42 Search Results for "de Wolf, Ronald"

Document
DOI: 10.4230/LIPIcs.TQC.2024.10
Guidable Local Hamiltonian Problems with Implications to Heuristic Ansatz State Preparation and the Quantum PCP Conjecture

Authors: Jordi Weggemans, Marten Folkertsma, and Chris Cade

Published in: LIPIcs, Volume 310, 19th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2024)

Abstract
We study "Merlinized" versions of the recently defined Guided Local Hamiltonian problem, which we call "Guidable Local Hamiltonian" problems. Unlike their guided counterparts, these problems do not have a guiding state provided as a part of the input, but merely come with the promise that one exists. We consider in particular two classes of guiding states: those that can be prepared efficiently by a quantum circuit; and those belonging to a class of quantum states we call classically evaluatable, for which it is possible to efficiently compute expectation values of local observables classically. We show that guidable local Hamiltonian problems for both classes of guiding states are QCMA-complete in the inverse-polynomial precision setting, but lie within NP (or NqP) in the constant precision regime when the guiding state is classically evaluatable. Our completeness results show that, from a complexity-theoretic perspective, classical Ansätze selected by classical heuristics are just as powerful as quantum Ansätze prepared by quantum heuristics, as long as one has access to quantum phase estimation. In relation to the quantum PCP conjecture, we (i) define a complexity class capturing quantum-classical probabilistically checkable proof systems and show that it is contained in BQP^NP[1] for constant proof queries; (ii) give a no-go result on "dequantizing" the known quantum reduction which maps a QPCP-verification circuit to a local Hamiltonian with constant promise gap; (iii) give several no-go results for the existence of quantum gap amplification procedures that preserve certain ground state properties; and (iv) propose two conjectures that can be viewed as stronger versions of the NLTS theorem. Finally, we show that many of our results can be directly modified to obtain similar results for the class MA.
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Jordi Weggemans, Marten Folkertsma, and Chris Cade. Guidable Local Hamiltonian Problems with Implications to Heuristic Ansatz State Preparation and the Quantum PCP Conjecture. In 19th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 310, pp. 10:1-10:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{weggemans_et_al:LIPIcs.TQC.2024.10,
  author =	{Weggemans, Jordi and Folkertsma, Marten and Cade, Chris},
  title =	{{Guidable Local Hamiltonian Problems with Implications to Heuristic Ansatz State Preparation and the Quantum PCP Conjecture}},
  booktitle =	{19th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2024)},
  pages =	{10:1--10:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-328-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{310},
  editor =	{Magniez, Fr\'{e}d\'{e}ric and Grilo, Alex Bredariol},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2024.10},
  URN =		{urn:nbn:de:0030-drops-206804},
  doi =		{10.4230/LIPIcs.TQC.2024.10},
  annote =	{Keywords: Quantum complexity theory, local Hamiltonian problem, quantum state ansatzes, QCMA, quantum PCP conjecture}
}
Document
DOI: 10.4230/LIPIcs.CCC.2024.15
Quantum Automating TC⁰-Frege Is LWE-Hard

Authors: Noel Arteche, Gaia Carenini, and Matthew Gray

Published in: LIPIcs, Volume 300, 39th Computational Complexity Conference (CCC 2024)

Abstract
We prove the first hardness results against efficient proof search by quantum algorithms. We show that under Learning with Errors (LWE), the standard lattice-based cryptographic assumption, no quantum algorithm can weakly automate TC⁰-Frege. This extends the line of results of Krajíček and Pudlák (Information and Computation, 1998), Bonet, Pitassi, and Raz (FOCS, 1997), and Bonet, Domingo, Gavaldà, Maciel, and Pitassi (Computational Complexity, 2004), who showed that Extended Frege, TC⁰-Frege and AC⁰-Frege, respectively, cannot be weakly automated by classical algorithms if either the RSA cryptosystem or the Diffie-Hellman key exchange protocol are secure. To the best of our knowledge, this is the first interaction between quantum computation and propositional proof search.
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Noel Arteche, Gaia Carenini, and Matthew Gray. Quantum Automating TC⁰-Frege Is LWE-Hard. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 15:1-15:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{arteche_et_al:LIPIcs.CCC.2024.15,
  author =	{Arteche, Noel and Carenini, Gaia and Gray, Matthew},
  title =	{{Quantum Automating TC⁰-Frege Is LWE-Hard}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{15:1--15:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-331-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{300},
  editor =	{Santhanam, Rahul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2024.15},
  URN =		{urn:nbn:de:0030-drops-204117},
  doi =		{10.4230/LIPIcs.CCC.2024.15},
  annote =	{Keywords: automatability, post-quantum cryptography, feasible interpolation}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.70
BQP, Meet NP: Search-To-Decision Reductions and Approximate Counting

