14 Search Results for "Marwaha, Kunal"

Document
DOI: 10.4230/LIPIcs.ITCS.2026.83
The Pure-State Consistency of Local Density Matrices Problem: In PSPACE and Complete for a Class Between QMA and QMA(2)

Authors: Jonas Kamminga and Dorian Rudolph

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

Abstract
In this work we investigate the computational complexity of the pure consistency of local density matrices (PureCLDM) and pure N-representability (Pure-N-Representability; analog of PureCLDM for bosonic or fermionic systems) problems. In these problems the input is a set of reduced density matrices and the task is to determine whether there exists a global pure state consistent with these reduced density matrices. While mixed CLDM, i.e. where the global state can be mixed, was proven to be QMA-complete by Broadbent and Grilo [JoC 2022], almost nothing was known about the complexity of the pure version. Before our work the best upper and lower bounds were QMA(2) and QMA. Our contribution to the understanding of these problems is twofold. Firstly, we define a pure state analogue of the complexity class QMA^+ of Aharanov and Regev [FOCS 2003], which we call PureSuperQMA. We prove that both pure-N-Representability and PureCLDM are complete for this new class. Along the way we supplement Broadbent and Grilo by proving hardness for 2-qubit reduced density matrices and showing that mixed N-Representability is QMA-complete. Secondly, we improve the upper bound on PureCLDM. Using methods from algebraic geometry, we prove that PureSuperQMA ⊆ PSPACE. Our methods, and the PSPACE upper bound, are also valid for PureCLDM with exponential or even perfect precision, hence precisePureCLDM is not preciseQMA(2) = NEXP-complete, unless PSPACE = NEXP. We view this as evidence for a negative answer to the longstanding open question whether PureCLDM is QMA(2)-complete. The techniques we develop for our PSPACE upper bound are quite general. We are able to use them for various applications: from proving PSPACE upper bounds on other quantum problems to giving an efficient parallel (NC) algorithm for (non-convex) quadratically constrained quadratic programs with few constraints.
Cite as

Jonas Kamminga and Dorian Rudolph. The Pure-State Consistency of Local Density Matrices Problem: In PSPACE and Complete for a Class Between QMA and QMA(2). In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 83:1-83:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{kamminga_et_al:LIPIcs.ITCS.2026.83,
  author =	{Kamminga, Jonas and Rudolph, Dorian},
  title =	{{The Pure-State Consistency of Local Density Matrices Problem: In PSPACE and Complete for a Class Between QMA and QMA(2)}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{83:1--83:23},
  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.2026.83},
  URN =		{urn:nbn:de:0030-drops-253701},
  doi =		{10.4230/LIPIcs.ITCS.2026.83},
  annote =	{Keywords: Quantum Complexity Theory, PSPACE, QMA(2), Consistency of Local Density Matrices, Polynomial Optimization}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.3
PDQMA = DQMA = NEXP: QMA with Hidden Variables and Non-Collapsing Measurements

Authors: Scott Aaronson, Sabee Grewal, Vishnu Iyer, Simon C. Marshall, and Ronak Ramachandran

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
We define and study a variant of QMA (Quantum Merlin Arthur) in which Arthur can make multiple non-collapsing measurements to Merlin’s witness state, in addition to ordinary collapsing measurements. By analogy to the class PDQP defined by Aaronson, Bouland, Fitzsimons, and Lee (2014), we call this class PDQMA. Our main result is that PDQMA = NEXP; this result builds on the PCP theorem and complements the result of Aaronson (2018) that PDQP/qpoly = ALL. While the result has little to do with quantum mechanics, we also show a more "quantum" result: namely, that QMA with the ability to inspect the entire history of a hidden variable is equal to NEXP, under mild assumptions on the hidden-variable theory. We also observe that a quantum computer, augmented with quantum advice and the ability to inspect the history of a hidden variable, can solve any decision problem in polynomial time.
Cite as

