14 Search Results for "Landau, Zeph"

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)

Copy BibTex To Clipboard

@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.2025.4
Optimal Quantum Algorithm for Estimating Fidelity to a Pure State

Authors: Wang Fang and Qisheng Wang

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

Abstract
We present an optimal quantum algorithm for fidelity estimation between two quantum states when one of them is pure. In particular, the (square root) fidelity of a mixed state to a pure state can be estimated to within additive error ε by using Θ(1/ε) queries to their state-preparation circuits, achieving a quadratic speedup over the folklore O(1/ε²). Our approach is technically simple, and can moreover estimate the quantity √{tr(ρσ²)} that is not common in the literature. To the best of our knowledge, this is the first query-optimal approach to fidelity estimation involving mixed states.
Cite as

Wang Fang and Qisheng Wang. Optimal Quantum Algorithm for Estimating Fidelity to a Pure State. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 4:1-4:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{fang_et_al:LIPIcs.ESA.2025.4,
  author =	{Fang, Wang and Wang, Qisheng},
  title =	{{Optimal Quantum Algorithm for Estimating Fidelity to a Pure State}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{4:1--4:12},
  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.2025.4},
  URN =		{urn:nbn:de:0030-drops-244727},
  doi =		{10.4230/LIPIcs.ESA.2025.4},
  annote =	{Keywords: Quantum computing, fidelity estimation, quantum algorithms, quantum query complexity}
}
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)

Copy BibTex To Clipboard

@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.ESA.2025.106
On Estimating the Quantum 𝓁_α Distance

Authors: Yupan Liu and Qisheng Wang

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

Abstract
We study the computational complexity of estimating the quantum 𝓁_α distance T_α(ρ₀,ρ₁), defined via the Schatten α-norm ‖A‖_α := tr(|A|^α)^{1/α}, given poly(n)-size state-preparation circuits of n-qubit quantum states ρ₀ and ρ₁. This quantity serves as a lower bound on the trace distance for α > 1. For any constant α > 1, we develop an efficient rank-independent quantum estimator for T_α(ρ₀,ρ₁) with time complexity poly(n), achieving an exponential speedup over the prior best results of exp(n) due to Wang, Guan, Liu, Zhang, and Ying (IEEE Trans. Inf. Theory 2024). Our improvement leverages efficiently computable uniform polynomial approximations of signed positive power functions within quantum singular value transformation, thereby eliminating the dependence on the rank of the states. Our quantum algorithm reveals a dichotomy in the computational complexity of the Quantum State Distinguishability Problem with Schatten α-norm (QSD_α), which involves deciding whether T_α(ρ₀,ρ₁) is at least 2/5 or at most 1/5. This dichotomy arises between the cases of constant α > 1 and α = 1: - For any 1+Ω(1) ≤ α ≤ O(1), QSD_α is BQP-complete. - For any 1 ≤ α ≤ 1+1/n, QSD_α is QSZK-complete, implying that no efficient quantum estimator for T_α(ρ₀,ρ₁) exists unless BQP = QSZK. The hardness results follow from reductions based on new rank-dependent inequalities for the quantum 𝓁_α distance with 1 ≤ α ≤ ∞, which are of independent interest.
Cite as

Yupan Liu and Qisheng Wang. On Estimating the Quantum 𝓁_α Distance. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 106:1-106:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{liu_et_al:LIPIcs.ESA.2025.106,
  author =	{Liu, Yupan and Wang, Qisheng},
  title =	{{On Estimating the Quantum 𝓁\underline\alpha Distance}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{106:1--106:19},
  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.2025.106},
  URN =		{urn:nbn:de:0030-drops-245758},
  doi =		{10.4230/LIPIcs.ESA.2025.106},
  annote =	{Keywords: quantum algorithms, quantum state testing, trace distance, Schatten norm}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.37
Hardness of Computation of Quantum Invariants on 3-Manifolds with Restricted Topology

