32 Search Results for "Sinha, Makrand"

Document
DOI: 10.4230/LIPIcs.ITCS.2026.56
The Hardness of Learning Quantum Circuits and Its Cryptographic Applications

Authors: Bill Fefferman, Soumik Ghosh, Makrand Sinha, and Henry Yuen

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

Abstract
We show that concrete hardness assumptions about learning or cloning the output state of a random quantum circuit can be used as the foundation for secure quantum cryptography. In particular, under these assumptions we construct secure one-way state generators (OWSGs), digital signature schemes, quantum bit commitments, and private key encryption schemes. We also discuss evidence for these hardness assumptions by analyzing the best-known quantum learning algorithms, as well as proving black-box lower bounds for cloning and learning given state preparation oracles. Our random circuit-based constructions provide concrete instantiations of quantum cryptographic primitives whose security do not depend on the existence of one-way functions. The use of random circuits in our constructions also opens the door to {NISQ-friendly quantum cryptography}. We discuss noise tolerant versions of our OWSG and digital signature constructions which can potentially be implementable on noisy quantum computers connected by a quantum network. On the other hand, they are still secure against {noiseless} quantum adversaries, raising the intriguing possibility of a useful implementation of an end-to-end cryptographic protocol on near-term quantum computers. Finally, our explorations suggest that the rich interconnections between learning theory and cryptography in classical theoretical computer science also extend to the quantum setting.
Cite as

Bill Fefferman, Soumik Ghosh, Makrand Sinha, and Henry Yuen. The Hardness of Learning Quantum Circuits and Its Cryptographic Applications. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 56:1-56:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{fefferman_et_al:LIPIcs.ITCS.2026.56,
  author =	{Fefferman, Bill and Ghosh, Soumik and Sinha, Makrand and Yuen, Henry},
  title =	{{The Hardness of Learning Quantum Circuits and Its Cryptographic Applications}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{56:1--56:21},
  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.2026.56},
  URN =		{urn:nbn:de:0030-drops-253431},
  doi =		{10.4230/LIPIcs.ITCS.2026.56},
  annote =	{Keywords: quantum learning, quantum circuits, cryptographic hardness, one-way state generators}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.61
Random Unitaries in Constant (Quantum) Time

Authors: Ben Foxman, Natalie Parham, Francisca Vasconcelos, and Henry Yuen

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

Abstract
Random unitaries are a central object of study in quantum information, with applications to quantum computation, quantum many-body physics, and quantum cryptography. Recent work has constructed unitary designs and pseudorandom unitaries (PRUs) using Θ(log log n)-depth unitary circuits with two-qubit gates. In this work, we show that unitary designs and PRUs can be efficiently constructed in several well-studied models of constant-time quantum computation (i.e., the time complexity on the quantum computer is independent of the system size). These models are constant-depth circuits augmented with certain nonlocal operations, such as (a) many-qubit TOFFOLI gates, (b) many-qubit FANOUT gates, or (c) mid-circuit measurements with classical feedforward control. Recent advances in quantum computing hardware suggest experimental feasibility of these models in the near future. Our results demonstrate that unitary designs and PRUs can be constructed in much weaker circuit models than previously thought. Furthermore, our construction of PRUs in constant-depth with many-qubit TOFFOLI gates shows that, under cryptographic assumptions, there is no polynomial-time learning algorithm for the circuit class QAC⁰. Finally, our results suggest a new approach towards proving that PARITY is not computable in QAC⁰, a long-standing question in quantum complexity theory.
Cite as

Ben Foxman, Natalie Parham, Francisca Vasconcelos, and Henry Yuen. Random Unitaries in Constant (Quantum) Time. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 61:1-61:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{foxman_et_al:LIPIcs.ITCS.2026.61,
  author =	{Foxman, Ben and Parham, Natalie and Vasconcelos, Francisca and Yuen, Henry},
  title =	{{Random Unitaries in Constant (Quantum) Time}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{61:1--61:25},
  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.2026.61},
  URN =		{urn:nbn:de:0030-drops-253481},
  doi =		{10.4230/LIPIcs.ITCS.2026.61},
  annote =	{Keywords: Quantum Information, Pseudorandomness, Circuit Complexity}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.57
Anti-Concentration for the Unitary Haar Measure and Applications to Random Quantum Circuits