Scott Aaronson, Sabee Grewal, Vishnu Iyer, Simon C. Marshall, and Ronak Ramachandran. PDQMA = DQMA = NEXP: QMA with Hidden Variables and Non-Collapsing Measurements. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 3:1-3:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{aaronson_et_al:LIPIcs.FSTTCS.2025.3,
  author =	{Aaronson, Scott and Grewal, Sabee and Iyer, Vishnu and Marshall, Simon C. and Ramachandran, Ronak},
  title =	{{PDQMA = DQMA = NEXP: QMA with Hidden Variables and Non-Collapsing Measurements}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{3:1--3:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.3},
  URN =		{urn:nbn:de:0030-drops-250828},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.3},
  annote =	{Keywords: quantum Merlin-Arthur, non-collapsing measurements, hidden-variable theories}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.101
Improved Algorithms for Quantum MaxCut via Partially Entangled Matchings

Authors: Anuj Apte, Eunou Lee, Kunal Marwaha, Ojas Parekh, and James Sud

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

Abstract
We introduce a 0.611-approximation algorithm for Quantum MaxCut and a (1+√5)/4 ≈ 0.809-approximation algorithm for the EPR Hamiltonian of [King, 2023]. A novel ingredient in both of these algorithms is to partially entangle pairs of qubits associated to edges in a matching, while preserving the direction of their single-qubit Bloch vectors. This allows us to interpolate between product states and matching-based states with a tunable parameter.
Cite as

Anuj Apte, Eunou Lee, Kunal Marwaha, Ojas Parekh, and James Sud. Improved Algorithms for Quantum MaxCut via Partially Entangled Matchings. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 101:1-101:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{apte_et_al:LIPIcs.ESA.2025.101,
  author =	{Apte, Anuj and Lee, Eunou and Marwaha, Kunal and Parekh, Ojas and Sud, James},
  title =	{{Improved Algorithms for Quantum MaxCut via Partially Entangled Matchings}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{101:1--101:14},
  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.2025.101},
  URN =		{urn:nbn:de:0030-drops-245705},
  doi =		{10.4230/LIPIcs.ESA.2025.101},
  annote =	{Keywords: Quantum computing, Quantum MaxCut, Maximum matching}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.24
Improved Approximation Algorithms for the EPR Hamiltonian

Authors: Nathan Ju and Ansh Nagda

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
The EPR Hamiltonian is a family of 2-local quantum Hamiltonians introduced by King [King, 2023]. We introduce a polynomial time (1+√5)/4≈0.809-approximation algorithm for the problem of computing the ground energy of the EPR Hamiltonian, improving upon the previous state of the art of 0.72 [Jorquera et al., 2024].
Cite as

Nathan Ju and Ansh Nagda. Improved Approximation Algorithms for the EPR Hamiltonian. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 24:1-24:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{ju_et_al:LIPIcs.APPROX/RANDOM.2025.24,
  author =	{Ju, Nathan and Nagda, Ansh},
  title =	{{Improved Approximation Algorithms for the EPR Hamiltonian}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{24:1--24:9},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.24},
  URN =		{urn:nbn:de:0030-drops-243909},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.24},
  annote =	{Keywords: Approximation Algorithms, Quantum Local Hamiltonian}
}
Document
DOI: 10.4230/LIPIcs.TQC.2025.1
Quantum Search with In-Place Queries

Authors: Blake Holman, Ronak Ramachandran, and Justin Yirka

Published in: LIPIcs, Volume 350, 20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025)

Abstract
Quantum query complexity is typically characterized in terms of xor queries |x,y⟩ ↦ |x,y⊕ f(x)⟩ or phase queries, which ensure that even queries to non-invertible functions are unitary. When querying a permutation, another natural model is unitary: in-place queries |x⟩↦ |f(x)⟩. Some problems are known to require exponentially fewer in-place queries than xor queries, but no separation has been shown in the opposite direction. A candidate for such a separation was the problem of inverting a permutation over N elements. This task, equivalent to unstructured search in the context of permutations, is solvable with O(√N) xor queries but was conjectured to require Ω(N) in-place queries. We refute this conjecture by designing a quantum algorithm for Permutation Inversion using O(√N) in-place queries. Our algorithm achieves the same speedup as Grover’s algorithm despite the inability to efficiently uncompute queries or perform straightforward oracle-controlled reflections. Nonetheless, we show that there are indeed problems which require fewer xor queries than in-place queries. We introduce a subspace-conversion problem called Function Erasure that requires 1 xor query and Θ(√N) in-place queries. Then, we build on a recent extension of the quantum adversary method to characterize exact conditions for a decision problem to exhibit such a separation, and we propose a candidate problem.
Cite as

