11 Search Results for "Love, Peter J."

Document
DOI: 10.4230/LIPIcs.ITCS.2026.101
Two Bases Suffice for QMA ₁-Completeness

Authors: Henry Ma and Anand Natarajan

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

Abstract
We introduce a basis-restricted variant of the Quantum-k-Sat problem, in which each term in the input Hamiltonian is required to be diagonal in either the standard or Hadamard basis. Our main result is that the Quantum-6-Sat problem with this basis restriction is already QMA₁-complete, defined with respect to a natural gateset. Our construction is based on the Feynman-Kitaev circuit-to-Hamiltonian construction, with a modified clock encoding that interleaves two clocks in the standard and Hadamard bases. In light of the central role played by CSS codes and the uncertainty principle in the proof of the NLTS theorem of Anshu, Breuckmann, and Nirkhe (STOC '23), we hope that the CSS-like structure of our Hamiltonians will make them useful for progress towards a quantum PCP theorem.
Cite as

Henry Ma and Anand Natarajan. Two Bases Suffice for QMA ₁-Completeness. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 101:1-101:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{ma_et_al:LIPIcs.ITCS.2026.101,
  author =	{Ma, Henry and Natarajan, Anand},
  title =	{{Two Bases Suffice for QMA ₁-Completeness}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{101:1--101:22},
  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.2026.101},
  URN =		{urn:nbn:de:0030-drops-253880},
  doi =		{10.4230/LIPIcs.ITCS.2026.101},
  annote =	{Keywords: quantum complexity theory, Hamiltonian complexity, Quantum Merlin Arthur (QMA), QMA₁, quantum satisfiability problem}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.55
Safe Sequences via Dominators in DAGs for Path-Covering Problems

Authors: Francisco Sena, Romeo Rizzi, and Alexandru I. Tomescu

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

Abstract
A path-covering problem on a directed acyclic graph (DAG) requires finding a set of source-to-sink paths that cover all the nodes, all the arcs, or subsets thereof, and additionally they are optimal with respect to some function. In this paper we study safe sequences of nodes or arcs, namely sequences that appear in some path of every path cover of a DAG. We show that safe sequences admit a simple characterization via cutnodes. Moreover, we establish a connection between maximal safe sequences and leaf-to-root paths in the source- and sink-dominator trees of the DAG, which may be of independent interest in the extensive literature on dominators. With dominator trees, safe sequences admit an O(n)-size representation and a linear-time output-sensitive enumeration algorithm running in time O(m + o), where n and m are the number of nodes and arcs, respectively, and o is the total length of the maximal safe sequences. We then apply maximal safe sequences to simplify Integer Linear Programs (ILPs) for two path-covering problems, LeastSquares and MinPathError, which are at the core of RNA transcript assembly problems from bioinformatics. On various datasets, maximal safe sequences can be computed in under 0.1 seconds per graph, on average, and ILP solvers whose search space is reduced in this manner exhibit significant speed-ups. For example on graphs with a large width, average speed-ups are in the range 50-250× for MinPathError and in the range 80-350× for LeastSquares. Optimizing ILPs using safe sequences can thus become a fast building block of practical RNA transcript assembly tools, and more generally, of path-covering problems.
Cite as

Francisco Sena, Romeo Rizzi, and Alexandru I. Tomescu. Safe Sequences via Dominators in DAGs for Path-Covering Problems. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 55:1-55:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{sena_et_al:LIPIcs.ESA.2025.55,
  author =	{Sena, Francisco and Rizzi, Romeo and Tomescu, Alexandru I.},
  title =	{{Safe Sequences via Dominators in DAGs for Path-Covering Problems}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{55:1--55:17},
  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.2025.55},
  URN =		{urn:nbn:de:0030-drops-245230},
  doi =		{10.4230/LIPIcs.ESA.2025.55},
  annote =	{Keywords: directed acyclic graph, path cover, dominator tree, integer linear programming, least squares, minimum path error}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.73
Classical Algorithms for Constant Approximation of the Ground State Energy of Local Hamiltonians

