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Documents authored by Morris, Jackson

Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2026.37
Hard-To-Sample Distributions from Robust Extractors

Authors: Farzan Byramji, Daniel M. Kane, Jackson Morris, and Anthony Ostuni

Published in: LIPIcs, Volume 392, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2026)

Abstract
We provide a unified method for constructing explicit distributions which are difficult for restricted models of computation to generate. Our constructions are based on a new notion of robust extractors, which are extractors that remain sound even when a small number of points violate the min-entropy constraint. Using such objects, we show that for a broad range of sampling models (e.g., low-depth circuits, small-space sources, etc.), every output of the model has distance 1 - o(1) from our target distribution, qualitatively recovering essentially all previously known hardness results. Our work extends that of Viola (SICOMP '14), who developed an earlier unified framework based on traditional extractors to rule out sampling with very small error. As a further application of our technique, we leverage a recent extractor construction of Chattopadhyay, Goodman, and Gurumukhani (ITCS '24) to present the first explicit distribution with distance 1 - o(1) from the output of any low-degree 𝔽₂-polynomial source. We note that a similar bound was obtained concurrently and independently by Khodabandeh and Shinkar (ECCC '26). We also describe a potential avenue toward proving a similar hardness result for AC⁰[⊕] circuits.
Cite as

Farzan Byramji, Daniel M. Kane, Jackson Morris, and Anthony Ostuni. Hard-To-Sample Distributions from Robust Extractors. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 392, pp. 37:1-37:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{byramji_et_al:LIPIcs.APPROX/RANDOM.2026.37,
  author =	{Byramji, Farzan and Kane, Daniel M. and Morris, Jackson and Ostuni, Anthony},
  title =	{{Hard-To-Sample Distributions from Robust Extractors}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2026)},
  pages =	{37:1--37:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-449-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{392},
  editor =	{Singh, Mohit and Gur, Tom},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2026.37},
  URN =		{urn:nbn:de:0030-drops-277543},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2026.37},
  annote =	{Keywords: sampling, extractor, low-degree polynomials}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2026.66
On the Advantage of Adaptivity for Sampling with Cell Probes

Authors: Farzan Byramji, Daniel M. Kane, Jackson Morris, and Anthony Ostuni

Published in: LIPIcs, Volume 392, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2026)

Abstract
We construct an explicit distribution 𝐃 over {0,1}^N that exhibits an essentially optimal separation between adaptive and non-adaptive cell-probe sampling. The distribution can be sampled exactly when each output bit is allowed two adaptive probes to an arbitrarily long sequence of independent uniform symbols from [N]. In contrast, any non-adaptive sampler requires Ω̃(N) non-adaptive cell probes to generate a distribution with total variation distance less than 1-o(1) from 𝐃. This provides a 2-vs-Ω̃(N) separation for sampling with adaptive versus non-adaptive cell probes, improving upon the 2-vs-Ω̃(log N) separation of Yu and Zhan (ITCS '24) and the (log N)^O(1)-vs-N^Ω(1) separation of Alekseev, Göös, Myasnikov, Riazanov, and Sokolov (STOC '26).
Cite as

Farzan Byramji, Daniel M. Kane, Jackson Morris, and Anthony Ostuni. On the Advantage of Adaptivity for Sampling with Cell Probes. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 392, pp. 66:1-66:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{byramji_et_al:LIPIcs.APPROX/RANDOM.2026.66,
  author =	{Byramji, Farzan and Kane, Daniel M. and Morris, Jackson and Ostuni, Anthony},
  title =	{{On the Advantage of Adaptivity for Sampling with Cell Probes}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2026)},
  pages =	{66:1--66:9},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-449-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{392},
  editor =	{Singh, Mohit and Gur, Tom},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2026.66},
  URN =		{urn:nbn:de:0030-drops-277839},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2026.66},
  annote =	{Keywords: sampling lower bound, cell probe model, adaptive sampling}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.73
Quantum Advantage from Sampling Shallow Circuits: Beyond Hardness of Marginals

Authors: Daniel Grier, Daniel M. Kane, Jackson Morris, Anthony Ostuni, and Kewen Wu

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

Abstract
We construct a family of distributions {𝒟_n}_n with 𝒟_n over {0, 1}ⁿ and a family of depth-7 quantum circuits {C_n}_n such that 𝒟_n is produced exactly by C_n with the all zeros state as input, yet any constant-depth classical circuit with bounded fan-in gates evaluated on any binary product distribution has total variation distance 1 - e^{-Ω(n)} from 𝒟_n. Moreover, the quantum circuits we construct are geometrically local and use a relatively standard gate set: Hadamard, controlled-phase, CNOT, and Toffoli gates. All previous separations of this type suffer from some undesirable constraint on the classical circuit model or the quantum circuits witnessing the separation. Our family of distributions is inspired by the Parity Halving Problem of Watts, Kothari, Schaeffer, and Tal (STOC, 2019), which built on the work of Bravyi, Gosset, and König (Science, 2018) to separate shallow quantum and classical circuits for relational problems.
Cite as

Daniel Grier, Daniel M. Kane, Jackson Morris, Anthony Ostuni, and Kewen Wu. Quantum Advantage from Sampling Shallow Circuits: Beyond Hardness of Marginals. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 73:1-73:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{grier_et_al:LIPIcs.ITCS.2026.73,
  author =	{Grier, Daniel and Kane, Daniel M. and Morris, Jackson and Ostuni, Anthony and Wu, Kewen},
  title =	{{Quantum Advantage from Sampling Shallow Circuits: Beyond Hardness of Marginals}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{73:1--73:14},
  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.2026.73},
  URN =		{urn:nbn:de:0030-drops-253607},
  doi =		{10.4230/LIPIcs.ITCS.2026.73},
  annote =	{Keywords: Shallow circuits, sampling, quantum circuits}
}
Document
DOI: 10.4230/LIPIcs.CCC.2025.3
Quantum Threshold Is Powerful

Authors: Daniel Grier and Jackson Morris

Published in: LIPIcs, Volume 339, 40th Computational Complexity Conference (CCC 2025)

Abstract
In 2005, Høyer and Špalek showed that constant-depth quantum circuits augmented with multi-qubit Fanout gates are quite powerful, able to compute a wide variety of Boolean functions as well as the quantum Fourier transform. They also asked what other multi-qubit gates could rival Fanout in terms of computational power, and suggested that the quantum Threshold gate might be one such candidate. Threshold is the gate that indicates if the Hamming weight of a classical basis state input is greater than some target value. We prove that Threshold is indeed powerful - there are polynomial-size constant-depth quantum circuits with Threshold gates that compute Fanout to high fidelity. Our proof is a generalization of a proof by Rosenthal that exponential-size constant-depth circuits with generalized Toffoli gates can compute Fanout. Our construction reveals that other quantum gates able to "weakly approximate" Parity can also be used as substitutes for Fanout.
Cite as

Daniel Grier and Jackson Morris. Quantum Threshold Is Powerful. In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 3:1-3:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{grier_et_al:LIPIcs.CCC.2025.3,
  author =	{Grier, Daniel and Morris, Jackson},
  title =	{{Quantum Threshold Is Powerful}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{3:1--3:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-379-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{339},
  editor =	{Srinivasan, Srikanth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2025.3},
  URN =		{urn:nbn:de:0030-drops-236979},
  doi =		{10.4230/LIPIcs.CCC.2025.3},
  annote =	{Keywords: Shallow Quantum Circuits, Circuit Complexity, Threshold Circuits}
}

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