Authors: Sevag Gharibian and Jonas Kamminga

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
What is the power of polynomial-time quantum computation with access to an NP oracle? In this work, we focus on two fundamental tasks from the study of Boolean satisfiability (SAT) problems: search-to-decision reductions, and approximate counting. We first show that, in strong contrast to the classical setting where a poly-time Turing machine requires Θ(n) queries to an NP oracle to compute a witness to a given SAT formula, quantumly Θ(log n) queries suffice. We then show this is tight in the black-box model - any quantum algorithm with "NP-like" query access to a formula requires Ω(log n) queries to extract a solution with constant probability. Moving to approximate counting of SAT solutions, by exploiting a quantum link between search-to-decision reductions and approximate counting, we show that existing classical approximate counting algorithms are likely optimal. First, we give a lower bound in the "NP-like" black-box query setting: Approximate counting requires Ω(log n) queries, even on a quantum computer. We then give a "white-box" lower bound (i.e. where the input formula is not hidden in the oracle) - if there exists a randomized poly-time classical or quantum algorithm for approximate counting making o(log n) NP queries, then BPP^NP[o(n)] contains a 𝖯^NP-complete problem if the algorithm is classical and FBQP^NP[o(n)] contains an FP^NP-complete problem if the algorithm is quantum.
Cite as

Sevag Gharibian and Jonas Kamminga. BQP, Meet NP: Search-To-Decision Reductions and Approximate Counting. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 70:1-70:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{gharibian_et_al:LIPIcs.ICALP.2024.70,
  author =	{Gharibian, Sevag and Kamminga, Jonas},
  title =	{{BQP, Meet NP: Search-To-Decision Reductions and Approximate Counting}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{70:1--70:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.70},
  URN =		{urn:nbn:de:0030-drops-202134},
  doi =		{10.4230/LIPIcs.ICALP.2024.70},
  annote =	{Keywords: Approximate Counting, Search to Decision Reduction, BQP, NP, Oracle Complexity Class}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2024.1
A Qubit, a Coin, and an Advice String Walk into a Relational Problem

Authors: Scott Aaronson, Harry Buhrman, and William Kretschmer

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)

Abstract
Relational problems (those with many possible valid outputs) are different from decision problems, but it is easy to forget just how different. This paper initiates the study of FBQP/qpoly, the class of relational problems solvable in quantum polynomial-time with the help of polynomial-sized quantum advice, along with its analogues for deterministic and randomized computation (FP, FBPP) and advice (/poly, /rpoly). Our first result is that FBQP/qpoly ≠ FBQP/poly, unconditionally, with no oracle - a striking contrast with what we know about the analogous decision classes. The proof repurposes the separation between quantum and classical one-way communication complexities due to Bar-Yossef, Jayram, and Kerenidis. We discuss how this separation raises the prospect of near-term experiments to demonstrate "quantum information supremacy," a form of quantum supremacy that would not depend on unproved complexity assumptions. Our second result is that FBPP ̸ ⊂ FP/poly - that is, Adleman’s Theorem fails for relational problems - unless PSPACE ⊂ NP/poly. Our proof uses IP = PSPACE and time-bounded Kolmogorov complexity. On the other hand, we show that proving FBPP ̸ ⊂ FP/poly will be hard, as it implies a superpolynomial circuit lower bound for PromiseBPEXP. We prove the following further results: - Unconditionally, FP ≠ FBPP and FP/poly ≠ FBPP/poly (even when these classes are carefully defined). - FBPP/poly = FBPP/rpoly (and likewise for FBQP). For sampling problems, by contrast, SampBPP/poly ≠ SampBPP/rpoly (and likewise for SampBQP).
Cite as

Scott Aaronson, Harry Buhrman, and William Kretschmer. A Qubit, a Coin, and an Advice String Walk into a Relational Problem. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 1:1-1:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{aaronson_et_al:LIPIcs.ITCS.2024.1,
  author =	{Aaronson, Scott and Buhrman, Harry and Kretschmer, William},
  title =	{{A Qubit, a Coin, and an Advice String Walk into a Relational Problem}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{1:1--1:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.1},
  URN =		{urn:nbn:de:0030-drops-195290},
  doi =		{10.4230/LIPIcs.ITCS.2024.1},
  annote =	{Keywords: Relational problems, quantum advice, randomized advice, FBQP, FBPP}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2023.32
Tight Bounds for the Randomized and Quantum Communication Complexities of Equality with Small Error

Authors: Olivier Lalonde, Nikhil S. Mande, and Ronald de Wolf

Published in: LIPIcs, Volume 284, 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)