Blake Holman, Ronak Ramachandran, and Justin Yirka. Quantum Search with In-Place Queries. In 20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 350, pp. 1:1-1:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{holman_et_al:LIPIcs.TQC.2025.1,
  author =	{Holman, Blake and Ramachandran, Ronak and Yirka, Justin},
  title =	{{Quantum Search with In-Place Queries}},
  booktitle =	{20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025)},
  pages =	{1:1--1:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-392-8},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{350},
  editor =	{Fefferman, Bill},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2025.1},
  URN =		{urn:nbn:de:0030-drops-240502},
  doi =		{10.4230/LIPIcs.TQC.2025.1},
  annote =	{Keywords: Quantum algorithms, query complexity, quantum complexity theory, quantum search, Grover’s algorithm, permutation inversion}
}
Document
DOI: 10.4230/LIPIcs.CCC.2025.12
New Lower-Bounds for Quantum Computation with Non-Collapsing Measurements

Authors: David Miloschewsky and Supartha Podder

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

Abstract
Aaronson, Bouland, Fitzsimons and Lee [Scott Aaronson et al., 2014] introduced the complexity class PDQP (which was original labeled naCQP), an alteration of BQP enhanced with the ability to obtain non-collapsing measurements, samples of quantum states without collapsing them. Although SZK ⊆ PDQP, it still requires Ω(N^(1/4)) queries to solve unstructured search. We formulate an alternative equivalent definition of PDQP, which we use to prove the positive weighted adversary lower-bounding method, establishing multiple tighter bounds and a trade-off between queries and non-collapsing measurements. We utilize the technique in order to analyze the query complexity of the well-studied majority and element distinctness problems. Additionally, we prove a tight Θ(N^(1/3)) bound on search. Furthermore, we use the lower-bound to explore PDQP under query restrictions, finding that when combined with non-adaptive queries, we limit the speed-up in several cases.
Cite as

David Miloschewsky and Supartha Podder. New Lower-Bounds for Quantum Computation with Non-Collapsing Measurements. In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 12:1-12:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{miloschewsky_et_al:LIPIcs.CCC.2025.12,
  author =	{Miloschewsky, David and Podder, Supartha},
  title =	{{New Lower-Bounds for Quantum Computation with Non-Collapsing Measurements}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{12:1--12:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-379-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{339},
  editor =	{Srinivasan, Srikanth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2025.12},
  URN =		{urn:nbn:de:0030-drops-237067},
  doi =		{10.4230/LIPIcs.CCC.2025.12},
  annote =	{Keywords: Non-collapsing measurements, Quantum lower-bounds, Quantum adversary method}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.61
Hardness of Sampling for the Anti-Ferromagnetic Ising Model on Random Graphs

Authors: Neng Huang, Will Perkins, and Aaron Potechin

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

Abstract
We prove a hardness of sampling result for the anti-ferromagnetic Ising model on random graphs of average degree d for large constant d, proving that when the normalized inverse temperature satisfies β > 1 (asymptotically corresponding to the condensation threshold), then w.h.p. over the random graph there is no stable sampling algorithm that can output a sample close in W₂ distance to the Gibbs measure. The results also apply to a fixed-magnetization version of the model, showing that there are no stable sampling algorithms for low but positive temperature max and min bisection distributions. These results show a gap in the tractability of search and sampling problems: while there are efficient algorithms to find near optimizers, stable sampling algorithms cannot access the Gibbs distribution concentrated on such solutions. Our techniques involve extensions of the interpolation technique relating behavior of the mean field Sherrington-Kirkpatrick model to behavior of Ising models on random graphs of average degree d for large d. While previous interpolation arguments compared the free energies of the two models, our argument compares the average energies and average overlaps in the two models.
Cite as

Neng Huang, Will Perkins, and Aaron Potechin. Hardness of Sampling for the Anti-Ferromagnetic Ising Model on Random Graphs. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 61:1-61:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{huang_et_al:LIPIcs.ITCS.2025.61,
  author =	{Huang, Neng and Perkins, Will and Potechin, Aaron},
  title =	{{Hardness of Sampling for the Anti-Ferromagnetic Ising Model on Random Graphs}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{61:1--61:23},
  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.2025.61},
  URN =		{urn:nbn:de:0030-drops-226899},
  doi =		{10.4230/LIPIcs.ITCS.2025.61},
  annote =	{Keywords: Random graph, spin glass, sampling algorithm}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2024.9
Quantum Merlin-Arthur and Proofs Without Relative Phase