Authors: François Le Gall

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

Abstract
We construct classical algorithms computing an approximation of the ground state energy of an arbitrary k-local Hamiltonian acting on n qubits. We first consider the setting where a good "guiding state" is available, which is the main setting where quantum algorithms are expected to achieve an exponential speedup over classical methods. We show that a constant approximation (i.e., an approximation with constant relative accuracy) of the ground state energy can be computed classically in poly (1/χ,n) time and poly(n) space, where χ denotes the overlap between the guiding state and the ground state (as in prior works in dequantization, we assume sample-and-query access to the guiding state). This gives a significant improvement over the recent classical algorithm by Gharibian and Le Gall (SICOMP 2023), and matches (up to a polynomial overhead) both the time and space complexities of quantum algorithms for constant approximation of the ground state energy. We also obtain classical algorithms for higher-precision approximation. For the setting where no guided state is given (i.e., the standard version of the local Hamiltonian problem), we obtain a classical algorithm computing a constant approximation of the ground state energy in 2^O(n) time and poly(n) space. To our knowledge, before this work it was unknown how to classically achieve these bounds simultaneously, even for constant approximation. We also discuss complexity-theoretic aspects of our results.
Cite as

François Le Gall. Classical Algorithms for Constant Approximation of the Ground State Energy of Local Hamiltonians. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 73:1-73:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{legall:LIPIcs.ESA.2025.73,
  author =	{Le Gall, Fran\c{c}ois},
  title =	{{Classical Algorithms for Constant Approximation of the Ground State Energy of Local Hamiltonians}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{73:1--73:19},
  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.2025.73},
  URN =		{urn:nbn:de:0030-drops-245419},
  doi =		{10.4230/LIPIcs.ESA.2025.73},
  annote =	{Keywords: approximation algorithms, quantum computing, dequantization}
}
Document
DOI: 10.4230/LIPIcs.CP.2025.38
Reducing Quantum Circuit Synthesis to #SAT

Authors: Dekel Zak, Jingyi Mei, Jean-Marie Lagniez, and Alfons Laarman

Published in: LIPIcs, Volume 340, 31st International Conference on Principles and Practice of Constraint Programming (CP 2025)

Abstract
Quantum circuit synthesis is the task of decomposing a given quantum operator into a sequence of elementary quantum gates. Since the finite target gate set cannot exactly implement any given operator, approximation is often necessary. Model counting, or #SAT, has recently been demonstrated as a promising new approach for tackling core problems in quantum circuit analysis. In this work, we show for the first time that the universal quantum circuit synthesis problem can be reduced to maximum model counting. We formulate a #SAT encoding for exact and approximate depth-optimal quantum circuit synthesis into the Clifford+T gate set. We evaluate our method with an open-source implementation that uses the maximum model counter d4Max as a backend. For this purpose, we extended d4Max with support for complex and negative weights to represent amplitudes. Experimental results show that existing classical tools have potential for the quantum circuit synthesis problem.
Cite as

Dekel Zak, Jingyi Mei, Jean-Marie Lagniez, and Alfons Laarman. Reducing Quantum Circuit Synthesis to #SAT. In 31st International Conference on Principles and Practice of Constraint Programming (CP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 340, pp. 38:1-38:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{zak_et_al:LIPIcs.CP.2025.38,
  author =	{Zak, Dekel and Mei, Jingyi and Lagniez, Jean-Marie and Laarman, Alfons},
  title =	{{Reducing Quantum Circuit Synthesis to #SAT}},
  booktitle =	{31st International Conference on Principles and Practice of Constraint Programming (CP 2025)},
  pages =	{38:1--38:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-380-5},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{340},
  editor =	{de la Banda, Maria Garcia},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2025.38},
  URN =		{urn:nbn:de:0030-drops-238997},
  doi =		{10.4230/LIPIcs.CP.2025.38},
  annote =	{Keywords: Maximum weighted model counting, quantum circuit synthesis}
}
Document
DOI: 10.4230/LIPIcs.FORC.2025.4
Hardness and Approximation Algorithms for Balanced Districting Problems

Authors: Prathamesh Dharangutte, Jie Gao, Shang-En Huang, and Fang-Yi Yu

Published in: LIPIcs, Volume 329, 6th Symposium on Foundations of Responsible Computing (FORC 2025)