Abstract
We investigate the randomized and quantum communication complexities of the well-studied Equality function with small error probability ε, getting the optimal constant factors in the leading terms in various different models. The following are our results in the randomized model: - We give a general technique to convert public-coin protocols to private-coin protocols by incurring a small multiplicative error at a small additive cost. This is an improvement over Newman’s theorem [Inf. Proc. Let.'91] in the dependence on the error parameter. - As a consequence we obtain a (log(n/ε²) + 4)-cost private-coin communication protocol that computes the n-bit Equality function, to error ε. This improves upon the log(n/ε³) + O(1) upper bound implied by Newman’s theorem, and matches the best known lower bound, which follows from Alon [Comb. Prob. Comput.'09], up to an additive log log(1/ε) + O(1). The following are our results in various quantum models: - We exhibit a one-way protocol with log(n/ε) + 4 qubits of communication for the n-bit Equality function, to error ε, that uses only pure states. This bound was implicitly already shown by Nayak [PhD thesis'99]. - We give a near-matching lower bound: any ε-error one-way protocol for n-bit Equality that uses only pure states communicates at least log(n/ε) - log log(1/ε) - O(1) qubits. - We exhibit a one-way protocol with log(√n/ε) + 3 qubits of communication that uses mixed states. This is tight up to additive log log(1/ε) + O(1), which follows from Alon’s result. - We exhibit a one-way entanglement-assisted protocol achieving error probability ε with ⌈log(1/ε)⌉ + 1 classical bits of communication and ⌈log(√n/ε)⌉ + 4 shared EPR-pairs between Alice and Bob. This matches the communication cost of the classical public coin protocol achieving the same error probability while improving upon the amount of prior entanglement that is needed for this protocol, which is ⌈log(n/ε)⌉ + O(1) shared EPR-pairs. Our upper bounds also yield upper bounds on the approximate rank, approximate nonnegative-rank, and approximate psd-rank of the Identity matrix. As a consequence we also obtain improved upper bounds on these measures for a function that was recently used to refute the randomized and quantum versions of the log-rank conjecture (Chattopadhyay, Mande and Sherif [J. ACM'20], Sinha and de Wolf [FOCS'19], Anshu, Boddu and Touchette [FOCS'19]).
Cite as

Olivier Lalonde, Nikhil S. Mande, and Ronald de Wolf. Tight Bounds for the Randomized and Quantum Communication Complexities of Equality with Small Error. In 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 284, pp. 32:1-32:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{lalonde_et_al:LIPIcs.FSTTCS.2023.32,
  author =	{Lalonde, Olivier and Mande, Nikhil S. and de Wolf, Ronald},
  title =	{{Tight Bounds for the Randomized and Quantum Communication Complexities of Equality with Small Error}},
  booktitle =	{43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)},
  pages =	{32:1--32:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-304-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{284},
  editor =	{Bouyer, Patricia and Srinivasan, Srikanth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2023.32},
  URN =		{urn:nbn:de:0030-drops-194055},
  doi =		{10.4230/LIPIcs.FSTTCS.2023.32},
  annote =	{Keywords: Communication complexity, quantum communication complexity}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.64
Improved Quantum Boosting

Authors: Adam Izdebski and Ronald de Wolf

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

Abstract
Boosting is a general method to convert a weak learner (which generates hypotheses that are just slightly better than random) into a strong learner (which generates hypotheses that are much better than random). Recently, Arunachalam and Maity [Srinivasan Arunachalam and Reevu Maity, 2020] gave the first quantum improvement for boosting, by combining Freund and Schapire’s AdaBoost algorithm with a quantum algorithm for approximate counting. Their booster is faster than classical boosting as a function of the VC-dimension of the weak learner’s hypothesis class, but worse as a function of the quality of the weak learner. In this paper we give a substantially faster and simpler quantum boosting algorithm, based on Servedio’s SmoothBoost algorithm [Servedio, 2003].
Cite as

Adam Izdebski and Ronald de Wolf. Improved Quantum Boosting. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 64:1-64:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{izdebski_et_al:LIPIcs.ESA.2023.64,
  author =	{Izdebski, Adam and de Wolf, Ronald},
  title =	{{Improved Quantum Boosting}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{64:1--64:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. 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.2023.64},
  URN =		{urn:nbn:de:0030-drops-187178},
  doi =		{10.4230/LIPIcs.ESA.2023.64},
  annote =	{Keywords: Learning theory, Boosting algorithms, Quantum computing}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.81
Tight Bounds for Quantum Phase Estimation and Related Problems