Authors: Bill Fefferman, Soumik Ghosh, and Wei Zhan

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

Abstract
We prove a Carbery-Wright style anti-concentration inequality for the unitary Haar measure, by showing that the probability of a polynomial in the entries of a random unitary falling into an ε range is at most a polynomial in ε. Using it, we show that the scrambling speed of a random quantum circuit is lower bounded: Namely, every input qubit has an influence that is at least inverse exponential in depth, on any output qubit touched by its lightcone. Our result on scrambling speed works with high probability over the choice of a circuit from an ensemble, as opposed to just working in expectation. As an application, we give the first polynomial-time algorithm for learning log-depth random quantum circuits with Haar random gates up to polynomially small diamond distance, given oracle access to the circuit. Other applications of this new scrambling speed lower bound include: - An optimal Ω(log ε^{-1}) depth lower bound for ε-approximate unitary designs on any circuit architecture; - A polynomial-time quantum algorithm that computes the depth of a bounded-depth circuit, given oracle access to the circuit. Our learning and depth-testing algorithms apply to architectures defined over any geometric dimension, and can be generalized to a wide class of architectures with good lightcone properties.
Cite as

Bill Fefferman, Soumik Ghosh, and Wei Zhan. Anti-Concentration for the Unitary Haar Measure and Applications to Random Quantum Circuits. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 57:1-57:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{fefferman_et_al:LIPIcs.ITCS.2026.57,
  author =	{Fefferman, Bill and Ghosh, Soumik and Zhan, Wei},
  title =	{{Anti-Concentration for the Unitary Haar Measure and Applications to Random Quantum Circuits}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{57:1--57:24},
  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.2026.57},
  URN =		{urn:nbn:de:0030-drops-253443},
  doi =		{10.4230/LIPIcs.ITCS.2026.57},
  annote =	{Keywords: Haar measure, anti-concentration, random quanytum circuit, learning}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.24
Unitary Complexity and the Uhlmann Transformation Problem

Authors: John Bostanci, Yuval Efron, Tony Metger, Alexander Poremba, Luowen Qian, and Henry Yuen

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

Abstract
State transformation problems such as compressing quantum information or breaking quantum commitments are fundamental quantum tasks. However, their computational difficulty cannot easily be characterized using traditional complexity theory, which focuses on tasks with classical inputs and outputs. To study the complexity of such state transformation tasks, we introduce a framework for unitary synthesis problems, including notions of reductions and unitary complexity classes. We use this framework to study the complexity of transforming one entangled state into another via local operations. We formalize this as the Uhlmann Transformation Problem, an algorithmic version of Uhlmann’s theorem. Then, we prove structural results relating the complexity of the Uhlmann Transformation Problem, polynomial space quantum computation, and zero knowledge protocols. The Uhlmann Transformation Problem allows us to characterize the complexity of a variety of tasks in quantum information processing, including decoding noisy quantum channels, breaking falsifiable quantum cryptographic assumptions, implementing optimal prover strategies in quantum interactive proofs, and decoding the Hawking radiation of black holes. Our framework for unitary complexity thus provides new avenues for studying the computational complexity of many natural quantum information processing tasks.
Cite as

John Bostanci, Yuval Efron, Tony Metger, Alexander Poremba, Luowen Qian, and Henry Yuen. Unitary Complexity and the Uhlmann Transformation Problem. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 24:1-24:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bostanci_et_al:LIPIcs.ITCS.2026.24,
  author =	{Bostanci, John and Efron, Yuval and Metger, Tony and Poremba, Alexander and Qian, Luowen and Yuen, Henry},
  title =	{{Unitary Complexity and the Uhlmann Transformation Problem}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{24:1--24:17},
  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.2026.24},
  URN =		{urn:nbn:de:0030-drops-253111},
  doi =		{10.4230/LIPIcs.ITCS.2026.24},
  annote =	{Keywords: Uhlmann’s theorem, unitary complexity theory}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.70
Unconditional Pseudorandomness Against Shallow Quantum Circuits