Abstract
We introduce and study the problem of balanced districting, where given an undirected graph with vertices carrying two types of weights (different population, resource types, etc) the goal is to maximize the total weights covered in vertex disjoint districts such that each district is a star or (in general) a connected induced subgraph with the two weights to be balanced. This problem is strongly motivated by political redistricting, where contiguity, population balance, and compactness are essential. We provide hardness and approximation algorithms for this problem. In particular, we show NP-hardness for an approximation better than n^{1/2-δ} for any constant δ > 0 in general graphs even when the districts are star graphs, as well as NP-hardness on complete graphs, tree graphs, planar graphs and other restricted settings. On the other hand, we develop an algorithm for balanced star districting that gives an O(√n)-approximation on any graph (which is basically tight considering matching hardness of approximation results), an O(log n) approximation on planar graphs with extensions to minor-free graphs. Our algorithm uses a modified Whack-a-Mole algorithm [Bhattacharya, Kiss, and Saranurak, SODA 2023] to find a sparse solution of a fractional packing linear program (despite exponentially many variables) which requires a new design of a separation oracle specific for our balanced districting problem. To turn the fractional solution to a feasible integer solution, we adopt the randomized rounding algorithm by [Chan and Har-Peled, SoCG 2009]. To get a good approximation ratio of the rounding procedure, a crucial element in the analysis is the balanced scattering separators for planar graphs and minor-free graphs - separators that can be partitioned into a small number of k-hop independent sets for some constant k - which may find independent interest in solving other packing style problems. Further, our algorithm is versatile - the very same algorithm can be analyzed in different ways on various graph classes, which leads to class-dependent approximation ratios. We also provide a FPTAS algorithm for complete graphs and tree graphs, as well as greedy algorithms and approximation ratios when the district cardinality is bounded, the graph has bounded degree or the weights are binary. We refer the readers to the full version of the paper for complete set of results and proofs.
Cite as

Prathamesh Dharangutte, Jie Gao, Shang-En Huang, and Fang-Yi Yu. Hardness and Approximation Algorithms for Balanced Districting Problems. In 6th Symposium on Foundations of Responsible Computing (FORC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 329, pp. 4:1-4:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dharangutte_et_al:LIPIcs.FORC.2025.4,
  author =	{Dharangutte, Prathamesh and Gao, Jie and Huang, Shang-En and Yu, Fang-Yi},
  title =	{{Hardness and Approximation Algorithms for Balanced Districting Problems}},
  booktitle =	{6th Symposium on Foundations of Responsible Computing (FORC 2025)},
  pages =	{4:1--4:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-367-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{329},
  editor =	{Bun, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2025.4},
  URN =		{urn:nbn:de:0030-drops-231310},
  doi =		{10.4230/LIPIcs.FORC.2025.4},
  annote =	{Keywords: Approximation algorithms, algorithmic fairness}
}
Document
DOI: 10.4230/LIPIcs.FORC.2025.20
Group Fairness and Multi-Criteria Optimization in School Assignment

Authors: Santhini K. A., Kamesh Munagala, Meghana Nasre, and Govind S. Sankar

Published in: LIPIcs, Volume 329, 6th Symposium on Foundations of Responsible Computing (FORC 2025)

Abstract
We consider the problem of assigning students to schools when students have different utilities for schools and schools have limited capacities. The students belong to demographic groups, and fairness over these groups is captured either by concave objectives, or additional constraints on the utility of the groups. We present approximation algorithms for this assignment problem with group fairness via convex program rounding. These algorithms achieve various trade-offs between capacity violation and running time. We also show that our techniques easily extend to the setting where there are arbitrary constraints on the feasible assignment, capturing multi-criteria optimization. We present simulation results that demonstrate that the rounding methods are practical even on large problem instances, with the empirical capacity violation being much better than the theoretical bounds.
Cite as

Santhini K. A., Kamesh Munagala, Meghana Nasre, and Govind S. Sankar. Group Fairness and Multi-Criteria Optimization in School Assignment. In 6th Symposium on Foundations of Responsible Computing (FORC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 329, pp. 20:1-20:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{k.a._et_al:LIPIcs.FORC.2025.20,
  author =	{K. A., Santhini and Munagala, Kamesh and Nasre, Meghana and S. Sankar, Govind},
  title =	{{Group Fairness and Multi-Criteria Optimization in School Assignment}},
  booktitle =	{6th Symposium on Foundations of Responsible Computing (FORC 2025)},
  pages =	{20:1--20:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-367-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{329},
  editor =	{Bun, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2025.20},
  URN =		{urn:nbn:de:0030-drops-231471},
  doi =		{10.4230/LIPIcs.FORC.2025.20},
  annote =	{Keywords: School Assignment, Approximation Algorithms, Group Fairness}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.33
Bosonic Quantum Computational Complexity