Authors: Nikhil S. Mande and Ronald de Wolf

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

Abstract
Phase estimation, due to Kitaev [arXiv'95], is one of the most fundamental subroutines in quantum computing, used in Shor’s factoring algorithm, optimization algorithms, quantum chemistry algorithms, and many others. In the basic scenario, one is given black-box access to a unitary U, and an eigenstate |ψ⟩ of U with unknown eigenvalue e^{iθ}, and the task is to estimate the eigenphase θ within ±δ, with high probability. The repeated application of U and U^{-1} is typically the most expensive part of phase estimation, so for us the cost of an algorithm will be that number of applications. Motivated by the "guided Hamiltonian problem" in quantum chemistry, we tightly characterize the cost of several variants of phase estimation where we are no longer given an arbitrary eigenstate, but are required to estimate the maximum eigenphase of U, aided by advice in the form of states (or a unitary preparing those states) which are promised to have at least a certain overlap γ with the top eigenspace. We give algorithms and matching lower bounds (up to logarithmic factors) for all ranges of parameters. We show a crossover point below which advice is not helpful: o(1/γ²) copies of the advice state (or o(1/γ) applications of an advice-preparing unitary) are not significantly better than having no advice at all. We also show that having knowledge of the eigenbasis of U does not significantly reduce cost. Our upper bounds use the subroutine of generalized maximum-finding of van Apeldoorn, Gilyén, Gribling, and de Wolf [Quantum'20], the state-based Hamiltonian simulation of Lloyd, Mohseni, and Rebentrost [Nature Physics'13], and several other techniques. Our lower bounds follow by reductions from a fractional version of the Boolean OR function with advice, which we lower bound by a simple modification of the adversary method of Ambainis [JCSS'02]. As an immediate consequence we also obtain a lower bound on the complexity of the Unitary recurrence time problem, matching an upper bound of She and Yuen [ITCS'23] and resolving an open question posed by them. Lastly, we study how efficiently one can reduce the error probability in the basic phase-estimation scenario. We show that an algorithm solving phase estimation to precision δ with error probability at most ε must have cost Ω(1/δ log(1/ε)), matching the obvious way to error-reduce the basic constant-error-probability phase estimation algorithm. This contrasts with some other scenarios in quantum computing (e.g. search) where error-reduction costs only a factor O(√{log(1/ε)}). Our lower bound technique uses a variant of the polynomial method with trigonometric polynomials.
Cite as

Nikhil S. Mande and Ronald de Wolf. Tight Bounds for Quantum Phase Estimation and Related Problems. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 81:1-81:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{mande_et_al:LIPIcs.ESA.2023.81,
  author =	{Mande, Nikhil S. and de Wolf, Ronald},
  title =	{{Tight Bounds for Quantum Phase Estimation and Related Problems}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{81:1--81:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. 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.2023.81},
  URN =		{urn:nbn:de:0030-drops-187346},
  doi =		{10.4230/LIPIcs.ESA.2023.81},
  annote =	{Keywords: Phase estimation, quantum computing}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2023.32
Improved Hardness Results for the Guided Local Hamiltonian Problem

Authors: Chris Cade, Marten Folkertsma, Sevag Gharibian, Ryu Hayakawa, François Le Gall, Tomoyuki Morimae, and Jordi Weggemans

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Abstract
Estimating the ground state energy of a local Hamiltonian is a central problem in quantum chemistry. In order to further investigate its complexity and the potential of quantum algorithms for quantum chemistry, Gharibian and Le Gall (STOC 2022) recently introduced the guided local Hamiltonian problem (GLH), which is a variant of the local Hamiltonian problem where an approximation of a ground state (which is called a guiding state) is given as an additional input. Gharibian and Le Gall showed quantum advantage (more precisely, BQP-completeness) for GLH with 6-local Hamiltonians when the guiding state has fidelity (inverse-polynomially) close to 1/2 with a ground state. In this paper, we optimally improve both the locality and the fidelity parameter: we show that the BQP-completeness persists even with 2-local Hamiltonians, and even when the guiding state has fidelity (inverse-polynomially) close to 1 with a ground state. Moreover, we show that the BQP-completeness also holds for 2-local physically motivated Hamiltonians on a 2D square lattice or a 2D triangular lattice. Beyond the hardness of estimating the ground state energy, we also show BQP-hardness persists when considering estimating energies of excited states of these Hamiltonians instead. Those make further steps towards establishing practical quantum advantage in quantum chemistry.
Cite as