Authors: Roozbeh Bassirian, Bill Fefferman, and Kunal Marwaha

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

Abstract
We study a variant of QMA where quantum proofs have no relative phase (i.e. non-negative amplitudes, up to a global phase). If only completeness is modified, this class is equal to QMA [Grilo et al., 2014]; but if both completeness and soundness are modified, the class (named QMA+ by Jeronimo and Wu [Jeronimo and Wu, 2023]) can be much more powerful. We show that QMA+ with some constant gap is equal to NEXP, yet QMA+ with some other constant gap is equal to QMA. One interpretation is that Merlin’s ability to "deceive" originates from relative phase at least as much as from entanglement, since QMA(2) ⊆ NEXP.
Cite as

Roozbeh Bassirian, Bill Fefferman, and Kunal Marwaha. Quantum Merlin-Arthur and Proofs Without Relative Phase. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 9:1-9:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{bassirian_et_al:LIPIcs.ITCS.2024.9,
  author =	{Bassirian, Roozbeh and Fefferman, Bill and Marwaha, Kunal},
  title =	{{Quantum Merlin-Arthur and Proofs Without Relative Phase}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{9:1--9:19},
  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.2024.9},
  URN =		{urn:nbn:de:0030-drops-195370},
  doi =		{10.4230/LIPIcs.ITCS.2024.9},
  annote =	{Keywords: quantum complexity, QMA(2), PCPs}
}
Document
DOI: 10.4230/LIPIcs.TQC.2023.11
On the Power of Nonstandard Quantum Oracles

Authors: Roozbeh Bassirian, Bill Fefferman, and Kunal Marwaha

Published in: LIPIcs, Volume 266, 18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023)

Abstract
We study how the choices made when designing an oracle affect the complexity of quantum property testing problems defined relative to this oracle. We encode a regular graph of even degree as an invertible function f, and present f in different oracle models. We first give a one-query QMA protocol to test if a graph encoded in f has a small disconnected subset. We then use representation theory to show that no classical witness can help a quantum verifier efficiently decide this problem relative to an in-place oracle. Perhaps surprisingly, a simple modification to the standard oracle prevents a quantum verifier from efficiently deciding this problem, even with access to an unbounded witness.
Cite as

Roozbeh Bassirian, Bill Fefferman, and Kunal Marwaha. On the Power of Nonstandard Quantum Oracles. In 18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 266, pp. 11:1-11:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{bassirian_et_al:LIPIcs.TQC.2023.11,
  author =	{Bassirian, Roozbeh and Fefferman, Bill and Marwaha, Kunal},
  title =	{{On the Power of Nonstandard Quantum Oracles}},
  booktitle =	{18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023)},
  pages =	{11:1--11:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-283-9},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{266},
  editor =	{Fawzi, Omar and Walter, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2023.11},
  URN =		{urn:nbn:de:0030-drops-183215},
  doi =		{10.4230/LIPIcs.TQC.2023.11},
  annote =	{Keywords: quantum complexity, QCMA, expander graphs, representation theory}
}
Document
DOI: 10.4230/LIPIcs.CCC.2023.22
A Distribution Testing Oracle Separating QMA and QCMA

Authors: Anand Natarajan and Chinmay Nirkhe

Published in: LIPIcs, Volume 264, 38th Computational Complexity Conference (CCC 2023)

Abstract
It is a long-standing open question in quantum complexity theory whether the definition of non-deterministic quantum computation requires quantum witnesses (QMA) or if classical witnesses suffice (QCMA). We make progress on this question by constructing a randomized classical oracle separating the respective computational complexity classes. Previous separations [Aaronson and Kuperberg, 2007; Bill Fefferman and Shelby Kimmel, 2018] required a quantum unitary oracle. The separating problem is deciding whether a distribution supported on regular un-directed graphs either consists of multiple connected components (yes instances) or consists of one expanding connected component (no instances) where the graph is given in an adjacency-list format by the oracle. Therefore, the oracle is a distribution over n-bit boolean functions.
Cite as

Anand Natarajan and Chinmay Nirkhe. A Distribution Testing Oracle Separating QMA and QCMA. In 38th Computational Complexity Conference (CCC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 264, pp. 22:1-22:27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{natarajan_et_al:LIPIcs.CCC.2023.22,
  author =	{Natarajan, Anand and Nirkhe, Chinmay},
  title =	{{A Distribution Testing Oracle Separating QMA and QCMA}},
  booktitle =	{38th Computational Complexity Conference (CCC 2023)},
  pages =	{22:1--22:27},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-282-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{264},
  editor =	{Ta-Shma, Amnon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2023.22},
  URN =		{urn:nbn:de:0030-drops-182928},
  doi =		{10.4230/LIPIcs.CCC.2023.22},
  annote =	{Keywords: quantum non-determinism, complexity theory}
}
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)

Copy BibTex To Clipboard

@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
DOI: 10.4230/LIPIcs.ITCS.2023.96
Unitary Property Testing Lower Bounds by Polynomials

Authors: Adrian She and Henry Yuen

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

Abstract
We study unitary property testing, where a quantum algorithm is given query access to a black-box unitary and has to decide whether it satisfies some property. In addition to containing the standard quantum query complexity model (where the unitary encodes a binary string) as a special case, this model contains "inherently quantum" problems that have no classical analogue. Characterizing the query complexity of these problems requires new algorithmic techniques and lower bound methods. Our main contribution is a generalized polynomial method for unitary property testing problems. By leveraging connections with invariant theory, we apply this method to obtain lower bounds on problems such as determining recurrence times of unitaries, approximating the dimension of a marked subspace, and approximating the entanglement entropy of a marked state. We also present a unitary property testing-based approach towards an oracle separation between QMA and QMA(2), a long standing question in quantum complexity theory.
Cite as

Adrian She and Henry Yuen. Unitary Property Testing Lower Bounds by Polynomials. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 96:1-96:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{she_et_al:LIPIcs.ITCS.2023.96,
  author =	{She, Adrian and Yuen, Henry},
  title =	{{Unitary Property Testing Lower Bounds by Polynomials}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{96:1--96:17},
  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.2023.96},
  URN =		{urn:nbn:de:0030-drops-175995},
  doi =		{10.4230/LIPIcs.ITCS.2023.96},
  annote =	{Keywords: Quantum query complexity, polynomial method, unitary property testing, quantum proofs, invariant theory, quantum recurrence time, entanglement entropy, BQP, QMA, QMA(2)}
}
Document
DOI: 10.4230/LIPIcs.TQC.2022.7
The Quantum Approximate Optimization Algorithm at High Depth for MaxCut on Large-Girth Regular Graphs and the Sherrington-Kirkpatrick Model

Authors: Joao Basso, Edward Farhi, Kunal Marwaha, Benjamin Villalonga, and Leo Zhou

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

Abstract
The Quantum Approximate Optimization Algorithm (QAOA) finds approximate solutions to combinatorial optimization problems. Its performance monotonically improves with its depth p. We apply the QAOA to MaxCut on large-girth D-regular graphs. We give an iterative formula to evaluate performance for any D at any depth p. Looking at random D-regular graphs, at optimal parameters and as D goes to infinity, we find that the p = 11 QAOA beats all classical algorithms (known to the authors) that are free of unproven conjectures. While the iterative formula for these D-regular graphs is derived by looking at a single tree subgraph, we prove that it also gives the ensemble-averaged performance of the QAOA on the Sherrington-Kirkpatrick (SK) model defined on the complete graph. We also generalize our formula to Max-q-XORSAT on large-girth regular hypergraphs. Our iteration is a compact procedure, but its computational complexity grows as O(p² 4^p). This iteration is more efficient than the previous procedure for analyzing QAOA performance on the SK model, and we are able to numerically go to p = 20. Encouraged by our findings, we make the optimistic conjecture that the QAOA, as p goes to infinity, will achieve the Parisi value. We analyze the performance of the quantum algorithm, but one needs to run it on a quantum computer to produce a string with the guaranteed performance.
Cite as

Joao Basso, Edward Farhi, Kunal Marwaha, Benjamin Villalonga, and Leo Zhou. The Quantum Approximate Optimization Algorithm at High Depth for MaxCut on Large-Girth Regular Graphs and the Sherrington-Kirkpatrick Model. In 17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 232, pp. 7:1-7:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{basso_et_al:LIPIcs.TQC.2022.7,
  author =	{Basso, Joao and Farhi, Edward and Marwaha, Kunal and Villalonga, Benjamin and Zhou, Leo},
  title =	{{The Quantum Approximate Optimization Algorithm at High Depth for MaxCut on Large-Girth Regular Graphs and the Sherrington-Kirkpatrick Model}},
  booktitle =	{17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022)},
  pages =	{7:1--7:21},
  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.2022.7},
  URN =		{urn:nbn:de:0030-drops-165144},
  doi =		{10.4230/LIPIcs.TQC.2022.7},
  annote =	{Keywords: Quantum algorithm, Max-Cut, spin glass, approximation algorithm}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2022.14
Classical Algorithms and Quantum Limitations for Maximum Cut on High-Girth Graphs

Authors: Boaz Barak and Kunal Marwaha

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

Abstract
We study the performance of local quantum algorithms such as the Quantum Approximate Optimization Algorithm (QAOA) for the maximum cut problem, and their relationship to that of randomized classical algorithms. 1) We prove that every (quantum or classical) one-local algorithm (where the value of a vertex only depends on its and its neighbors' state) achieves on D-regular graphs of girth > 5 a maximum cut of at most 1/2 + C/√D for C = 1/√2 ≈ 0.7071. This is the first such result showing that one-local algorithms achieve a value that is bounded away from the true optimum for random graphs, which is 1/2 + P_*/√D + o(1/√D) for P_* ≈ 0.7632 [Dembo et al., 2017]. 2) We show that there is a classical k-local algorithm that achieves a value of 1/2 + C/√D - O(1/√k) for D-regular graphs of girth > 2k+1, where C = 2/π ≈ 0.6366. This is an algorithmic version of the existential bound of [Lyons, 2017] and is related to the algorithm of [Aizenman et al., 1987] (ALR) for the Sherrington-Kirkpatrick model. This bound is better than that achieved by the one-local and two-local versions of QAOA on high-girth graphs [M. B. Hastings, 2019; Marwaha, 2021]. 3) Through computational experiments, we give evidence that the ALR algorithm achieves better performance than constant-locality QAOA for random D-regular graphs, as well as other natural instances, including graphs that do have short cycles. While our theoretical bounds require the locality and girth assumptions, our experimental work suggests that it could be possible to extend them beyond these constraints. This points at the tantalizing possibility that O(1)-local quantum maximum-cut algorithms might be pointwise dominated by polynomial-time classical algorithms, in the sense that there is a classical algorithm outputting cuts of equal or better quality on every possible instance. This is in contrast to the evidence that polynomial-time algorithms cannot simulate the probability distributions induced by local quantum algorithms.
Cite as

Boaz Barak and Kunal Marwaha. Classical Algorithms and Quantum Limitations for Maximum Cut on High-Girth Graphs. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 14:1-14:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{barak_et_al:LIPIcs.ITCS.2022.14,
  author =	{Barak, Boaz and Marwaha, Kunal},
  title =	{{Classical Algorithms and Quantum Limitations for Maximum Cut on High-Girth Graphs}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{14:1--14:21},
  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.2022.14},
  URN =		{urn:nbn:de:0030-drops-156105},
  doi =		{10.4230/LIPIcs.ITCS.2022.14},
  annote =	{Keywords: approximation algorithms, QAOA, maximum cut, local distributions}
}
  • Refine by Type
  • 14 Document/PDF
  • 7 Document/HTML

  • Refine by Publication Year
  • 1 2026
  • 6 2025
  • 1 2024
  • 4 2023
  • 2 2022

  • Refine by Author
  • 6 Marwaha, Kunal
  • 2 Bassirian, Roozbeh
  • 2 Fefferman, Bill
  • 2 Ramachandran, Ronak
  • 1 Aaronson, Scott
  • Show More...

  • Refine by Series/Journal
  • 14 LIPIcs

  • Refine by Classification
  • 5 Theory of computation → Quantum complexity theory
  • 4 Theory of computation → Approximation algorithms analysis
  • 3 Theory of computation → Quantum computation theory
  • 2 Mathematics of computing → Probability and statistics
  • 2 Theory of computation → Quantum query complexity
  • Show More...

  • Refine by Keyword
  • 3 QMA(2)
  • 3 spin glass
  • 2 quantum complexity
  • 1 Approximation Algorithms
  • 1 BQP
  • 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
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact