness assumption called the Hamiltonian Phase State (HPS) problem, which is the task of decoding output states of a random instantaneous quantum polynomial-time (IQP) circuit. Hamiltonian phase states can be generated very efficiently using only Hadamard gates, single-qubit Z rotations and CNOT circuits. We show that the hardness of our problem reduces to a worst-case version of the problem, and we provide evidence that our assumption is plausibly fully quantum; meaning, it cannot be used to construct one-way functions. We also show information-theoretic hardness when only few copies of HPS are available by proving an approximate t-design property of our ensemble. Finally, we show that our HPS assumption and its variants allow us to efficiently construct many pseudorandom quantum primitives, ranging from pseudorandom states, to quantum pseudoentanglement, to pseudorandom unitaries, and even primitives such as public-key encryption with quantum keys.
Cite as
John Bostanci, Jonas Haferkamp, Dominik Hangleiter, and Alexander Poremba. Efficient Quantum Pseudorandomness from Hamiltonian Phase States. In 20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 350, pp. 9:1-9:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{bostanci_et_al:LIPIcs.TQC.2025.9,
author = {Bostanci, John and Haferkamp, Jonas and Hangleiter, Dominik and Poremba, Alexander},
title = {{Efficient Quantum Pseudorandomness from Hamiltonian Phase States}},
booktitle = {20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025)},
pages = {9:1--9:18},
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.2025.9},
URN = {urn:nbn:de:0030-drops-240586},
doi = {10.4230/LIPIcs.TQC.2025.9},
annote = {Keywords: Quantum pseudorandomness, quantum phase states, quantum cryptography}
}
Document
Hamiltonian Locality Testing via Trotterized Postselection
Abstract
The (tolerant) Hamiltonian locality testing problem, introduced in [Bluhm, Caro, Oufkir '24], is to determine whether a Hamiltonian H is ε₁-close to being k-local (i.e. can be written as the sum of weight-k Pauli operators) or ε₂-far from any k-local Hamiltonian, given access to its time evolution operator and using as little total evolution time as possible, with distance typically defined by the normalized Frobenius norm. We give the tightest known bounds for this problem, proving an O(√(ε₂/((ε₂-ε₁)⁵)) evolution time upper bound and an Ω(1/(ε₂-ε₁)) lower bound. Our algorithm does not require reverse time evolution or controlled application of the time evolution operator, although our lower bound applies to algorithms using either tool.
Furthermore, we show that if we are allowed reverse time evolution, this lower bound is tight, giving a matching O(1/(ε₂-ε₁)) evolution time algorithm.
Cite as
John Kallaugher and Daniel Liang. Hamiltonian Locality Testing via Trotterized Postselection. In 20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 350, pp. 10:1-10:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{kallaugher_et_al:LIPIcs.TQC.2025.10,
author = {Kallaugher, John and Liang, Daniel},
title = {{Hamiltonian Locality Testing via Trotterized Postselection}},
booktitle = {20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025)},
pages = {10:1--10:20},
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.2025.10},
URN = {urn:nbn:de:0030-drops-240593},
doi = {10.4230/LIPIcs.TQC.2025.10},
annote = {Keywords: quantum algorithms, property testing, hamiltonians}
}
Document
Quantum Catalytic Space
Abstract
Space complexity is a key field of study in theoretical computer science. In the quantum setting there are clear motivations to understand the power of space-restricted computation, as qubits are an especially precious and limited resource.
Recently, a new branch of space-bounded complexity called catalytic computing has shown that reusing space is a very powerful computational resource, especially for subroutines that incur little to no space overhead. While quantum catalysis in an information theoretic context, and the power of "dirty" qubits for quantum computation, has been studied over the years, these models are generally not suitable for use in quantum space-bounded algorithms, as they either rely on specific catalytic states or destroy the memory being borrowed.
We define the notion of catalytic computing in the quantum setting and show a number of initial results about the model. First, we show that quantum catalytic logspace can always be computed quantumly in polynomial time; the classical analogue of this is the largest open question in catalytic computing. This also allows quantum catalytic space to be defined in an equivalent way with respect to circuits instead of Turing machines. We also prove that quantum catalytic logspace can simulate log-depth threshold circuits, a class which is known to contain (and believed to strictly contain) quantum logspace, thus showcasing the power of quantum catalytic space. Finally we show that both unitary quantum catalytic logspace and classical catalytic logspace can be simulated in the one-clean qubit model.
Cite as
Harry Buhrman, Marten Folkertsma, Ian Mertz, Florian Speelman, Sergii Strelchuk, Sathyawageeswar Subramanian, and Quinten Tupker. Quantum Catalytic Space. In 20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 350, pp. 11:1-11:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{buhrman_et_al:LIPIcs.TQC.2025.11,
author = {Buhrman, Harry and Folkertsma, Marten and Mertz, Ian and Speelman, Florian and Strelchuk, Sergii and Subramanian, Sathyawageeswar and Tupker, Quinten},
title = {{Quantum Catalytic Space}},
booktitle = {20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025)},
pages = {11:1--11:24},
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.2025.11},
URN = {urn:nbn:de:0030-drops-240606},
doi = {10.4230/LIPIcs.TQC.2025.11},
annote = {Keywords: quantum computing, quantum complexity, space-bounded algorithms, catalytic computation, one clean qubit}
}
Document
The Rotation-Invariant Hamiltonian Problem Is QMA_EXP-Complete
Abstract
In this work we study a variant of the local Hamiltonian problem where we restrict to Hamiltonians that live on a lattice and are invariant under translations and rotations of the lattice. In the one-dimensional case this problem is known to be QMA_EXP-complete. On the other hand, if we fix the lattice length then in the high-dimensional limit the ground state becomes unentangled due to arguments from mean-field theory. We take steps towards understanding this complexity spectrum by studying a problem that is intermediate between these two extremes. Namely, we consider the regime where the lattice dimension is arbitrary but fixed and the lattice length is scaled. We prove that this rotation-invariant Hamiltonian problem is QMA_EXP-complete answering an open question of [Gottesman and Irani, 2013]. This characterizes a broad parameter range in which these rotation-invariant Hamiltonians have high computational complexity.
Cite as
Jon Nelson and Daniel Gottesman. The Rotation-Invariant Hamiltonian Problem Is QMA_EXP-Complete. In 20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 350, pp. 12:1-12:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{nelson_et_al:LIPIcs.TQC.2025.12,
author = {Nelson, Jon and Gottesman, Daniel},
title = {{The Rotation-Invariant Hamiltonian Problem Is QMA\underlineEXP-Complete}},
booktitle = {20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025)},
pages = {12:1--12:18},
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.2025.12},
URN = {urn:nbn:de:0030-drops-240615},
doi = {10.4230/LIPIcs.TQC.2025.12},
annote = {Keywords: Hamiltonian complexity, Local Hamiltonian problem, Monogamy of entanglement}
}