Authors: Ulysse Chabaud, Michael Joseph, Saeed Mehraban, and Arsalan Motamedi

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

Abstract
In recent years, quantum computing involving physical systems with continuous degrees of freedom, such as the bosonic quantum states of light, has attracted significant interest. However, a well-defined quantum complexity theory for these bosonic computations over infinite-dimensional Hilbert spaces is missing. In this work, we lay the foundations for such a research program. We introduce natural complexity classes and problems based on bosonic generalizations of BQP, the local Hamiltonian problem, and QMA. We uncover several relationships and subtle differences between standard Boolean classical and discrete-variable quantum complexity classes, and identify outstanding open problems. Our main contributions include the following: 1) Bosonic computations. We show that the power of Gaussian computations up to logspace reductions is equivalent to bounded-error quantum logspace (BQL, characterized by the problem of inverting well-conditioned matrices). More generally, we define classes of continuous-variable quantum polynomial time computations with a bounded probability of error (CVBQP) based on gates generated by polynomial bosonic Hamiltonians and particle-number measurements. Due to the infinite-dimensional Hilbert space, it is not a priori clear whether a decidable upper bound can be obtained for these classes. We identify complete problems for these classes, and we demonstrate a BQP lower bound and an EXPSPACE upper bound by proving bounds on the average energy throughout the computation. We further show that the problem of computing expectation values of polynomial bosonic observables at the output of bosonic quantum circuits using Gaussian and cubic phase gates is in PSPACE. 2) Bosonic ground energy problems. We prove that the problem of deciding whether the spectrum of a bosonic Hamiltonian is bounded from below is co-NP-hard. Furthermore, we show that the problem of finding the minimum energy of a bosonic Hamiltonian critically depends on the non-Gaussian stellar rank of the family of energy-constrained states one optimizes over: for zero stellar rank, i.e., optimizing over Gaussian states, it is NP-complete; for polynomially-bounded stellar rank, it is in QMA; for unbounded stellar rank, it is RE-hard, i.e., undecidable.
Cite as

Ulysse Chabaud, Michael Joseph, Saeed Mehraban, and Arsalan Motamedi. Bosonic Quantum Computational Complexity. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 33:1-33:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chabaud_et_al:LIPIcs.ITCS.2025.33,
  author =	{Chabaud, Ulysse and Joseph, Michael and Mehraban, Saeed and Motamedi, Arsalan},
  title =	{{Bosonic Quantum Computational Complexity}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{33:1--33:19},
  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.2025.33},
  URN =		{urn:nbn:de:0030-drops-226612},
  doi =		{10.4230/LIPIcs.ITCS.2025.33},
  annote =	{Keywords: continuous-variable quantum computing, infinite-dimensional quantum systems, stellar rank, Hamiltonian complexity}
}
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)

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@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}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.60
List Decoding Bounds for Binary Codes with Noiseless Feedback

Authors: Meghal Gupta and Rachel Yun Zhang

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

Abstract
In an error-correcting code, a sender encodes a message x ∈ {0, 1}^k such that it is still decodable by a receiver on the other end of a noisy channel. In the setting of error-correcting codes with feedback, after sending each bit, the sender learns what was received at the other end and can tailor future messages accordingly. While the unique decoding radius of feedback codes has long been known to be 1/3, the list decoding capabilities of feedback codes is not well understood. In this paper, we provide the first nontrivial bounds on the list decoding radius of feedback codes for lists of size 𝓁. For 𝓁 = 2, we fully determine the 2-list decoding radius to be 3/7. For larger values of 𝓁, we show an upper bound of 1/2 - 1/{2^(𝓁+2) - 2}, and show that the same techniques for the 𝓁 = 2 case cannot match this upper bound in general.
Cite as

Meghal Gupta and Rachel Yun Zhang. List Decoding Bounds for Binary Codes with Noiseless Feedback. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 60:1-60:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gupta_et_al:LIPIcs.ITCS.2025.60,
  author =	{Gupta, Meghal and Zhang, Rachel Yun},
  title =	{{List Decoding Bounds for Binary Codes with Noiseless Feedback}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{60:1--60:20},
  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.2025.60},
  URN =		{urn:nbn:de:0030-drops-226880},
  doi =		{10.4230/LIPIcs.ITCS.2025.60},
  annote =	{Keywords: error-correcting codes, feedback, list decoding}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2023.77
Random Max-CSPs Inherit Algorithmic Hardness from Spin Glasses

