30 Search Results for "Yuen, Henry"

Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2024.54
Parallel Repetition of k-Player Projection Games

Authors: Amey Bhangale, Mark Braverman, Subhash Khot, Yang P. Liu, and Dor Minzer

Published in: LIPIcs, Volume 317, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)

Abstract
We study parallel repetition of k-player games where the constraints satisfy the projection property. We prove exponential decay in the value of a parallel repetition of projection games with a value less than 1.
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Amey Bhangale, Mark Braverman, Subhash Khot, Yang P. Liu, and Dor Minzer. Parallel Repetition of k-Player Projection Games. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 54:1-54:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bhangale_et_al:LIPIcs.APPROX/RANDOM.2024.54,
  author =	{Bhangale, Amey and Braverman, Mark and Khot, Subhash and Liu, Yang P. and Minzer, Dor},
  title =	{{Parallel Repetition of k-Player Projection Games}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{54:1--54:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-348-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{317},
  editor =	{Kumar, Amit and Ron-Zewi, Noga},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2024.54},
  URN =		{urn:nbn:de:0030-drops-210475},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.54},
  annote =	{Keywords: Parallel Repetition, Multiplayer games, Projection games}
}
Document
DOI: 10.4230/LIPIcs.TQC.2024.4
One-Wayness in Quantum Cryptography

Authors: Tomoyuki Morimae and Takashi Yamakawa

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

Abstract
The existence of one-way functions is one of the most fundamental assumptions in classical cryptography. In the quantum world, on the other hand, there are evidences that some cryptographic primitives can exist even if one-way functions do not exist [Kretschmer, TQC 2021; Morimae and Yamakawa, CRYPTO 2022; Ananth, Qian, and Yuen, CRYPTO 2022]. We therefore have the following important open problem in quantum cryptography: What is the most fundamental assumption in quantum cryptography? In this direction, [Brakerski, Canetti, and Qian, ITCS 2023] recently defined a notion called EFI pairs, which are pairs of efficiently generatable states that are statistically distinguishable but computationally indistinguishable, and showed its equivalence with some cryptographic primitives including commitments, oblivious transfer, and general multi-party computations. However, their work focuses on decision-type primitives and does not cover search-type primitives like quantum money and digital signatures. In this paper, we study properties of one-way state generators (OWSGs), which are a quantum analogue of one-way functions proposed by Morimae and Yamakawa. We first revisit the definition of OWSGs and generalize it by allowing mixed output states. Then we show the following results. 1) We define a weaker version of OWSGs, which we call weak OWSGs, and show that they are equivalent to OWSGs. It is a quantum analogue of the amplification theorem for classical weak one-way functions. 2) (Bounded-time-secure) quantum digital signatures with quantum public keys are equivalent to OWSGs. 3) Private-key quantum money schemes (with pure money states) imply OWSGs. 4) Quantum pseudo one-time pad schemes imply both OWSGs and EFI pairs. For EFI pairs, single-copy security suffices. 5) We introduce an incomparable variant of OWSGs, which we call secretly-verifiable and statistically-invertible OWSGs, and show that they are equivalent to EFI pairs.
Cite as

Tomoyuki Morimae and Takashi Yamakawa. One-Wayness in Quantum Cryptography. In 19th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 310, pp. 4:1-4:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{morimae_et_al:LIPIcs.TQC.2024.4,
  author =	{Morimae, Tomoyuki and Yamakawa, Takashi},
  title =	{{One-Wayness in Quantum Cryptography}},
  booktitle =	{19th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2024)},
  pages =	{4:1--4:21},
  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.2024.4},
  URN =		{urn:nbn:de:0030-drops-206744},
  doi =		{10.4230/LIPIcs.TQC.2024.4},
  annote =	{Keywords: Quantum Cryptography}
}
Document
DOI: 10.4230/LIPIcs.TQC.2024.12
Quantum Delegation with an Off-The-Shelf Device

Authors: Anne Broadbent, Arthur Mehta, and Yuming Zhao

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

Abstract
Given that reliable cloud quantum computers are becoming closer to reality, the concept of delegation of quantum computations and its verifiability is of central interest. Many models have been proposed, each with specific strengths and weaknesses. Here, we put forth a new model where the client trusts only its classical processing, makes no computational assumptions, and interacts with a quantum server in a single round. In addition, during a set-up phase, the client specifies the size n of the computation and receives an untrusted, off-the-shelf (OTS) quantum device that is used to report the outcome of a single measurement. We show how to delegate polynomial-time quantum computations in the OTS model. This also yields an interactive proof system for all of QMA, which, furthermore, we show can be accomplished in statistical zero-knowledge. This provides the first relativistic (one-round), two-prover zero-knowledge proof system for QMA. As a proof approach, we provide a new self-test for n EPR pairs using only constant-sized Pauli measurements, and show how it provides a new avenue for the use of simulatable codes for local Hamiltonian verification. Along the way, we also provide an enhanced version of a well-known stability result due to Gowers and Hatami and show how it completes a common argument used in self-testing.
Cite as

Anne Broadbent, Arthur Mehta, and Yuming Zhao. Quantum Delegation with an Off-The-Shelf Device. In 19th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 310, pp. 12:1-12:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{broadbent_et_al:LIPIcs.TQC.2024.12,
  author =	{Broadbent, Anne and Mehta, Arthur and Zhao, Yuming},
  title =	{{Quantum Delegation with an Off-The-Shelf Device}},
  booktitle =	{19th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2024)},
  pages =	{12:1--12:23},
  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.2024.12},
  URN =		{urn:nbn:de:0030-drops-206824},
  doi =		{10.4230/LIPIcs.TQC.2024.12},
  annote =	{Keywords: Delegated quantum computation, zero-knowledge proofs, device-independence}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.7
Quantum Polynomial Hierarchies: Karp-Lipton, Error Reduction, and Lower Bounds

Authors: Avantika Agarwal, Sevag Gharibian, Venkata Koppula, and Dorian Rudolph

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
The Polynomial-Time Hierarchy (PH) is a staple of classical complexity theory, with applications spanning randomized computation to circuit lower bounds to "quantum advantage" analyses for near-term quantum computers. Quantumly, however, despite the fact that at least four definitions of quantum PH exist, it has been challenging to prove analogues for these of even basic facts from PH. This work studies three quantum-verifier based generalizations of PH, two of which are from [Gharibian, Santha, Sikora, Sundaram, Yirka, 2022] and use classical strings (QCPH) and quantum mixed states (QPH) as proofs, and one of which is new to this work, utilizing quantum pure states (QPHpure) as proofs. We first resolve several open problems from [GSSSY22], including a collapse theorem and a Karp-Lipton theorem for QCPH. Then, for our new class QPHpure, we show one-sided error reduction QPHpure, as well as the first bounds relating these quantum variants of PH, namely QCPH ⊆ QPHpure ⊆ EXP^PP.
Cite as

Avantika Agarwal, Sevag Gharibian, Venkata Koppula, and Dorian Rudolph. Quantum Polynomial Hierarchies: Karp-Lipton, Error Reduction, and Lower Bounds. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 7:1-7:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{agarwal_et_al:LIPIcs.MFCS.2024.7,
  author =	{Agarwal, Avantika and Gharibian, Sevag and Koppula, Venkata and Rudolph, Dorian},
  title =	{{Quantum Polynomial Hierarchies: Karp-Lipton, Error Reduction, and Lower Bounds}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{7:1--7:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.7},
  URN =		{urn:nbn:de:0030-drops-205632},
  doi =		{10.4230/LIPIcs.MFCS.2024.7},
  annote =	{Keywords: Quantum complexity, polynomial hierarchy}
}
Document
DOI: 10.4230/LIPIcs.CCC.2024.21
Public-Key Pseudoentanglement and the Hardness of Learning Ground State Entanglement Structure

Authors: Adam Bouland, Bill Fefferman, Soumik Ghosh, Tony Metger, Umesh Vazirani, Chenyi Zhang, and Zixin Zhou

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

Abstract
Given a local Hamiltonian, how difficult is it to determine the entanglement structure of its ground state? We show that this problem is computationally intractable even if one is only trying to decide if the ground state is volume-law vs near area-law entangled. We prove this by constructing strong forms of pseudoentanglement in a public-key setting, where the circuits used to prepare the states are public knowledge. In particular, we construct two families of quantum circuits which produce volume-law vs near area-law entangled states, but nonetheless the classical descriptions of the circuits are indistinguishable under the Learning with Errors (LWE) assumption. Indistinguishability of the circuits then allows us to translate our construction to Hamiltonians. Our work opens new directions in Hamiltonian complexity, for example whether it is difficult to learn certain phases of matter.
Cite as

Adam Bouland, Bill Fefferman, Soumik Ghosh, Tony Metger, Umesh Vazirani, Chenyi Zhang, and Zixin Zhou. Public-Key Pseudoentanglement and the Hardness of Learning Ground State Entanglement Structure. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 21:1-21:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bouland_et_al:LIPIcs.CCC.2024.21,
  author =	{Bouland, Adam and Fefferman, Bill and Ghosh, Soumik and Metger, Tony and Vazirani, Umesh and Zhang, Chenyi and Zhou, Zixin},
  title =	{{Public-Key Pseudoentanglement and the Hardness of Learning Ground State Entanglement Structure}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{21:1--21:23},
  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.2024.21},
  URN =		{urn:nbn:de:0030-drops-204175},
  doi =		{10.4230/LIPIcs.CCC.2024.21},
  annote =	{Keywords: Quantum computing, Quantum complexity theory, entanglement}
}
Document
DOI: 10.4230/LIPIcs.CCC.2024.26
Dimension Independent Disentanglers from Unentanglement and Applications

Authors: Fernando Granha Jeronimo and Pei Wu

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

Abstract
Quantum entanglement, a distinctive form of quantum correlation, has become a key enabling ingredient in diverse applications in quantum computation, complexity, cryptography, etc. However, the presence of unwanted adversarial entanglement also poses challenges and even prevents the correct behaviour of many protocols and applications. In this paper, we explore methods to "break" the quantum correlations. Specifically, we construct a dimension-independent k-partite disentangler (like) channel from bipartite unentangled input. In particular, we show: For every d,𝓁 ≥ k ∈ ℕ^+, there is an efficient channel Λ : ℂ^{d𝓁} ⊗ ℂ^{d𝓁} → ℂ^{dk} such that for every bipartite separable density operator ρ₁⊗ ρ₂, the output Λ(ρ₁⊗ρ₂) is close to a k-partite separable state. Concretely, for some distribution μ on states from C^d, ║ Λ(ρ₁⊗ρ₂) - ∫ |ψ⟩⟨ψ|^{⊗k} dμ(ψ) ║₁ ≤ Õ((k³/𝓁)^{1/4}). Moreover, Λ(|ψ⟩⟨ψ|^{⊗𝓁} ⊗ |ψ⟩⟨ψ|^{⊗𝓁}) = |ψ⟩⟨ψ|^{⊗k}. Without the bipartite unentanglement assumption, the above bound is conjectured to be impossible and would imply QMA(2) = QMA. Leveraging multipartite unentanglement ensured by our disentanglers, we achieve the following: (i) a new proof that QMA(2) admits arbitrary gap amplification; (ii) a variant of the swap test and product test with improved soundness, addressing a major limitation of their original versions. More importantly, we demonstrate that unentangled quantum proofs of almost general real amplitudes capture NEXP, thereby greatly relaxing the non-negative amplitudes assumption in the recent work of QMA^+(2) = NEXP [Jeronimo and Wu, STOC 2023]. Specifically, our findings show that to capture NEXP, it suffices to have unentangled proofs of the form |ψ⟩ = √a |ψ_{+}⟩ + √{1-a} |ψ_{-}⟩ where |ψ_{+}⟩ has non-negative amplitudes, |ψ_{-}⟩ only has negative amplitudes and |a-(1-a)| ≥ 1/poly(n) with a ∈ [0,1]. Additionally, we present a protocol achieving an almost largest possible completeness-soundness gap before obtaining QMA^ℝ(k) = NEXP, namely, a 1/poly(n) additive improvement to the gap results in this equality.
Cite as

Fernando Granha Jeronimo and Pei Wu. Dimension Independent Disentanglers from Unentanglement and Applications. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 26:1-26:28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{jeronimo_et_al:LIPIcs.CCC.2024.26,
  author =	{Jeronimo, Fernando Granha and Wu, Pei},
  title =	{{Dimension Independent Disentanglers from Unentanglement and Applications}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{26:1--26:28},
  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.2024.26},
  URN =		{urn:nbn:de:0030-drops-204228},
  doi =		{10.4230/LIPIcs.CCC.2024.26},
  annote =	{Keywords: QMA(2), disentangler, quantum proofs}
}
Document
DOI: 10.4230/LIPIcs.CCC.2024.30
The Computational Advantage of MIP^∗ Vanishes in the Presence of Noise

Authors: Yangjing Dong, Honghao Fu, Anand Natarajan, Minglong Qin, Haochen Xu, and Penghui Yao

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

Abstract
The class MIP^* of quantum multiprover interactive proof systems with entanglement is much more powerful than its classical counterpart MIP [Babai et al., 1991; Zhengfeng Ji et al., 2020; Zhengfeng Ji et al., 2020]: while MIP = NEXP, the quantum class MIP^* is equal to RE, a class including the halting problem. This is because the provers in MIP^* can share unbounded quantum entanglement. However, recent works [Qin and Yao, 2021; Qin and Yao, 2023] have shown that this advantage is significantly reduced if the provers' shared state contains noise. This paper attempts to exactly characterize the effect of noise on the computational power of quantum multiprover interactive proof systems. We investigate the quantum two-prover one-round interactive system MIP^*[poly,O(1)], where the verifier sends polynomially many bits to the provers and the provers send back constantly many bits. We show noise completely destroys the computational advantage given by shared entanglement in this model. Specifically, we show that if the provers are allowed to share arbitrarily many EPR states, where each EPR state is affected by an arbitrarily small constant amount of noise, the resulting complexity class is equivalent to NEXP = MIP. This improves significantly on the previous best-known bound of NEEEXP (nondeterministic triply exponential time) [Qin and Yao, 2021]. We also show that this collapse in power is due to the noise, rather than the O(1) answer size, by showing that allowing for noiseless EPR states gives the class the full power of RE = MIP^*[poly, poly]. Along the way, we develop two technical tools of independent interest. First, we give a new, deterministic tester for the positivity of an exponentially large matrix, provided it has a low-degree Fourier decomposition in terms of Pauli matrices. Secondly, we develop a new invariance principle for smooth matrix functions having bounded third-order Fréchet derivatives or which are Lipschitz continuous.
Cite as

Yangjing Dong, Honghao Fu, Anand Natarajan, Minglong Qin, Haochen Xu, and Penghui Yao. The Computational Advantage of MIP^∗ Vanishes in the Presence of Noise. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 30:1-30:71, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{dong_et_al:LIPIcs.CCC.2024.30,
  author =	{Dong, Yangjing and Fu, Honghao and Natarajan, Anand and Qin, Minglong and Xu, Haochen and Yao, Penghui},
  title =	{{The Computational Advantage of MIP^∗ Vanishes in the Presence of Noise}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{30:1--30:71},
  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.2024.30},
  URN =		{urn:nbn:de:0030-drops-204263},
  doi =		{10.4230/LIPIcs.CCC.2024.30},
  annote =	{Keywords: Interactive proofs, Quantum complexity theory, Quantum entanglement, Fourier analysis, Matrix analysis, Invariance principle, Derandomization, PCP, Locally testable code, Positivity testing}
}
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
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.13
Learning Low-Degree Quantum Objects

Authors: Srinivasan Arunachalam, Arkopal Dutt, Francisco Escudero Gutiérrez, and Carlos Palazuelos

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

Abstract
We consider the problem of learning low-degree quantum objects up to ε-error in 𝓁₂-distance. We show the following results: (i) unknown n-qubit degree-d (in the Pauli basis) quantum channels and unitaries can be learned using O(1/ε^d) queries (which is independent of n), (ii) polynomials p:{-1,1}ⁿ → [-1,1] arising from d-query quantum algorithms can be learned from O((1/ε)^d ⋅ log n) many random examples (x,p(x)) (which implies learnability even for d = O(log n)), and (iii) degree-d polynomials p:{-1,1}ⁿ → [-1,1] can be learned through O(1/ε^d) queries to a quantum unitary U_p that block-encodes p. Our main technical contributions are new Bohnenblust-Hille inequalities for quantum channels and completely bounded polynomials.
Cite as

Srinivasan Arunachalam, Arkopal Dutt, Francisco Escudero Gutiérrez, and Carlos Palazuelos. Learning Low-Degree Quantum Objects. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 13:1-13:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{arunachalam_et_al:LIPIcs.ICALP.2024.13,
  author =	{Arunachalam, Srinivasan and Dutt, Arkopal and Escudero Guti\'{e}rrez, Francisco and Palazuelos, Carlos},
  title =	{{Learning Low-Degree Quantum Objects}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{13:1--13:19},
  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.2024.13},
  URN =		{urn:nbn:de:0030-drops-201563},
  doi =		{10.4230/LIPIcs.ICALP.2024.13},
  annote =	{Keywords: Tomography}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2024.6
Pseudorandom Strings from Pseudorandom Quantum States

Authors: Prabhanjan Ananth, Yao-Ting Lin, and Henry Yuen

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

Abstract
We study the relationship between notions of pseudorandomness in the quantum and classical worlds. Pseudorandom quantum state generator (PRSG), a pseudorandomness notion in the quantum world, is an efficient circuit that produces states that are computationally indistinguishable from Haar random states. PRSGs have found applications in quantum gravity, quantum machine learning, quantum complexity theory, and quantum cryptography. Pseudorandom generators, on the other hand, a pseudorandomness notion in the classical world, is ubiquitous to theoretical computer science. While some separation results were known between PRSGs, for some parameter regimes, and PRGs, their relationship has not been completely understood. In this work, we show that a natural variant of pseudorandom generators called quantum pseudorandom generators (QPRGs) can be based on the existence of logarithmic output length PRSGs. Our result along with the previous separations gives a better picture regarding the relationship between the two notions. We also study the relationship between other notions, namely, pseudorandom function-like state generators and pseudorandom functions. We provide evidence that QPRGs can be as useful as PRGs by providing cryptographic applications of QPRGs such as commitments and encryption schemes. Our primary technical contribution is a method for pseudodeterministically extracting uniformly random strings from Haar-random states.
Cite as

Prabhanjan Ananth, Yao-Ting Lin, and Henry Yuen. Pseudorandom Strings from Pseudorandom Quantum States. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 6:1-6:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{ananth_et_al:LIPIcs.ITCS.2024.6,
  author =	{Ananth, Prabhanjan and Lin, Yao-Ting and Yuen, Henry},
  title =	{{Pseudorandom Strings from Pseudorandom Quantum States}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{6:1--6:22},
  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.2024.6},
  URN =		{urn:nbn:de:0030-drops-195348},
  doi =		{10.4230/LIPIcs.ITCS.2024.6},
  annote =	{Keywords: Quantum Cryptography}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2024.92
Parity vs. AC0 with Simple Quantum Preprocessing

Authors: Joseph Slote

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

Abstract
A recent line of work [Bravyi et al., 2018; Watts et al., 2019; Grier and Schaeffer, 2020; Bravyi et al., 2020; Watts and Parham, 2023] has shown the unconditional advantage of constant-depth quantum computation, or QNC⁰, over NC⁰, AC⁰, and related models of classical computation. Problems exhibiting this advantage include search and sampling tasks related to the parity function, and it is natural to ask whether QNC⁰ can be used to help compute parity itself. Namely, we study AC⁰∘QNC⁰ - a hybrid circuit model where AC⁰ operates on measurement outcomes of a QNC⁰ circuit - and we ask whether Par ∈ AC⁰∘QNC⁰. We believe the answer is negative. In fact, we conjecture AC⁰∘QNC⁰ cannot even achieve Ω(1) correlation with parity. As evidence for this conjecture, we prove: - When the QNC⁰ circuit is ancilla-free, this model can achieve only negligible correlation with parity, even when AC⁰ is replaced with any function having LMN-like decay in its Fourier spectrum. - For the general (non-ancilla-free) case, we show via a connection to nonlocal games that the conjecture holds for any class of postprocessing functions that has approximate degree o(n) and is closed under restrictions. Moreover, this is true even when the QNC⁰ circuit is given arbitrary quantum advice. By known results [Bun et al., 2019], this confirms the conjecture for linear-size AC⁰ circuits. - Another approach to proving the conjecture is to show a switching lemma for AC⁰∘QNC⁰. Towards this goal, we study the effect of quantum preprocessing on the decision tree complexity of Boolean functions. We find that from the point of view of decision tree complexity, nonlocal channels are no better than randomness: a Boolean function f precomposed with an n-party nonlocal channel is together equal to a randomized decision tree with worst-case depth at most DT_depth[f]. Taken together, our results suggest that while QNC⁰ is surprisingly powerful for search and sampling tasks, that power is "locked away" in the global correlations of its output, inaccessible to simple classical computation for solving decision problems.
Cite as

Joseph Slote. Parity vs. AC0 with Simple Quantum Preprocessing. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 92:1-92:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{slote:LIPIcs.ITCS.2024.92,
  author =	{Slote, Joseph},
  title =	{{Parity vs. AC0 with Simple Quantum Preprocessing}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{92:1--92:21},
  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.2024.92},
  URN =		{urn:nbn:de:0030-drops-196209},
  doi =		{10.4230/LIPIcs.ITCS.2024.92},
  annote =	{Keywords: QNC0, AC0, Nonlocal games, k-wise indistinguishability, approximate degree, switching lemma, Fourier concentration}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2023.24
On the Computational Hardness Needed for Quantum Cryptography

Authors: Zvika Brakerski, Ran Canetti, and Luowen Qian

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

Abstract
In the classical model of computation, it is well established that one-way functions (OWF) are minimal for computational cryptography: They are essential for almost any cryptographic application that cannot be realized with respect to computationally unbounded adversaries. In the quantum setting, however, OWFs appear not to be essential (Kretschmer 2021; Ananth et al., Morimae and Yamakawa 2022), and the question of whether such a minimal primitive exists remains open. We consider EFI pairs - efficiently samplable, statistically far but computationally indistinguishable pairs of (mixed) quantum states. Building on the work of Yan (2022), which shows equivalence between EFI pairs and statistical commitment schemes, we show that EFI pairs are necessary for a large class of quantum-cryptographic applications. Specifically, we construct EFI pairs from minimalistic versions of commitments schemes, oblivious transfer, and general secure multiparty computation, as well as from QCZK proofs from essentially any non-trivial language. We also construct quantum computational zero knowledge (QCZK) proofs for all of QIP from any EFI pair. This suggests that, for much of quantum cryptography, EFI pairs play a similar role to that played by OWFs in the classical setting: they are simple to describe, essential, and also serve as a linchpin for demonstrating equivalence between primitives.
Cite as

Zvika Brakerski, Ran Canetti, and Luowen Qian. On the Computational Hardness Needed for Quantum Cryptography. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 24:1-24:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{brakerski_et_al:LIPIcs.ITCS.2023.24,
  author =	{Brakerski, Zvika and Canetti, Ran and Qian, Luowen},
  title =	{{On the Computational Hardness Needed for Quantum Cryptography}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{24:1--24:21},
  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.2023.24},
  URN =		{urn:nbn:de:0030-drops-175278},
  doi =		{10.4230/LIPIcs.ITCS.2023.24},
  annote =	{Keywords: quantum cryptography, efi, commitment scheme, oblivious transfer, zero knowledge, secure multiparty computation}
}
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)

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@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.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)

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@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.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)

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@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}
}
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