Chris Cade, Marten Folkertsma, Sevag Gharibian, Ryu Hayakawa, François Le Gall, Tomoyuki Morimae, and Jordi Weggemans. Improved Hardness Results for the Guided Local Hamiltonian Problem. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 32:1-32:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{cade_et_al:LIPIcs.ICALP.2023.32,
  author =	{Cade, Chris and Folkertsma, Marten and Gharibian, Sevag and Hayakawa, Ryu and Le Gall, Fran\c{c}ois and Morimae, Tomoyuki and Weggemans, Jordi},
  title =	{{Improved Hardness Results for the Guided Local Hamiltonian Problem}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{32:1--32:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.32},
  URN =		{urn:nbn:de:0030-drops-180840},
  doi =		{10.4230/LIPIcs.ICALP.2023.32},
  annote =	{Keywords: Quantum computing, Quantum advantage, Quantum Chemistry, Guided Local Hamiltonian Problem}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2023.38
Quantum Algorithms and Lower Bounds for Linear Regression with Norm Constraints

Authors: Yanlin Chen and Ronald de Wolf

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Abstract
Lasso and Ridge are important minimization problems in machine learning and statistics. They are versions of linear regression with squared loss where the vector θ ∈ ℝ^d of coefficients is constrained in either 𝓁₁-norm (for Lasso) or in 𝓁₂-norm (for Ridge). We study the complexity of quantum algorithms for finding ε-minimizers for these minimization problems. We show that for Lasso we can get a quadratic quantum speedup in terms of d by speeding up the cost-per-iteration of the Frank-Wolfe algorithm, while for Ridge the best quantum algorithms are linear in d, as are the best classical algorithms. As a byproduct of our quantum lower bound for Lasso, we also prove the first classical lower bound for Lasso that is tight up to polylog-factors.
Cite as

Yanlin Chen and Ronald de Wolf. Quantum Algorithms and Lower Bounds for Linear Regression with Norm Constraints. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 38:1-38:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{chen_et_al:LIPIcs.ICALP.2023.38,
  author =	{Chen, Yanlin and de Wolf, Ronald},
  title =	{{Quantum Algorithms and Lower Bounds for Linear Regression with Norm Constraints}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{38:1--38:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.38},
  URN =		{urn:nbn:de:0030-drops-180907},
  doi =		{10.4230/LIPIcs.ICALP.2023.38},
  annote =	{Keywords: Quantum algorithms, Regularized linear regression, Lasso, Ridge, Lower bounds}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2022.15
Improved Quantum Query Upper Bounds Based on Classical Decision Trees

Authors: Arjan Cornelissen, Nikhil S. Mande, and Subhasree Patro

Published in: LIPIcs, Volume 250, 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)

Abstract
We consider the following question in query complexity: Given a classical query algorithm in the form of a decision tree, when does there exist a quantum query algorithm with a speed-up (i.e., that makes fewer queries) over the classical one? We provide a general construction based on the structure of the underlying decision tree, and prove that this can give us an up-to-quadratic quantum speed-up in the number of queries. In particular, our results give a bounded-error quantum query algorithm of cost O(√s) to compute a Boolean function (more generally, a relation) that can be computed by a classical (even randomized) decision tree of size s. This recovers an O(√n) algorithm for the Search problem, for example. Lin and Lin [Theory of Computing'16] and Beigi and Taghavi [Quantum'20] showed results of a similar flavor. Their upper bounds are in terms of a quantity which we call the "guessing complexity" of a decision tree. We identify that the guessing complexity of a decision tree equals its rank, a notion introduced by Ehrenfeucht and Haussler [Information and Computation'89] in the context of learning theory. This answers a question posed by Lin and Lin, who asked whether the guessing complexity of a decision tree is related to any measure studied in classical complexity theory. We also show a polynomial separation between rank and its natural randomized analog for the complete binary AND-OR tree. Beigi and Taghavi constructed span programs and dual adversary solutions for Boolean functions given classical decision trees computing them and an assignment of non-negative weights to edges of the tree. We explore the effect of changing these weights on the resulting span program complexity and objective value of the dual adversary bound, and capture the best possible weighting scheme by an optimization program. We exhibit a solution to this program and argue its optimality from first principles. We also exhibit decision trees for which our bounds are strictly stronger than those of Lin and Lin, and Beigi and Taghavi. This answers a question of Beigi and Taghavi, who asked whether different weighting schemes in their construction could yield better upper bounds.
Cite as

Arjan Cornelissen, Nikhil S. Mande, and Subhasree Patro. Improved Quantum Query Upper Bounds Based on Classical Decision Trees. In 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 250, pp. 15:1-15:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{cornelissen_et_al:LIPIcs.FSTTCS.2022.15,
  author =	{Cornelissen, Arjan and Mande, Nikhil S. and Patro, Subhasree},
  title =	{{Improved Quantum Query Upper Bounds Based on Classical Decision Trees}},
  booktitle =	{42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)},
  pages =	{15:1--15:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-261-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{250},
  editor =	{Dawar, Anuj and Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2022.15},
  URN =		{urn:nbn:de:0030-drops-174071},
  doi =		{10.4230/LIPIcs.FSTTCS.2022.15},
  annote =	{Keywords: Quantum Query Complexity, Decision Trees, Decision Tree Rank}
}
Document
DOI: 10.4230/LIPIcs.CCC.2022.28
Influence in Completely Bounded Block-Multilinear Forms and Classical Simulation of Quantum Algorithms

