Search Results

Documents authored by Carolan, Joseph

Document
DOI: 10.4230/LIPIcs.ITCS.2025.31
Quantum Advantage and Lower Bounds in Parallel Query Complexity

Authors: Joseph Carolan, Amin Shiraz Gilani, and Mahathi Vempati

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

Abstract
It is well known that quantum, randomized and deterministic (sequential) query complexities are polynomially related for total boolean functions. We find that significantly larger separations between the parallel generalizations of these measures are possible. In particular, 1) We employ the cheatsheet framework to obtain an unbounded parallel quantum query advantage over its randomized analogue for a total function, falsifying a conjecture of [https://arxiv.org/abs/1309.6116]. 2) We strengthen 1 by constructing a total function which exhibits an unbounded parallel quantum query advantage despite having no sequential advantage, suggesting that genuine quantum advantage could occur entirely due to parallelism. 3) We construct a total function that exhibits a polynomial separation between 2-round quantum and randomized query complexities, contrasting a result of [https://arxiv.org/abs/1001.0018] that there is at most a constant separation for 1-round (nonadaptive) algorithms. 4) We develop a new technique for deriving parallel quantum lower bounds from sequential upper bounds. We employ this technique to give lower bounds for Boolean symmetric functions and read-once formulas, ruling out large parallel query advantages for them. We also provide separations between randomized and deterministic parallel query complexities analogous to items 1-3.
Cite as

Joseph Carolan, Amin Shiraz Gilani, and Mahathi Vempati. Quantum Advantage and Lower Bounds in Parallel Query Complexity. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 31:1-31:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{carolan_et_al:LIPIcs.ITCS.2025.31,
  author =	{Carolan, Joseph and Gilani, Amin Shiraz and Vempati, Mahathi},
  title =	{{Quantum Advantage and Lower Bounds in Parallel Query Complexity}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{31:1--31:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.31},
  URN =		{urn:nbn:de:0030-drops-226597},
  doi =		{10.4230/LIPIcs.ITCS.2025.31},
  annote =	{Keywords: Computational complexity theory, quantum, lower bounds, parallel}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.32
Succinct Fermion Data Structures

Authors: Joseph Carolan and Luke Schaeffer

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

Abstract
Simulating fermionic systems on a quantum computer requires representing fermionic states using qubits. The complexity of many simulation algorithms depends on the complexity of implementing rotations generated by fermionic creation-annihilation operators, and the space depends on the number of qubits used. While standard fermion encodings like Jordan-Wigner are space optimal for arbitrary fermionic systems, physical symmetries like particle conservation can reduce the number of physical configurations, allowing improved space complexity. Such space saving is only feasible if the gate overhead is small, suggesting a (quantum) data structures problem, wherein one would like to minimize space used to represent a fermionic state, while still enabling efficient rotations. We define a structure which naturally captures mappings from fermions to systems of qubits. We then instantiate it in two ways, giving rise to two new second-quantized fermion encodings of F fermions in M modes. An information theoretic minimum of I: = ⌈log₂ binom(M,F)⌉ qubits is required for such systems, a bound we nearly match over the entire parameter regime. 1) Our first construction uses I + o(I) qubits when F = o(M), and allows rotations generated by creation-annihilation operators in O(I) gates and O(log M log log M) depth. 2) Our second construction uses I + O(1) qubits when F = Θ(M), and allows rotations generated by creation-annihilation operators in O(I³) gates. In relation to comparable prior work, the first represents a polynomial improvement in both space and gate complexity (against Kirby et al. 2022), and the second represents an exponential improvement in gate complexity at the cost of only a constant number of additional qubits (against Harrison et al. or Shee et al. 2022), in the described parameter regimes.
Cite as

Joseph Carolan and Luke Schaeffer. Succinct Fermion Data Structures. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 32:1-32:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{carolan_et_al:LIPIcs.ITCS.2025.32,
  author =	{Carolan, Joseph and Schaeffer, Luke},
  title =	{{Succinct Fermion Data Structures}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{32:1--32:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.32},
  URN =		{urn:nbn:de:0030-drops-226600},
  doi =		{10.4230/LIPIcs.ITCS.2025.32},
  annote =	{Keywords: quantum computing, data structures, fermion encodings}
}
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact