6 Search Results for "França, Daniel Stilck"

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.2026.108
The Learning Stabilizers with Noise Problem

Authors: Alexander Poremba, Yihui Quek, and Peter Shor

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

Abstract
Random classical codes have good error correcting properties, and yet they are notoriously hard to decode in practice. Despite many decades of extensive study, the fastest known algorithms still run in exponential time. The Learning Parity with Noise (LPN) problem, which can be seen as the task of decoding a random linear code in the presence of noise, has thus emerged as a prominent hardness assumption with numerous applications in both cryptography and learning theory. Is there a natural quantum analog of the LPN problem? In this work, we introduce the Learning Stabilizers with Noise (LSN) problem, the task of decoding a random stabilizer code in the presence of local depolarizing noise. We give both polynomial-time and exponential-time quantum algorithms for solving LSN in various depolarizing noise regimes, ranging from extremely low noise, to low constant noise rates, and even higher noise rates up to a threshold. Next, we provide concrete evidence that LSN is hard. First, we show that LSN includes LPN as a special case, which suggests that it is at least as hard as its classical counterpart. Second, we prove worst-case to average-case reductions for variants of LSN. We then ask: what is the computational complexity of solving LSN? Because the task features quantum inputs, its complexity cannot be characterized by traditional complexity classes. Instead, we show that the LSN problem lies in a recently introduced (distributional and oracle) unitary synthesis class. Finally, we identify several applications of our LSN assumption, ranging from the construction of quantum bit commitment schemes to the computational limitations of learning from quantum data.
Cite as

Alexander Poremba, Yihui Quek, and Peter Shor. The Learning Stabilizers with Noise Problem. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 108:1-108:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{poremba_et_al:LIPIcs.ITCS.2026.108,
  author =	{Poremba, Alexander and Quek, Yihui and Shor, Peter},
  title =	{{The Learning Stabilizers with Noise Problem}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{108:1--108:19},
  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.2026.108},
  URN =		{urn:nbn:de:0030-drops-253950},
  doi =		{10.4230/LIPIcs.ITCS.2026.108},
  annote =	{Keywords: Random quantum stabilizer codes, average-case hardness}
}
Document
DOI: 10.4230/LIPIcs.TQC.2025.3
Mixing Time of Quantum Gibbs Sampling for Random Sparse Hamiltonians

Authors: Akshar Ramkumar and Mehdi Soleimanifar

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

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
DOI: 10.4230/LIPIcs.ICDT.2025.16
Quantum Data Sketches

Authors: Qin Zhang and Mohsen Heidari

Published in: LIPIcs, Volume 328, 28th International Conference on Database Theory (ICDT 2025)

Abstract
Recent advancements in quantum technologies, particularly in quantum sensing and simulation, have facilitated the generation and analysis of inherently quantum data. This progress underscores the necessity for developing efficient and scalable quantum data management strategies. This goal faces immense challenges due to the exponential dimensionality of quantum data and its unique quantum properties such as no-cloning and measurement stochasticity. Specifically, classical storage and manipulation of an arbitrary n-qubit quantum state requires exponential space and time. Hence, there is a critical need to revisit foundational data management concepts and algorithms for quantum data. In this paper, we propose succinct quantum data sketches to support basic database operations such as search and selection. We view our work as an initial step towards the development of quantum data management model, opening up many possibilities for future research in this direction.
Cite as

Qin Zhang and Mohsen Heidari. Quantum Data Sketches. In 28th International Conference on Database Theory (ICDT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 328, pp. 16:1-16:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{zhang_et_al:LIPIcs.ICDT.2025.16,
  author =	{Zhang, Qin and Heidari, Mohsen},
  title =	{{Quantum Data Sketches}},
  booktitle =	{28th International Conference on Database Theory (ICDT 2025)},
  pages =	{16:1--16:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-364-5},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{328},
  editor =	{Roy, Sudeepa and Kara, Ahmet},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2025.16},
  URN =		{urn:nbn:de:0030-drops-229570},
  doi =		{10.4230/LIPIcs.ICDT.2025.16},
  annote =	{Keywords: quantum data representation, data sketching, query execution}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2023.5
Concentration Bounds for Quantum States and Limitations on the QAOA from Polynomial Approximations