Authors: Soumik Ghosh, Sathyawageeswar Subramanian, and Wei Zhan

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

Abstract
Quantum computational pseudorandomness has emerged as a fundamental notion that spans connections to complexity theory, cryptography and fundamental physics. However, all known constructions of efficient quantum-secure pseudorandom objects rely on complexity theoretic assumptions. In this work, we establish the first unconditionally secure efficient pseudorandom constructions against shallow-depth quantum circuit classes. We prove that: - Any quantum state 2-design yields unconditional pseudorandomness against both QNC⁰ circuits with arbitrarily many ancillae and AC⁰∘QNC⁰ circuits with nearly linear ancillae. - Random phased subspace states, where the phases are picked using a 4-wise independent function, are unconditionally pseudoentangled against the above circuit classes. - Any unitary 2-design yields unconditionally secure parallel-query pseudorandom unitaries against geometrically local QNC⁰ adversaries, even with limited AC⁰ postprocessing. Our results stand in stark contrast to the standard guarantee of the 2-design property, which only ensures that they cannot be distinguished from Haar random ensembles using two copies or queries. Our work demonstrates that quantum computational pseudorandomness can be achieved unconditionally for natural classes of restricted adversaries, opening new directions in quantum complexity theory.
Cite as

Soumik Ghosh, Sathyawageeswar Subramanian, and Wei Zhan. Unconditional Pseudorandomness Against Shallow Quantum Circuits. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 70:1-70:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{ghosh_et_al:LIPIcs.ITCS.2026.70,
  author =	{Ghosh, Soumik and Subramanian, Sathyawageeswar and Zhan, Wei},
  title =	{{Unconditional Pseudorandomness Against Shallow Quantum Circuits}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{70:1--70:25},
  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.2026.70},
  URN =		{urn:nbn:de:0030-drops-253578},
  doi =		{10.4230/LIPIcs.ITCS.2026.70},
  annote =	{Keywords: quantum pseudorandomness, shallow quantum circuits, pseudorandomness, t-designs}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.72
Forrelation Is Extremally Hard

Authors: Uma Girish and Rocco Servedio

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

Abstract
The Forrelation problem is a central problem that demonstrates an exponential separation between quantum and classical capabilities. In this problem, given query access to n-bit Boolean functions f and g, the goal is to estimate the Forrelation function forr(f,g), which measures the correlation between g and the Fourier transform of f. In this work we provide a new linear algebraic perspective on the Forrelation problem, as opposed to prior analytic approaches. We establish a connection between the Forrelation problem and bent Boolean functions and through this connection, analyze an extremal version of the Forrelation problem where the goal is to distinguish between extremal instances of Forrelation, namely (f,g) with forr(f,g) = 1 and forr(f,g) = -1. We show that this problem can be solved with one quantum query and success probability one, yet requires Ω̃(2^{n/4}) classical randomized queries, even for algorithms with a one-third failure probability, highlighting the remarkable power of one exact quantum query. We also study a restricted variant of this problem where the inputs f,g are computable by small classical circuits and show classical hardness under cryptographic assumptions.
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Uma Girish and Rocco Servedio. Forrelation Is Extremally Hard. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 72:1-72:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{girish_et_al:LIPIcs.ITCS.2026.72,
  author =	{Girish, Uma and Servedio, Rocco},
  title =	{{Forrelation Is Extremally Hard}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{72:1--72:22},
  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.2026.72},
  URN =		{urn:nbn:de:0030-drops-253594},
  doi =		{10.4230/LIPIcs.ITCS.2026.72},
  annote =	{Keywords: Forrelation, exact quantum, query complexity}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.109
Cloning Games, Black Holes and Cryptography