Authors: Henrique Ennes and Clément Maria

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

Abstract
Quantum invariants in low-dimensional topology offer a wide variety of valuable invariants about knots and 3-manifolds, presented by explicit formulas that are readily computable. Their computational complexity has been actively studied and is tightly connected to topological quantum computing. In this article, we prove that for any 3-manifold quantum invariant in the Reshetikhin-Turaev model, there is a deterministic polynomial time algorithm that, given as input an arbitrary closed 3-manifold M, outputs a closed 3-manifold M' with the same quantum invariant, such that M' is hyperbolic, contains no low genus embedded incompressible surface, and is presented by a strongly irreducible Heegaard diagram. Our construction relies on properties of Heegaard splittings and the Hempel distance. At the level of computational complexity, this proves that the hardness of computing a given quantum invariant of 3-manifolds is preserved even when severely restricting the topology and the combinatorics of the input. This positively answers a question raised by Samperton [Samperton, 2023].
Cite as

Henrique Ennes and Clément Maria. Hardness of Computation of Quantum Invariants on 3-Manifolds with Restricted Topology. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 37:1-37:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{ennes_et_al:LIPIcs.ESA.2025.37,
  author =	{Ennes, Henrique and Maria, Cl\'{e}ment},
  title =	{{Hardness of Computation of Quantum Invariants on 3-Manifolds with Restricted Topology}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{37:1--37:16},
  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.2025.37},
  URN =		{urn:nbn:de:0030-drops-245057},
  doi =		{10.4230/LIPIcs.ESA.2025.37},
  annote =	{Keywords: 3-manifold, Heegaard splitting, Hempel distance, Quantum invariant, polynomial time reduction}
}
Document
DOI: 10.4230/LIPIcs.CCC.2025.5
Improved Separation Between Quantum and Classical Computers for Sampling and Functional Tasks

Authors: Simon C. Marshall, Scott Aaronson, and Vedran Dunjko

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

Abstract
This paper furthers existing evidence that quantum computers are capable of computations beyond classical computers. Specifically, we strengthen the collapse of the polynomial hierarchy to the second level if: (i) Quantum computers with postselection are as powerful as classical computers with postselection (PostBQP = PostBPP), (ii) any one of several quantum sampling experiments (BosonSampling, IQP, DQC1) can be approximately performed by a classical computer (contingent on existing assumptions). This last result implies that if any of these experiment’s hardness conjectures hold, then quantum computers can implement functions classical computers cannot (FBQP≠ FBPP) unless the polynomial hierarchy collapses to its 2nd level. These results are an improvement over previous work which either achieved a collapse to the third level or were concerned with exact sampling, a physically impractical case. The workhorse of these results is a new technical complexity-theoretic result which we believe could have value beyond quantum computation. In particular, we prove that if there exists an equivalence between problems solvable with an exact counting oracle and problems solvable with an approximate counting oracle, then the polynomial hierarchy collapses to its second level, indeed to ZPP^NP.
Cite as

Simon C. Marshall, Scott Aaronson, and Vedran Dunjko. Improved Separation Between Quantum and Classical Computers for Sampling and Functional Tasks. In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 5:1-5:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{marshall_et_al:LIPIcs.CCC.2025.5,
  author =	{Marshall, Simon C. and Aaronson, Scott and Dunjko, Vedran},
  title =	{{Improved Separation Between Quantum and Classical Computers for Sampling and Functional Tasks}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{5:1--5:14},
  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.2025.5},
  URN =		{urn:nbn:de:0030-drops-236991},
  doi =		{10.4230/LIPIcs.CCC.2025.5},
  annote =	{Keywords: Quantum advantage, Approximate counting, Boson sampling}
}
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)

Copy BibTex To Clipboard

@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.STACS.2025.11
Generalized Inner Product Estimation with Limited Quantum Communication