Authors: Anurag Anshu and Tony Metger

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)

Abstract
We prove concentration bounds for the following classes of quantum states: (i) output states of shallow quantum circuits, answering an open question from [De Palma et al., 2022]; (ii) injective matrix product states; (iii) output states of dense Hamiltonian evolution, i.e. states of the form e^{ιH^{(p)}} ⋯ e^{ιH^{(1)}} |ψ₀⟩ for any n-qubit product state |ψ₀⟩, where each H^{(i)} can be any local commuting Hamiltonian satisfying a norm constraint, including dense Hamiltonians with interactions between any qubits. Our proofs use polynomial approximations to show that these states are close to local operators. This implies that the distribution of the Hamming weight of a computational basis measurement (and of other related observables) concentrates. An example of (iii) are the states produced by the quantum approximate optimisation algorithm (QAOA). Using our concentration results for these states, we show that for a random spin model, the QAOA can only succeed with negligible probability even at super-constant level p = o(log log n), assuming a strengthened version of the so-called overlap gap property. This gives the first limitations on the QAOA on dense instances at super-constant level, improving upon the recent result [Basso et al., 2022].
Cite as

Anurag Anshu and Tony Metger. Concentration Bounds for Quantum States and Limitations on the QAOA from Polynomial Approximations. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 5:1-5:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{anshu_et_al:LIPIcs.ITCS.2023.5,
  author =	{Anshu, Anurag and Metger, Tony},
  title =	{{Concentration Bounds for Quantum States and Limitations on the QAOA from Polynomial Approximations}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{5:1--5:8},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.5},
  URN =		{urn:nbn:de:0030-drops-175085},
  doi =		{10.4230/LIPIcs.ITCS.2023.5},
  annote =	{Keywords: quantum computing, polynomial approximation, quantum optimization algorithm, QAOA, overlap gap property}
}
Document
DOI: 10.4230/LIPIcs.TQC.2021.7
Fast and Robust Quantum State Tomography from Few Basis Measurements

Authors: Daniel Stilck França, Fernando G.S L. Brandão, and Richard Kueng

Published in: LIPIcs, Volume 197, 16th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2021)

Abstract
Quantum state tomography is a powerful but resource-intensive, general solution for numerous quantum information processing tasks. This motivates the design of robust tomography procedures that use relevant resources as sparingly as possible. Important cost factors include the number of state copies and measurement settings, as well as classical postprocessing time and memory. In this work, we present and analyze an online tomography algorithm designed to optimize all the aforementioned resources at the cost of a worse dependence on accuracy. The protocol is the first to give provably optimal performance in terms of rank and dimension for state copies, measurement settings and memory. Classical runtime is also reduced substantially and numerical experiments demonstrate a favorable comparison with other state-of-the-art techniques. Further improvements are possible by executing the algorithm on a quantum computer, giving a quantum speedup for quantum state tomography.
Cite as

Daniel Stilck França, Fernando G.S L. Brandão, and Richard Kueng. Fast and Robust Quantum State Tomography from Few Basis Measurements. In 16th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 197, pp. 7:1-7:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{franca_et_al:LIPIcs.TQC.2021.7,
  author =	{Fran\c{c}a, Daniel Stilck and Brand\~{a}o, Fernando G.S L. and Kueng, Richard},
  title =	{{Fast and Robust Quantum State Tomography from Few Basis Measurements}},
  booktitle =	{16th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2021)},
  pages =	{7:1--7:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-198-6},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{197},
  editor =	{Hsieh, Min-Hsiu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2021.7},
  URN =		{urn:nbn:de:0030-drops-140023},
  doi =		{10.4230/LIPIcs.TQC.2021.7},
  annote =	{Keywords: quantum tomography, low-rank tomography, Gibbs states, random measurements}
}
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