Authors: Alexander Poremba, Seyoon Ragavan, and Vinod Vaikuntanathan

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

Abstract
In this work, we introduce a new toolkit for analyzing cloning games, a notion that captures stronger and more quantitative versions of the celebrated quantum no-cloning theorem. This framework allows us to analyze a new cloning game based on binary phase states. Our results provide evidence that these games may be able to overcome important limitations of previous candidates based on BB84 states and subspace coset states: in a model where the adversaries are restricted to making a single oracle query, we show that the binary phase variant is t-copy secure when t = o(n/log n). Moreover, for constant t, we obtain the first optimal bounds of O(2^{-n}), asymptotically matching the value attained by a trivial adversarial strategy. We also show a worst-case to average-case reduction which allows us to show the same quantitative results for the new and natural notion of Haar cloning games. Our analytic toolkit, which we believe will find further applications, is based on binary subtypes and uses novel bounds on the operator norms of block-wise tensor products of matrices. To illustrate the effectiveness of these new techniques, we present two applications: first, in black-hole physics, where our asymptotically optimal bound offers quantitative insights into information scrambling in idealized models of black holes; and second, in unclonable cryptography, where we (a) construct succinct unclonable encryption schemes from the existence of pseudorandom unitaries, and (b) propose and provide evidence for the security of multi-copy unclonable encryption schemes.
Cite as

Alexander Poremba, Seyoon Ragavan, and Vinod Vaikuntanathan. Cloning Games, Black Holes and Cryptography. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 109:1-109:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{poremba_et_al:LIPIcs.ITCS.2026.109,
  author =	{Poremba, Alexander and Ragavan, Seyoon and Vaikuntanathan, Vinod},
  title =	{{Cloning Games, Black Holes and Cryptography}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{109:1--109:21},
  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.2026.109},
  URN =		{urn:nbn:de:0030-drops-253961},
  doi =		{10.4230/LIPIcs.ITCS.2026.109},
  annote =	{Keywords: Unclonable cryptography, quantum pseudorandomness, black hole physics}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.34
Testing Classical Properties from Quantum Data

Authors: Matthias C. Caro, Preksha Naik, and Joseph Slote

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

Abstract
Many properties of Boolean functions can be tested far more efficiently than the function itself can be learned. However, this dramatic advantage often disappears when testers are limited to random samples of f instead of adaptively chosen queries to f. In this work we investigate the quantum version of this restriction: quantum algorithms that test properties of a Boolean function f solely from copies of either the function state |f⟩∝ ∑_x|x,f(x)⟩ or the phase state |(-1)^f⟩∝ ∑_x (-1)^{f(x)}|x⟩. Quantum advantage in testing from data. For monotonicity, symmetry, and triangle-freeness, we show passive quantum testers are unboundedly or super-polynomially better than their classical passive testing counterparts. They are competitive with classic query-based testers in each case. Inadequacy of Fourier sampling. Our new testers use techniques beyond quantum Fourier sampling, and it turns out this is necessary: we show a certain class of bent functions can be tested from 𝒪(1) function states but has a sample complexity lower bound of 2^{Ω(n)} for any tester relying exclusively on Fourier and classical samples. Classical queries vs. quantum data. Our passive quantum testers are competitive with classical query-based testers, but this isn't universal: we exhibit a testing problem that can be solved from 𝒪(1) classical queries but requires Ω(2^{n/2}) function state copies. The Forrelation problem provides a separation of the same magnitude in the opposite direction, so we conclude that quantum data and classical queries are "maximally incomparable" resources for testing. Towards lower bounds. We also begin the study of lower bounds for testing from quantum data. For quantum monotonicity testing, we prove that the ensembles of [Goldreich et al., 2000; Black, 2024], which give exponential lower bounds for classical sample-based testing, do not yield any nontrivial lower bounds for testing from quantum data. New insights specific to quantum data will be required for proving copy complexity lower bounds for testing in this model.
Cite as