Authors: Srinivasan Arunachalam and Louis Schatzki

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
In this work, we consider the fundamental task of distributed inner product estimation when allowed limited communication. Suppose Alice and Bob are given k copies of an unknown n-qubit quantum state |ψ⟩,|ϕ⟩ respectively, are allowed to send q qubits to one another, and the task is to estimate |⟨ψ|ϕ⟩|² up to constant additive error. We show that k = Θ(√{2^{n-q}}) copies are essentially necessary and sufficient for this task (extending the work of Anshu, Landau and Liu (STOC'22) who considered the case when q = 0). Additionally, we also consider the task when the goal of the players is to estimate |⟨ψ|M|ϕ⟩|², for arbitrary Hermitian M. For this task we show that certain norms on M determine the sample complexity of estimating |⟨ψ|M|ϕ⟩|² when using only classical communication.
Cite as

Srinivasan Arunachalam and Louis Schatzki. Generalized Inner Product Estimation with Limited Quantum Communication. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 11:1-11:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{arunachalam_et_al:LIPIcs.STACS.2025.11,
  author =	{Arunachalam, Srinivasan and Schatzki, Louis},
  title =	{{Generalized Inner Product Estimation with Limited Quantum Communication}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{11:1--11:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.11},
  URN =		{urn:nbn:de:0030-drops-228366},
  doi =		{10.4230/LIPIcs.STACS.2025.11},
  annote =	{Keywords: Quantum property testing, Quantum Distributed Algorithms}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.63
Complexity Classification of Product State Problems for Local Hamiltonians

Authors: John Kallaugher, Ojas Parekh, Kevin Thompson, Yipu Wang, and Justin Yirka

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

Abstract
Product states, unentangled tensor products of single qubits, are a ubiquitous ansatz in quantum computation, including for state-of-the-art Hamiltonian approximation algorithms. A natural question is whether we should expect to efficiently solve product state problems on any interesting families of Hamiltonians. We completely classify the complexity of finding minimum-energy product states for Hamiltonians defined by any fixed set of allowed 2-qubit interactions. Our results follow a line of work classifying the complexity of solving Hamiltonian problems and classical constraint satisfaction problems based on the allowed constraints. We prove that estimating the minimum energy of a product state is in 𝖯 if and only if all allowed interactions are 1-local, and NP-complete otherwise. Equivalently, any family of non-trivial two-body interactions generates Hamiltonians with NP-complete product-state problems. Our hardness constructions only require coupling strengths of constant magnitude. A crucial component of our proofs is a collection of hardness results for a new variant of the Vector Max-Cut problem, which should be of independent interest. Our definition involves sums of distances rather than squared distances and allows linear stretches. We similarly give a proof that the original Vector Max-Cut problem is NP-complete in 3 dimensions. This implies hardness of optimizing product states for Quantum Max-Cut (the quantum Heisenberg model) is NP-complete, even when every term is guaranteed to have positive unit weight.
Cite as

John Kallaugher, Ojas Parekh, Kevin Thompson, Yipu Wang, and Justin Yirka. Complexity Classification of Product State Problems for Local Hamiltonians. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 63:1-63:32, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{kallaugher_et_al:LIPIcs.ITCS.2025.63,
  author =	{Kallaugher, John and Parekh, Ojas and Thompson, Kevin and Wang, Yipu and Yirka, Justin},
  title =	{{Complexity Classification of Product State Problems for Local Hamiltonians}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{63:1--63:32},
  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.2025.63},
  URN =		{urn:nbn:de:0030-drops-226910},
  doi =		{10.4230/LIPIcs.ITCS.2025.63},
  annote =	{Keywords: quantum complexity, quantum algorithms, local hamiltonians}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.85
Quantum 2-SAT on Low Dimensional Systems Is QMAsubscript{1}-Complete: Direct Embeddings and Black-Box Simulation