Authors: Nikhil Bansal, Makrand Sinha, and Ronald de Wolf

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

Abstract
The Aaronson-Ambainis conjecture (Theory of Computing '14) says that every low-degree bounded polynomial on the Boolean hypercube has an influential variable. This conjecture, if true, would imply that the acceptance probability of every d-query quantum algorithm can be well-approximated almost everywhere (i.e., on almost all inputs) by a poly(d)-query classical algorithm. We prove a special case of the conjecture: in every completely bounded degree-d block-multilinear form with constant variance, there always exists a variable with influence at least 1/poly(d). In a certain sense, such polynomials characterize the acceptance probability of quantum query algorithms, as shown by Arunachalam, Briët and Palazuelos (SICOMP '19). As a corollary we obtain efficient classical almost-everywhere simulation for a particular class of quantum algorithms that includes for instance k-fold Forrelation. Our main technical result relies on connections to free probability theory.
Cite as

Nikhil Bansal, Makrand Sinha, and Ronald de Wolf. Influence in Completely Bounded Block-Multilinear Forms and Classical Simulation of Quantum Algorithms. In 37th Computational Complexity Conference (CCC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 234, pp. 28:1-28:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bansal_et_al:LIPIcs.CCC.2022.28,
  author =	{Bansal, Nikhil and Sinha, Makrand and de Wolf, Ronald},
  title =	{{Influence in Completely Bounded Block-Multilinear Forms and Classical Simulation of Quantum Algorithms}},
  booktitle =	{37th Computational Complexity Conference (CCC 2022)},
  pages =	{28:1--28:21},
  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.2022.28},
  URN =		{urn:nbn:de:0030-drops-165908},
  doi =		{10.4230/LIPIcs.CCC.2022.28},
  annote =	{Keywords: Aaronson-Ambainis conjecture, Quantum query complexity, Classical query complexity, Free probability, Completely bounded norm, Analysis of Boolean functions, Influence}
}
Document
DOI: 10.4230/LIPIcs.STACS.2022.20
Symmetry and Quantum Query-To-Communication Simulation

Authors: Sourav Chakraborty, Arkadev Chattopadhyay, Peter Høyer, Nikhil S. Mande, Manaswi Paraashar, and Ronald de Wolf

Published in: LIPIcs, Volume 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)

Abstract
Buhrman, Cleve and Wigderson (STOC'98) showed that for every Boolean function f : {-1,1}ⁿ → {-1,1} and G ∈ {AND₂, XOR₂}, the bounded-error quantum communication complexity of the composed function f∘G equals O(𝖰(f) log n), where 𝖰(f) denotes the bounded-error quantum query complexity of f. This is achieved by Alice running the optimal quantum query algorithm for f, using a round of O(log n) qubits of communication to implement each query. This is in contrast with the classical setting, where it is easy to show that 𝖱^{cc}(f∘G) ≤ 2𝖱(f), where 𝖱^{cc} and 𝖱 denote bounded-error communication and query complexity, respectively. Chakraborty et al. (CCC'20) exhibited a total function for which the log n overhead in the BCW simulation is required. This established the somewhat surprising fact that quantum reductions are in some cases inherently more expensive than classical reductions. We improve upon their result in several ways. - We show that the log n overhead is not required when f is symmetric (i.e., depends only on the Hamming weight of its input), generalizing a result of Aaronson and Ambainis for the Set-Disjointness function (Theory of Computing'05). Our upper bound assumes a shared entangled state, though for most symmetric functions the assumed number of entangled qubits is less than the communication and hence could be part of the communication. - In order to prove the above, we design an efficient distributed version of noisy amplitude amplification that allows us to prove the result when f is the OR function. This also provides a different, and arguably simpler, proof of Aaronson and Ambainis’s O(√n) communication upper bound for Set-Disjointness. - In view of our first result above, one may ask whether the log n overhead in the BCW simulation can be avoided even when f is transitive, which is a weaker notion of symmetry. We give a strong negative answer by showing that the log n overhead is still necessary for some transitive functions even when we allow the quantum communication protocol an error probability that can be arbitrarily close to 1/2 (this corresponds to the unbounded-error model of communication). - We also give, among other things, a general recipe to construct functions for which the log n overhead is required in the BCW simulation in the bounded-error communication model, even if the parties are allowed to share an arbitrary prior entangled state for free.
Cite as

Sourav Chakraborty, Arkadev Chattopadhyay, Peter Høyer, Nikhil S. Mande, Manaswi Paraashar, and Ronald de Wolf. Symmetry and Quantum Query-To-Communication Simulation. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 20:1-20:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{chakraborty_et_al:LIPIcs.STACS.2022.20,
  author =	{Chakraborty, Sourav and Chattopadhyay, Arkadev and H{\o}yer, Peter and Mande, Nikhil S. and Paraashar, Manaswi and de Wolf, Ronald},
  title =	{{Symmetry and Quantum Query-To-Communication Simulation}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{20:1--20:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-222-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{219},
  editor =	{Berenbrink, Petra and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022.20},
  URN =		{urn:nbn:de:0030-drops-158309},
  doi =		{10.4230/LIPIcs.STACS.2022.20},
  annote =	{Keywords: Classical and quantum communication complexity, query-to-communication-simulation, quantum computing}
}
Document
DOI: 10.4230/LIPIcs.STACS.2022.35
Improved Quantum Lower and Upper Bounds for Matrix Scaling

Authors: Sander Gribling and Harold Nieuwboer

Published in: LIPIcs, Volume 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)

Abstract
Matrix scaling is a simple to state, yet widely applicable linear-algebraic problem: the goal is to scale the rows and columns of a given non-negative matrix such that the rescaled matrix has prescribed row and column sums. Motivated by recent results on first-order quantum algorithms for matrix scaling, we investigate the possibilities for quantum speedups for classical second-order algorithms, which comprise the state-of-the-art in the classical setting. We first show that there can be essentially no quantum speedup in terms of the input size in the high-precision regime: any quantum algorithm that solves the matrix scaling problem for n × n matrices with at most m non-zero entries and with 𝓁₂-error ε = Θ~(1/m) must make Ω(m) queries to the matrix, even when the success probability is exponentially small in n. Additionally, we show that for ε ∈ [1/n,1/2], any quantum algorithm capable of producing ε/100-𝓁₁-approximations of the row-sum vector of a (dense) normalized matrix uses Ω(n/ε) queries, and that there exists a constant ε₀ > 0 for which this problem takes Ω(n^{1.5}) queries. To complement these results we give improved quantum algorithms in the low-precision regime: with quantum graph sparsification and amplitude estimation, a box-constrained Newton method can be sped up in the large-ε regime, and outperforms previous quantum algorithms. For entrywise-positive matrices, we find an ε-𝓁₁-scaling in time O~(n^{1.5}/ε²), whereas the best previously known bounds were O~(n²polylog(1/ε)) (classical) and O~(n^{1.5}/ε³) (quantum).
Cite as

Sander Gribling and Harold Nieuwboer. Improved Quantum Lower and Upper Bounds for Matrix Scaling. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 35:1-35:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{gribling_et_al:LIPIcs.STACS.2022.35,
  author =	{Gribling, Sander and Nieuwboer, Harold},
  title =	{{Improved Quantum Lower and Upper Bounds for Matrix Scaling}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{35:1--35:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-222-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{219},
  editor =	{Berenbrink, Petra and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022.35},
  URN =		{urn:nbn:de:0030-drops-158458},
  doi =		{10.4230/LIPIcs.STACS.2022.35},
  annote =	{Keywords: Matrix scaling, quantum algorithms, lower bounds}
}
Document
DOI: 10.4230/LIPIcs.STACS.2022.49
One-Way Communication Complexity and Non-Adaptive Decision Trees

Authors: Nikhil S. Mande, Swagato Sanyal, and Suhail Sherif

Published in: LIPIcs, Volume 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)

Abstract
We study the relationship between various one-way communication complexity measures of a composed function with the analogous decision tree complexity of the outer function. We consider two gadgets: the AND function on 2 inputs, and the Inner Product on a constant number of inputs. More generally, we show the following when the gadget is Inner Product on 2b input bits for all b ≥ 2, denoted IP. - If f is a total Boolean function that depends on all of its n input bits, then the bounded-error one-way quantum communication complexity of f∘IP equals Ω(n(b-1)). - If f is a partial Boolean function, then the deterministic one-way communication complexity of f∘IP is at least Ω(b ⋅ 𝖣_{dt}^ → (f)), where 𝖣_{dt}^ → (f) denotes non-adaptive decision tree complexity of f. To prove our quantum lower bound, we first show a lower bound on the VC-dimension of f∘IP. We then appeal to a result of Klauck [STOC'00], which immediately yields our quantum lower bound. Our deterministic lower bound relies on a combinatorial result independently proven by Ahlswede and Khachatrian [Adv. Appl. Math.'98], and Frankl and Tokushige [Comb.'99]. It is known due to a result of Montanaro and Osborne [arXiv'09] that the deterministic one-way communication complexity of f∘XOR equals the non-adaptive parity decision tree complexity of f. In contrast, we show the following when the inner gadget is the AND function on 2 input bits. - There exists a function for which even the quantum non-adaptive AND decision tree complexity of f is exponentially large in the deterministic one-way communication complexity of f∘AND. - However, for symmetric functions f, the non-adaptive AND decision tree complexity of f is at most quadratic in the (even two-way) communication complexity of f∘AND. In view of the first bullet, a lower bound on non-adaptive AND decision tree complexity of f does not lift to a lower bound on one-way communication complexity of f∘AND. The proof of the first bullet above uses the well-studied Odd-Max-Bit function. For the second bullet, we first observe a connection between the one-way communication complexity of f and the Möbius sparsity of f, and then give a lower bound on the Möbius sparsity of symmetric functions. An upper bound on the non-adaptive AND decision tree complexity of symmetric functions follows implicitly from prior work on combinatorial group testing; for the sake of completeness, we include a proof of this result. It is well known that the rank of the communication matrix of a function F is an upper bound on its deterministic one-way communication complexity. This bound is known to be tight for some F. However, in our final result we show that this is not the case when F = f∘AND. More precisely we show that for all f, the deterministic one-way communication complexity of F = f∘AND is at most (rank(M_{F}))(1 - Ω(1)), where M_{F} denotes the communication matrix of F.
Cite as

Nikhil S. Mande, Swagato Sanyal, and Suhail Sherif. One-Way Communication Complexity and Non-Adaptive Decision Trees. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 49:1-49:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{mande_et_al:LIPIcs.STACS.2022.49,
  author =	{Mande, Nikhil S. and Sanyal, Swagato and Sherif, Suhail},
  title =	{{One-Way Communication Complexity and Non-Adaptive Decision Trees}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{49:1--49:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-222-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{219},
  editor =	{Berenbrink, Petra and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022.49},
  URN =		{urn:nbn:de:0030-drops-158598},
  doi =		{10.4230/LIPIcs.STACS.2022.49},
  annote =	{Keywords: Decision trees, communication complexity, composed Boolean functions}
}
Document
DOI: 10.4230/LIPIcs.CCC.2021.28
Quantum Complexity of Minimum Cut

Authors: Simon Apers and Troy Lee

Published in: LIPIcs, Volume 200, 36th Computational Complexity Conference (CCC 2021)

Abstract
The minimum cut problem in an undirected and weighted graph G is to find the minimum total weight of a set of edges whose removal disconnects G. We completely characterize the quantum query and time complexity of the minimum cut problem in the adjacency matrix model. If G has n vertices and edge weights at least 1 and at most τ, we give a quantum algorithm to solve the minimum cut problem using Õ(n^{3/2}√{τ}) queries and time. Moreover, for every integer 1 ≤ τ ≤ n we give an example of a graph G with edge weights 1 and τ such that solving the minimum cut problem on G requires Ω(n^{3/2}√{τ}) queries to the adjacency matrix of G. These results contrast with the classical randomized case where Ω(n²) queries to the adjacency matrix are needed in the worst case even to decide if an unweighted graph is connected or not. In the adjacency array model, when G has m edges the classical randomized complexity of the minimum cut problem is ̃ Θ(m). We show that the quantum query and time complexity are Õ(√{mnτ}) and Õ(√{mnτ} + n^{3/2}), respectively, where again the edge weights are between 1 and τ. For dense graphs we give lower bounds on the quantum query complexity of Ω(n^{3/2}) for τ > 1 and Ω(τ n) for any 1 ≤ τ ≤ n. Our query algorithm uses a quantum algorithm for graph sparsification by Apers and de Wolf (FOCS 2020) and results on the structure of near-minimum cuts by Kawarabayashi and Thorup (STOC 2015) and Rubinstein, Schramm and Weinberg (ITCS 2018). Our time efficient implementation builds on Karger’s tree packing technique (STOC 1996).
Cite as

Simon Apers and Troy Lee. Quantum Complexity of Minimum Cut. In 36th Computational Complexity Conference (CCC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 200, pp. 28:1-28:33, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{apers_et_al:LIPIcs.CCC.2021.28,
  author =	{Apers, Simon and Lee, Troy},
  title =	{{Quantum Complexity of Minimum Cut}},
  booktitle =	{36th Computational Complexity Conference (CCC 2021)},
  pages =	{28:1--28:33},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-193-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{200},
  editor =	{Kabanets, Valentine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2021.28},
  URN =		{urn:nbn:de:0030-drops-143026},
  doi =		{10.4230/LIPIcs.CCC.2021.28},
  annote =	{Keywords: Quantum algorithms, quantum query complexity, minimum cut}
}
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