Matthias C. Caro, Preksha Naik, and Joseph Slote. Testing Classical Properties from Quantum Data. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 34:1-34:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{caro_et_al:LIPIcs.ITCS.2026.34,
  author =	{Caro, Matthias C. and Naik, Preksha and Slote, Joseph},
  title =	{{Testing Classical Properties from Quantum Data}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{34:1--34:26},
  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.2026.34},
  URN =		{urn:nbn:de:0030-drops-253213},
  doi =		{10.4230/LIPIcs.ITCS.2026.34},
  annote =	{Keywords: Quantum Property Testing, Quantum Data, Boolean Functions}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.94
Smoothed Analysis of Online Metric Matching with a Single Sample: Beyond Metric Distortion

Authors: Yingxi Li, Ellen Vitercik, and Mingwei Yang

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

Abstract
In the online metric matching problem, n servers and n requests lie in a metric space. Servers are available upfront, and requests arrive sequentially. An arriving request must be matched immediately and irrevocably to an available server, incurring a cost equal to their distance. The goal is to minimize the total matching cost. We study this problem in [0, 1]^d with the Euclidean metric, when servers are adversarial and requests are independently drawn from distinct distributions that satisfy a mild smoothness condition. Our main result is an O(1)-competitive algorithm for d ≠ 2 that requires no distributional knowledge, relying only on a single sample from each request distribution. To our knowledge, this is the first algorithm to achieve an o(log n) competitive ratio for non-trivial metrics beyond the i.i.d. setting. Our approach bypasses the Ω(log n) barrier introduced by probabilistic metric embeddings: instead of analyzing the embedding distortion and the algorithm separately, we directly bound the cost of the algorithm on the target metric space of a simple deterministic embedding. We then combine this analysis with lower bounds on the offline optimum for Euclidean metrics, derived via majorization arguments, to obtain our guarantees.
Cite as

Yingxi Li, Ellen Vitercik, and Mingwei Yang. Smoothed Analysis of Online Metric Matching with a Single Sample: Beyond Metric Distortion. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 94:1-94:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{li_et_al:LIPIcs.ITCS.2026.94,
  author =	{Li, Yingxi and Vitercik, Ellen and Yang, Mingwei},
  title =	{{Smoothed Analysis of Online Metric Matching with a Single Sample: Beyond Metric Distortion}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{94:1--94:23},
  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.2026.94},
  URN =		{urn:nbn:de:0030-drops-253815},
  doi =		{10.4230/LIPIcs.ITCS.2026.94},
  annote =	{Keywords: Online algorithm, Metric matching, Competitive analysis, Smoothed analysis}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.37
Communication Complexity of Equality and Error-Correcting Codes

Authors: Dale Jacobs, John Jeang, Vladimir Podolskii, Morgan Prior, and Ilya Volkovich

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
We study the public-coin randomized communication complexity of the equality function. The communication complexity of this function is known to be low when the error probability is constant and the players have access to many random bits. The complexity grows, however, if the allowed error probability and the amount of randomness are restricted. We show that public-coin randomized protocols for equality and error-correcting codes are essentially the same object. That is, given a protocol for equality, we can construct a code, and vice versa. We substantially extend the protocol-implies-code direction: any protocol computing a function with a large fooling set can be converted into an error-correcting code. As a corollary, we show that among functions with a fooling set of size s, equality on log s bits has the least randomized communication complexity, regardless of the restrictions on the error probability and the amount of randomness. Finally, we use the connection to error-correcting codes to analyze the randomized communication complexity of equality for varying restrictions on the error probability and the amount of randomness. In most cases, we provide tight bounds. We pinpoint the setting in which tight bounds are still unknown.
Cite as

Dale Jacobs, John Jeang, Vladimir Podolskii, Morgan Prior, and Ilya Volkovich. Communication Complexity of Equality and Error-Correcting Codes. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 37:1-37:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{jacobs_et_al:LIPIcs.FSTTCS.2025.37,
  author =	{Jacobs, Dale and Jeang, John and Podolskii, Vladimir and Prior, Morgan and Volkovich, Ilya},
  title =	{{Communication Complexity of Equality and Error-Correcting Codes}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{37:1--37:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.37},
  URN =		{urn:nbn:de:0030-drops-251175},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.37},
  annote =	{Keywords: communication complexity, randomized communication complexity, error-correcting codes}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.51
Quantum Approximate k-Minimum Finding

Authors: Minbo Gao, Zhengfeng Ji, and Qisheng Wang

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
Quantum k-minimum finding is a fundamental subroutine with numerous applications in combinatorial problems and machine learning. Previous approaches typically assume oracle access to exact function values, making it challenging to integrate this subroutine with other quantum algorithms. In this paper, we propose an (almost) optimal quantum k-minimum finding algorithm that works with approximate values for all k ≥ 1, extending a result of van Apeldoorn, Gilyén, Gribling, and de Wolf (FOCS 2017) for k = 1. As practical applications, we present efficient quantum algorithms for identifying the k smallest expectation values among multiple observables and for determining the k lowest ground state energies of a Hamiltonian with a known eigenbasis.
Cite as

Minbo Gao, Zhengfeng Ji, and Qisheng Wang. Quantum Approximate k-Minimum Finding. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 51:1-51:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gao_et_al:LIPIcs.ESA.2025.51,
  author =	{Gao, Minbo and Ji, Zhengfeng and Wang, Qisheng},
  title =	{{Quantum Approximate k-Minimum Finding}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{51:1--51:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.51},
  URN =		{urn:nbn:de:0030-drops-245192},
  doi =		{10.4230/LIPIcs.ESA.2025.51},
  annote =	{Keywords: Quantum Computing, Quantum Algorithms, Quantum Minimum Finding}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.100
Cut-Query Algorithms with Few Rounds

Authors: Yotam Kenneth-Mordoch and Robert Krauthgamer

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
In the cut-query model, the algorithm can access the input graph G = (V,E) only via cut queries that report, given a set S ⊆ V, the total weight of edges crossing the cut between S and V⧵ S. This model was introduced by Rubinstein, Schramm and Weinberg [ITCS'18] and its investigation has so far focused on the number of queries needed to solve optimization problems, such as global minimum cut. We turn attention to the round complexity of cut-query algorithms, and show that several classical problems can be solved in this model with only a constant number of rounds. Our main results are algorithms for finding a minimum cut in a graph, that offer different tradeoffs between round complexity and query complexity, where n = |V| and δ(G) denotes the minimum degree of G: (i) Õ(n^{4/3}) cut queries in two rounds in unweighted graphs; (ii) Õ(rn^{1+1/r}/δ(G)^{1/r}) queries in 2r+1 rounds for any integer r ≥ 1 again in unweighted graphs; and (iii) Õ(rn^{1+(1+log_n W)/r}) queries in 4r+3 rounds for any r ≥ 1 in weighted graphs. We also provide algorithms that find a minimum (s,t)-cut and approximate the maximum cut in a few rounds.
Cite as

Yotam Kenneth-Mordoch and Robert Krauthgamer. Cut-Query Algorithms with Few Rounds. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 100:1-100:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kennethmordoch_et_al:LIPIcs.ESA.2025.100,
  author =	{Kenneth-Mordoch, Yotam and Krauthgamer, Robert},
  title =	{{Cut-Query Algorithms with Few Rounds}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{100:1--100:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.100},
  URN =		{urn:nbn:de:0030-drops-245692},
  doi =		{10.4230/LIPIcs.ESA.2025.100},
  annote =	{Keywords: Cut Queries, Round Complexity, Submodular Optimization}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.115
Smoothed Analysis of Online Metric Problems

Authors: Christian Coester and Jack Umenberger

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
We study three classical online problems - k-server, k-taxi, and chasing size k sets - through a lens of smoothed analysis. Our setting allows request locations to be adversarial up to small perturbations, interpolating between worst-case and average-case models. Specifically, we show that if the metric space is contained in a ball in any normed space and requests are drawn from distributions whose density functions are upper bounded by 1/σ times the uniform density over the ball, then all three problems admit polylog(k/σ)-competitive algorithms. Our approach is simple: it reduces smoothed instances to fully adversarial instances on finite metrics and leverages existing algorithms in a black-box manner. We also provide a lower bound showing that no algorithm can achieve a competitive ratio sub-polylogarithmic in k/σ, matching our upper bounds up to the exponent of the polylogarithm. In contrast, the best known competitive ratios for these problems in the fully adversarial setting are 2k-1, ∞ and Θ(k²), respectively.
Cite as

Christian Coester and Jack Umenberger. Smoothed Analysis of Online Metric Problems. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 115:1-115:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{coester_et_al:LIPIcs.ESA.2025.115,
  author =	{Coester, Christian and Umenberger, Jack},
  title =	{{Smoothed Analysis of Online Metric Problems}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{115:1--115:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.115},
  URN =		{urn:nbn:de:0030-drops-245847},
  doi =		{10.4230/LIPIcs.ESA.2025.115},
  annote =	{Keywords: Online Algorithms, Competitive Analysis, Smoothed Analysis, k-server, k-taxi, Metrical Service Systems}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.66
Testing Isomorphism of Boolean Functions over Finite Abelian Groups

Authors: Swarnalipa Datta, Arijit Ghosh, Chandrima Kayal, Manaswi Paraashar, and Manmatha Roy

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
Let f and g be Boolean functions over a finite Abelian group 𝒢, where g is fully known and f is accessible via queries; that is, given any x ∈ 𝒢, we can obtain the value f(x). We study the problem of tolerant isomorphism testing: given parameters ε ≥ 0 and τ > 0, the goal is to determine, using as few queries as possible, whether there exists an automorphism σ of 𝒢 such that the fractional Hamming distance between f∘σ and g is at most ε, or whether for every automorphism σ, the distance is at least ε + τ. We design an efficient tolerant property testing algorithm for this problem over finite Abelian groups with constant exponent. The exponent of a finite group refers to the largest order of any element in the group. The query complexity of our algorithm is polynomial in s and 1/τ, where s bounds the spectral norm of the function g, and τ is the tolerance parameter. In addition, we present an improved algorithm in the case where g is Fourier sparse, meaning that its Fourier expansion contains only a small number of nonzero coefficients. Our approach draws on key ideas from Abelian group theory and Fourier analysis, including the annihilator of a subgroup, Pontryagin duality, and a pseudo inner product defined over finite Abelian groups. We believe that these techniques will be useful more broadly in the design of property testing algorithms.
Cite as

Swarnalipa Datta, Arijit Ghosh, Chandrima Kayal, Manaswi Paraashar, and Manmatha Roy. Testing Isomorphism of Boolean Functions over Finite Abelian Groups. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 66:1-66:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{datta_et_al:LIPIcs.APPROX/RANDOM.2025.66,
  author =	{Datta, Swarnalipa and Ghosh, Arijit and Kayal, Chandrima and Paraashar, Manaswi and Roy, Manmatha},
  title =	{{Testing Isomorphism of Boolean Functions over Finite Abelian Groups}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{66:1--66:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.66},
  URN =		{urn:nbn:de:0030-drops-244328},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.66},
  annote =	{Keywords: Analysis of Boolean functions, Abelian groups, Automorphism group, Function isomorphism, Spectral norm}
}
Document
DOI: 10.4230/LIPIcs.TQC.2025.9
Efficient Quantum Pseudorandomness from Hamiltonian Phase States

Authors: John Bostanci, Jonas Haferkamp, Dominik Hangleiter, and Alexander Poremba

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

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}
}
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