Authors: Dorian Rudolph, Sevag Gharibian, and Daniel Nagaj

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

Abstract
Despite the fundamental role the Quantum Satisfiability (QSAT) problem has played in quantum complexity theory, a central question remains open: At which local dimension does the complexity of QSAT transition from "easy" to "hard"? Here, we study QSAT with each constraint acting on a d_A-dimensional and d_B-dimensional qudit pair, denoted (d_A×d_B)-QSAT. Our first main result shows that, surprisingly, QSAT on qubits can remain QMA_1-hard, in that (2×5)-QSAT is QMA_1-complete. (QMA_1 is a quantum analogue of MA with perfect completeness.) In contrast, (2×2)-QSAT (i.e. Quantum 2-SAT on qubits) is well-known to be poly-time solvable [Bravyi, 2006]. Our second main result proves that (3×d)-QSAT on the 1D line with d ∈ O(1) is also QMA_1-hard. Finally, we initiate the study of (2×d)-QSAT on the 1D line by giving a frustration-free 1D Hamiltonian with a unique, entangled ground state. As implied by our title, our first result uses a direct embedding: We combine a novel clock construction with the 2D circuit-to-Hamiltonian construction of [Gosset and Nagaj, 2013]. Of note is a new simplified and analytic proof for the latter (as opposed to a partially numeric proof in [GN13]). This exploits Unitary Labelled Graphs [Bausch, Cubitt, Ozols, 2017] together with a new "Nullspace Connection Lemma", allowing us to break low energy analyses into small patches of projectors, and to improve the soundness analysis of [GN13] from Ω(1/T⁶) to Ω(1/T²), for T the number of gates. Our second result goes via black-box reduction: Given an arbitrary 1D Hamiltonian H on d'-dimensional qudits, we show how to embed it into an effective 1D (3×d)-QSAT instance, for d ∈ O(1). Our approach may be viewed as a weaker notion of "analog simulation" (à la [Bravyi, Hastings 2017], [Cubitt, Montanaro, Piddock 2018]). As far as we are aware, this gives the first "black-box simulation"-based QMA_1-hardness result.
Cite as

Dorian Rudolph, Sevag Gharibian, and Daniel Nagaj. Quantum 2-SAT on Low Dimensional Systems Is QMAsubscript{1}-Complete: Direct Embeddings and Black-Box Simulation. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 85:1-85:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{rudolph_et_al:LIPIcs.ITCS.2025.85,
  author =	{Rudolph, Dorian and Gharibian, Sevag and Nagaj, Daniel},
  title =	{{Quantum 2-SAT on Low Dimensional Systems Is QMAsubscript\{1\}-Complete: Direct Embeddings and Black-Box Simulation}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{85:1--85:24},
  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.2025.85},
  URN =		{urn:nbn:de:0030-drops-227139},
  doi =		{10.4230/LIPIcs.ITCS.2025.85},
  annote =	{Keywords: quantum complexity theory, Quantum Merlin Arthur (QMA), Quantum Satisfiability Problem (QSAT), Hamiltonian simulation}
}
Document
DOI: 10.4230/LIPIcs.CCC.2022.5
Quantum Search-To-Decision Reductions and the State Synthesis Problem

Authors: Sandy Irani, Anand Natarajan, Chinmay Nirkhe, Sujit Rao, and Henry Yuen

Published in: LIPIcs, Volume 234, 37th Computational Complexity Conference (CCC 2022)

Abstract
It is a useful fact in classical computer science that many search problems are reducible to decision problems; this has led to decision problems being regarded as the de facto computational task to study in complexity theory. In this work, we explore search-to-decision reductions for quantum search problems, wherein a quantum algorithm makes queries to a classical decision oracle to output a desired quantum state. In particular, we focus on search-to-decision reductions for QMA, and show that there exists a quantum polynomial-time algorithm that can generate a witness for a QMA problem up to inverse polynomial precision by making one query to a PP decision oracle. We complement this result by showing that QMA-search does not reduce to QMA-decision in polynomial-time, relative to a quantum oracle. We also explore the more general state synthesis problem, in which the goal is to efficiently synthesize a target state by making queries to a classical oracle encoding the state. We prove that there exists a classical oracle with which any quantum state can be synthesized to inverse polynomial precision using only one oracle query and to inverse exponential precision using two oracle queries. This answers an open question of Aaronson [Aaronson, 2016], who presented a state synthesis algorithm that makes O(n) queries to a classical oracle to prepare an n-qubit state, and asked if the query complexity could be made sublinear.
Cite as