Authors: Chris Jones, Kunal Marwaha, Juspreet Singh Sandhu, and Jonathan Shi

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

Abstract
We study random constraint satisfaction problems (CSPs) at large clause density. We relate the structure of near-optimal solutions for any Boolean Max-CSP to that for an associated spin glass on the hypercube, using the Guerra-Toninelli interpolation from statistical physics. The noise stability polynomial of the CSP’s predicate is, up to a constant, the mixture polynomial of the associated spin glass. We show two main consequences: 1) We prove that the maximum fraction of constraints that can be satisfied in a random Max-CSP at large clause density is determined by the ground state energy density of the corresponding spin glass. Since the latter value can be computed with the Parisi formula [Parisi, 1980; Talagrand, 2006; Auffinger and Chen, 2017], we provide numerical values for some popular CSPs. 2) We prove that a Max-CSP at large clause density possesses generalized versions of the overlap gap property if and only if the same holds for the corresponding spin glass. We transfer results from [Huang and Sellke, 2021] to obstruct algorithms with overlap concentration on a large class of Max-CSPs. This immediately includes local classical and local quantum algorithms [Chou et al., 2022].
Cite as

Chris Jones, Kunal Marwaha, Juspreet Singh Sandhu, and Jonathan Shi. Random Max-CSPs Inherit Algorithmic Hardness from Spin Glasses. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 77:1-77:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{jones_et_al:LIPIcs.ITCS.2023.77,
  author =	{Jones, Chris and Marwaha, Kunal and Sandhu, Juspreet Singh and Shi, Jonathan},
  title =	{{Random Max-CSPs Inherit Algorithmic Hardness from Spin Glasses}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{77:1--77:26},
  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.2023.77},
  URN =		{urn:nbn:de:0030-drops-175804},
  doi =		{10.4230/LIPIcs.ITCS.2023.77},
  annote =	{Keywords: spin glass, overlap gap property, constraint satisfaction problem, Guerra-Toninelli interpolation}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.41
Limitations of Local Quantum Algorithms on Random MAX-k-XOR and Beyond

Authors: Chi-Ning Chou, Peter J. Love, Juspreet Singh Sandhu, and Jonathan Shi

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract
We introduce a notion of generic local algorithm, which strictly generalizes existing frameworks of local algorithms such as factors of i.i.d. by capturing local quantum algorithms such as the Quantum Approximate Optimization Algorithm (QAOA). Motivated by a question of Farhi et al. [arXiv:1910.08187, 2019], we then show limitations of generic local algorithms including QAOA on random instances of constraint satisfaction problems (CSPs). Specifically, we show that any generic local algorithm whose assignment to a vertex depends only on a local neighborhood with o(n) other vertices (such as the QAOA at depth less than εlog(n)) cannot arbitrarily-well approximate boolean CSPs if the problem satisfies a geometric property from statistical physics called the coupled overlap-gap property (OGP) [Chen et al., Annals of Probability, 47(3), 2019]. We show that the random MAX-k-XOR problem has this property when k ≥ 4 is even by extending the corresponding result for diluted k-spin glasses. Our concentration lemmas confirm a conjecture of Brandao et al. [arXiv:1812.04170, 2018] asserting that the landscape independence of QAOA extends to logarithmic depth - in other words, for every fixed choice of QAOA angle parameters, the algorithm at logarithmic depth performs almost equally well on almost all instances. One of these lemmas is a strengthening of McDiarmid’s inequality, applicable when the random variables have a highly biased distribution, and may be of independent interest.
Cite as

Chi-Ning Chou, Peter J. Love, Juspreet Singh Sandhu, and Jonathan Shi. Limitations of Local Quantum Algorithms on Random MAX-k-XOR and Beyond. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 41:1-41:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{chou_et_al:LIPIcs.ICALP.2022.41,
  author =	{Chou, Chi-Ning and Love, Peter J. and Sandhu, Juspreet Singh and Shi, Jonathan},
  title =	{{Limitations of Local Quantum Algorithms on Random MAX-k-XOR and Beyond}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{41:1--41:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.41},
  URN =		{urn:nbn:de:0030-drops-163822},
  doi =		{10.4230/LIPIcs.ICALP.2022.41},
  annote =	{Keywords: Quantum Algorithms, Spin Glasses, Hardness of Approximation, Local Algorithms, Concentration Inequalities, Overlap Gap Property}
}
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