Sandy Irani, Anand Natarajan, Chinmay Nirkhe, Sujit Rao, and Henry Yuen. Quantum Search-To-Decision Reductions and the State Synthesis Problem. In 37th Computational Complexity Conference (CCC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 234, pp. 5:1-5:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{irani_et_al:LIPIcs.CCC.2022.5,
  author =	{Irani, Sandy and Natarajan, Anand and Nirkhe, Chinmay and Rao, Sujit and Yuen, Henry},
  title =	{{Quantum Search-To-Decision Reductions and the State Synthesis Problem}},
  booktitle =	{37th Computational Complexity Conference (CCC 2022)},
  pages =	{5:1--5:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-241-9},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{234},
  editor =	{Lovett, Shachar},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2022.5},
  URN =		{urn:nbn:de:0030-drops-165674},
  doi =		{10.4230/LIPIcs.CCC.2022.5},
  annote =	{Keywords: Search-to-decision, state synthesis, quantum computing}
}
Document
DOI: 10.4230/LIPIcs.TQC.2022.3
The Parametrized Complexity of Quantum Verification

Authors: Srinivasan Arunachalam, Sergey Bravyi, Chinmay Nirkhe, and Bryan O'Gorman

Published in: LIPIcs, Volume 232, 17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022)

Abstract
We initiate the study of parameterized complexity of QMA problems in terms of the number of non-Clifford gates in the problem description. We show that for the problem of parameterized quantum circuit satisfiability, there exists a classical algorithm solving the problem with a runtime scaling exponentially in the number of non-Clifford gates but only polynomially with the system size. This result follows from our main result, that for any Clifford + t T-gate quantum circuit satisfiability problem, the search space of optimal witnesses can be reduced to a stabilizer subspace isomorphic to at most t qubits (independent of the system size). Furthermore, we derive new lower bounds on the T-count of circuit satisfiability instances and the T-count of the W-state assuming the classical exponential time hypothesis (ETH). Lastly, we explore the parameterized complexity of the quantum non-identity check problem.
Cite as

Srinivasan Arunachalam, Sergey Bravyi, Chinmay Nirkhe, and Bryan O'Gorman. The Parametrized Complexity of Quantum Verification. In 17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 232, pp. 3:1-3:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{arunachalam_et_al:LIPIcs.TQC.2022.3,
  author =	{Arunachalam, Srinivasan and Bravyi, Sergey and Nirkhe, Chinmay and O'Gorman, Bryan},
  title =	{{The Parametrized Complexity of Quantum Verification}},
  booktitle =	{17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022)},
  pages =	{3:1--3:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-237-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{232},
  editor =	{Le Gall, Fran\c{c}ois and Morimae, Tomoyuki},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2022.3},
  URN =		{urn:nbn:de:0030-drops-165104},
  doi =		{10.4230/LIPIcs.TQC.2022.3},
  annote =	{Keywords: parametrized complexity, quantum verification, QMA}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2022.6
Circuit Lower Bounds for Low-Energy States of Quantum Code Hamiltonians

Authors: Anurag Anshu and Chinmay Nirkhe

Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)

Abstract
The No Low-energy Trivial States (NLTS) conjecture of Freedman and Hastings [Freedman and Hastings, 2014] - which posits the existence of a local Hamiltonian with a super-constant quantum circuit lower bound on the complexity of all low-energy states - identifies a fundamental obstacle to the resolution of the quantum PCP conjecture. In this work, we provide new techniques, based on entropic and local indistinguishability arguments, that prove circuit lower bounds for all the low-energy states of local Hamiltonians arising from quantum error-correcting codes. For local Hamiltonians arising from nearly linear-rate or nearly linear-distance LDPC stabilizer codes, we prove super-constant circuit lower bounds for the complexity of all states of energy o(n). Such codes are known to exist and are not necessarily locally-testable, a property previously suspected to be essential for the NLTS conjecture. Curiously, such codes can also be constructed on a two-dimensional lattice, showing that low-depth states cannot accurately approximate the ground-energy even in physically relevant systems.
Cite as

Anurag Anshu and Chinmay Nirkhe. Circuit Lower Bounds for Low-Energy States of Quantum Code Hamiltonians. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 6:1-6:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{anshu_et_al:LIPIcs.ITCS.2022.6,
  author =	{Anshu, Anurag and Nirkhe, Chinmay},
  title =	{{Circuit Lower Bounds for Low-Energy States of Quantum Code Hamiltonians}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{6:1--6:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.6},
  URN =		{urn:nbn:de:0030-drops-156023},
  doi =		{10.4230/LIPIcs.ITCS.2022.6},
  annote =	{Keywords: quantum pcps, local hamiltonians, error-correcting codes}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2017.46
Rigorous Rg Algorithms and Area Laws for Low Energy Eigenstates In 1D

Authors: Itai Arad, Zeph Landau, Umesh V. Vazirani, and Thomas Vidick

Published in: LIPIcs, Volume 67, 8th Innovations in Theoretical Computer Science Conference (ITCS 2017)

Abstract
One of the central challenges in the study of quantum many-body systems is the complexity of simulating them on a classical computer. A recent advance by Landau et al. gave a polynomial time algorithm to compute a succinct classical description for unique ground states of gapped 1D quantum systems. Despite this progress many questions remained unresolved, including whether there exist rigorous efficient algorithms when the ground space is degenerate (and poly(n) dimensional), or for the poly(n) lowest energy states for 1D systems, or even whether such states admit succinct classical descriptions or area laws. In this paper we give a new algorithm for finding low energy states for 1D systems, based on a rigorously justified renormalization group (RG)-type transformation. In the process we resolve some of the aforementioned open questions, including giving a polynomial time algorithm for poly(n) degenerate ground spaces and an n^{O(\log n)} algorithm for the poly(n) lowest energy states for 1D systems (under a mild density condition). We note that for these classes of systems the existence of a succinct classical description and area laws were not rigorously proved before this work. The algorithms are natural and efficient, and for the case of finding unique ground states for frustration-free Hamiltonians the running time is O(nM(n)), where M(n) is the time required to multiply two n by n matrices.
Cite as

Itai Arad, Zeph Landau, Umesh V. Vazirani, and Thomas Vidick. Rigorous Rg Algorithms and Area Laws for Low Energy Eigenstates In 1D. In 8th Innovations in Theoretical Computer Science Conference (ITCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 67, pp. 46:1-46:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

Copy BibTex To Clipboard

@InProceedings{arad_et_al:LIPIcs.ITCS.2017.46,
  author =	{Arad, Itai and Landau, Zeph and Vazirani, Umesh V. and Vidick, Thomas},
  title =	{{Rigorous Rg Algorithms and Area Laws for Low Energy Eigenstates In 1D}},
  booktitle =	{8th Innovations in Theoretical Computer Science Conference (ITCS 2017)},
  pages =	{46:1--46:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-029-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{67},
  editor =	{Papadimitriou, Christos H.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2017.46},
  URN =		{urn:nbn:de:0030-drops-81920},
  doi =		{10.4230/LIPIcs.ITCS.2017.46},
  annote =	{Keywords: Hamiltonian complexity, area law, gapped ground states, algorithm}
}
  • Refine by Type
  • 14 Document/PDF
  • 10 Document/HTML

  • Refine by Publication Year
  • 10 2025
  • 3 2022
  • 1 2017

  • Refine by Author
  • 3 Nirkhe, Chinmay
  • 3 Wang, Qisheng
  • 2 Arunachalam, Srinivasan
  • 1 Aaronson, Scott
  • 1 Anshu, Anurag
  • Show More...

  • Refine by Series/Journal
  • 14 LIPIcs

  • Refine by Classification
  • 4 Theory of computation → Quantum complexity theory
  • 4 Theory of computation → Quantum computation theory
  • 3 Theory of computation → Quantum information theory
  • 3 Theory of computation → Quantum query complexity
  • 2 Theory of computation → Approximation algorithms analysis
  • Show More...

  • Refine by Keyword
  • 3 quantum algorithms
  • 2 local hamiltonians
  • 2 quantum computing
  • 1 3-manifold
  • 1 Approximate counting
  • Show More...

Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact