107 Search Results for "Vidick, Thomas"

Volume

LIPIcs, Volume 151

11th Innovations in Theoretical Computer Science Conference (ITCS 2020)

ITCS 2020, January 12-14, 2020, Seattle, Washington, USA

Editors: Thomas Vidick

Document
DOI: 10.4230/LIPIcs.ITCS.2024.24
Classical Verification of Quantum Learning

Authors: Matthias C. Caro, Marcel Hinsche, Marios Ioannou, Alexander Nietner, and Ryan Sweke

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

Abstract
Quantum data access and quantum processing can make certain classically intractable learning tasks feasible. However, quantum capabilities will only be available to a select few in the near future. Thus, reliable schemes that allow classical clients to delegate learning to untrusted quantum servers are required to facilitate widespread access to quantum learning advantages. Building on a recently introduced framework of interactive proof systems for classical machine learning, we develop a framework for classical verification of quantum learning. We exhibit learning problems that a classical learner cannot efficiently solve on their own, but that they can efficiently and reliably solve when interacting with an untrusted quantum prover. Concretely, we consider the problems of agnostic learning parities and Fourier-sparse functions with respect to distributions with uniform input marginal. We propose a new quantum data access model that we call "mixture-of-superpositions" quantum examples, based on which we give efficient quantum learning algorithms for these tasks. Moreover, we prove that agnostic quantum parity and Fourier-sparse learning can be efficiently verified by a classical verifier with only random example or statistical query access. Finally, we showcase two general scenarios in learning and verification in which quantum mixture-of-superpositions examples do not lead to sample complexity improvements over classical data. Our results demonstrate that the potential power of quantum data for learning tasks, while not unlimited, can be utilized by classical agents through interaction with untrusted quantum entities.
Cite as

Matthias C. Caro, Marcel Hinsche, Marios Ioannou, Alexander Nietner, and Ryan Sweke. Classical Verification of Quantum Learning. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 24:1-24:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{caro_et_al:LIPIcs.ITCS.2024.24,
  author =	{Caro, Matthias C. and Hinsche, Marcel and Ioannou, Marios and Nietner, Alexander and Sweke, Ryan},
  title =	{{Classical Verification of Quantum Learning}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{24:1--24:23},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.24},
  URN =		{urn:nbn:de:0030-drops-195524},
  doi =		{10.4230/LIPIcs.ITCS.2024.24},
  annote =	{Keywords: computational learning theory, quantum learning theory, interactive proofs, quantum oracles, agnostic learning}
}
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-dev.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
Invited Talk
DOI: 10.4230/LIPIcs.ICALP.2023.4
Quantum Codes, Local Testability and Interactive Proofs: State of the Art and Open Questions (Invited Talk)

Authors: Thomas Vidick

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

Abstract
The study of multiprover interactive proof systems, of locally testable codes, and of property testing are deeply linked, conceptually if not formally, through their role in the proof of the PCP theorem in complexity theory. Recently there has been substantial progress on an analogous research programme in quantum complexity theory. Two years ago we characterized the power of multiprover interactive proof systems with provers sharing entanglement, showing that MIP^* = RE [Ji et al., 2020], a hugely surprising increase in power from the classical result MIP = NEXP of [Babai et al., 1991]. The following year Panteleev and Kalachev gave the first construction of quantum low-density parity-check codes (QLDPC) [Panteleev and Kalachev, 2022], thus marking a major step towards the possible realization of good quantum locally testable codes - the classical analogue of which was only constructed quite recently [Dinur et al., 2022]. And finally, less than a year ago Anshu, Breuckmann and Nirkhe used facts evidenced in the construction of good decoders for the new QLDPC codes to resolve the NLTS conjecture [Anshu et al., 2022], widely viewed as a crucial step on the way to a possible quantum PCP theorem. In the talk I will survey these results, making an effort to motivate and present them to the non-expert. I will explain the connections between them and point to where, in my opinion, our understanding is currently lacking. Along the way I will highlight a number of open problems whose resolution could lead to further progress on one of the most important research programmes in quantum complexity theory.
Cite as

Thomas Vidick. Quantum Codes, Local Testability and Interactive Proofs: State of the Art and Open Questions (Invited Talk). In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, p. 4:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{vidick:LIPIcs.ICALP.2023.4,
  author =	{Vidick, Thomas},
  title =	{{Quantum Codes, Local Testability and Interactive Proofs: State of the Art and Open Questions}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{4:1--4:1},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.4},
  URN =		{urn:nbn:de:0030-drops-180569},
  doi =		{10.4230/LIPIcs.ICALP.2023.4},
  annote =	{Keywords: quantum interactive proofs, quantum codes}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2023.64
Parallel Self-Testing of EPR Pairs Under Computational Assumptions

Authors: Honghao Fu, Daochen Wang, and Qi Zhao

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

Abstract
Self-testing is a fundamental feature of quantum mechanics that allows a classical verifier to force untrusted quantum devices to prepare certain states and perform certain measurements on them. The standard approach assumes at least two spatially separated devices. Recently, Metger and Vidick [Metger and Vidick, 2021] showed that a single EPR pair of a single quantum device can be self-tested under computational assumptions. In this work, we generalize their results to give the first parallel self-test of N EPR pairs and measurements on them in the single-device setting under the same computational assumptions. We show that our protocol can be passed with probability negligibly close to 1 by an honest quantum device using poly(N) resources. Moreover, we show that any quantum device that fails our protocol with probability at most ε must be poly(N,ε)-close to being honest in the appropriate sense. In particular, our protocol can test any distribution over tensor products of computational or Hadamard basis measurements, making it suitable for applications such as device-independent quantum key distribution [Metger et al., 2021] under computational assumptions. Moreover, a simplified version of our protocol is the first that can efficiently certify an arbitrary number of qubits of a single cloud quantum computer using only classical communication.
Cite as

Honghao Fu, Daochen Wang, and Qi Zhao. Parallel Self-Testing of EPR Pairs Under Computational Assumptions. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 64:1-64:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{fu_et_al:LIPIcs.ICALP.2023.64,
  author =	{Fu, Honghao and Wang, Daochen and Zhao, Qi},
  title =	{{Parallel Self-Testing of EPR Pairs Under Computational Assumptions}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{64:1--64:19},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.64},
  URN =		{urn:nbn:de:0030-drops-181160},
  doi =		{10.4230/LIPIcs.ICALP.2023.64},
  annote =	{Keywords: Quantum complexity theory, self-testing, LWE}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2023.67
Quantum Cryptography with Classical Communication: Parallel Remote State Preparation for Copy-Protection, Verification, and More

Authors: Alexandru Gheorghiu, Tony Metger, and Alexander Poremba

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

Abstract
Quantum mechanical effects have enabled the construction of cryptographic primitives that are impossible classically. For example, quantum copy-protection allows for a program to be encoded in a quantum state in such a way that the program can be evaluated, but not copied. Many of these cryptographic primitives are two-party protocols, where one party, Bob, has full quantum computational capabilities, and the other party, Alice, is only required to send random BB84 states to Bob. In this work, we show how such protocols can generically be converted to ones where Alice is fully classical, assuming that Bob cannot efficiently solve the LWE problem. In particular, this means that all communication between (classical) Alice and (quantum) Bob is classical, yet they can still make use of cryptographic primitives that would be impossible if both parties were classical. We apply this conversion procedure to obtain quantum cryptographic protocols with classical communication for unclonable encryption, copy-protection, computing on encrypted data, and verifiable blind delegated computation. The key technical ingredient for our result is a protocol for classically-instructed parallel remote state preparation of BB84 states. This is a multi-round protocol between (classical) Alice and (quantum polynomial-time) Bob that allows Alice to certify that Bob must have prepared n uniformly random BB84 states (up to a change of basis on his space). While previous approaches could only certify one- or two-qubit states, our protocol allows for the certification of an n-fold tensor product of BB84 states. Furthermore, Alice knows which specific BB84 states Bob has prepared, while Bob himself does not. Hence, the situation at the end of this protocol is (almost) equivalent to one where Alice sent n random BB84 states to Bob. This allows us to replace the step of preparing and sending BB84 states in existing protocols by our remote-state preparation protocol in a generic and modular way.
Cite as

Alexandru Gheorghiu, Tony Metger, and Alexander Poremba. Quantum Cryptography with Classical Communication: Parallel Remote State Preparation for Copy-Protection, Verification, and More. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 67:1-67:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{gheorghiu_et_al:LIPIcs.ICALP.2023.67,
  author =	{Gheorghiu, Alexandru and Metger, Tony and Poremba, Alexander},
  title =	{{Quantum Cryptography with Classical Communication: Parallel Remote State Preparation for Copy-Protection, Verification, and More}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{67:1--67:17},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.67},
  URN =		{urn:nbn:de:0030-drops-181197},
  doi =		{10.4230/LIPIcs.ICALP.2023.67},
  annote =	{Keywords: Quantum cryptography, Remote state preparation, Self-testing, Learning with errors, Quantum copy-protection, Unclonable encryption, Quantum verification}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2023.90
Quantum Proofs of Deletion for Learning with Errors

Authors: Alexander Poremba

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

Abstract
Quantum information has the property that measurement is an inherently destructive process. This feature is most apparent in the principle of complementarity, which states that mutually incompatible observables cannot be measured at the same time. Recent work by Broadbent and Islam (TCC 2020) builds on this aspect of quantum mechanics to realize a cryptographic notion called certified deletion. While this remarkable notion enables a classical verifier to be convinced that a (private-key) quantum ciphertext has been deleted by an untrusted party, it offers no additional layer of functionality. In this work, we augment the proof-of-deletion paradigm with fully homomorphic encryption (FHE). We construct the first fully homomorphic encryption scheme with certified deletion - an interactive protocol which enables an untrusted quantum server to compute on encrypted data and, if requested, to simultaneously prove data deletion to a client. Our scheme has the desirable property that verification of a deletion certificate is public; meaning anyone can verify that deletion has taken place. Our main technical ingredient is an interactive protocol by which a quantum prover can convince a classical verifier that a sample from the Learning with Errors (LWE) distribution in the form of a quantum state was deleted. As an application of our protocol, we construct a Dual-Regev public-key encryption scheme with certified deletion, which we then extend towards a (leveled) FHE scheme of the same type. We introduce the notion of Gaussian-collapsing hash functions - a special case of collapsing hash functions defined by Unruh (Eurocrypt 2016) - and we prove the security of our schemes under the assumption that the Ajtai hash function satisfies a certain strong Gaussian-collapsing property in the presence of leakage.
Cite as

Alexander Poremba. Quantum Proofs of Deletion for Learning with Errors. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 90:1-90:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{poremba:LIPIcs.ITCS.2023.90,
  author =	{Poremba, Alexander},
  title =	{{Quantum Proofs of Deletion for Learning with Errors}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{90:1--90:14},
  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.2023.90},
  URN =		{urn:nbn:de:0030-drops-175934},
  doi =		{10.4230/LIPIcs.ITCS.2023.90},
  annote =	{Keywords: Learning with errors, certified deletion, fully homomorphic encryption}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2021.19
Self-Testing of a Single Quantum Device Under Computational Assumptions

Authors: Tony Metger and Thomas Vidick

Published in: LIPIcs, Volume 185, 12th Innovations in Theoretical Computer Science Conference (ITCS 2021)

Abstract
Self-testing is a method to characterise an arbitrary quantum system based only on its classical input-output correlations, and plays an important role in device-independent quantum information processing as well as quantum complexity theory. Prior works on self-testing require the assumption that the system’s state is shared among multiple parties that only perform local measurements and cannot communicate. Here, we replace the setting of multiple non-communicating parties, which is difficult to enforce in practice, by a single computationally bounded party. Specifically, we construct a protocol that allows a classical verifier to robustly certify that a single computationally bounded quantum device must have prepared a Bell pair and performed single-qubit measurements on it, up to a change of basis applied to both the device’s state and measurements. This means that under computational assumptions, the verifier is able to certify the presence of entanglement, a property usually closely associated with two separated subsystems, inside a single quantum device. To achieve this, we build on techniques first introduced by Brakerski et al. (2018) and Mahadev (2018) which allow a classical verifier to constrain the actions of a quantum device assuming the device does not break post-quantum cryptography.
Cite as

Tony Metger and Thomas Vidick. Self-Testing of a Single Quantum Device Under Computational Assumptions. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 19:1-19:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{metger_et_al:LIPIcs.ITCS.2021.19,
  author =	{Metger, Tony and Vidick, Thomas},
  title =	{{Self-Testing of a Single Quantum Device Under Computational Assumptions}},
  booktitle =	{12th Innovations in Theoretical Computer Science Conference (ITCS 2021)},
  pages =	{19:1--19:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-177-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{185},
  editor =	{Lee, James R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2021.19},
  URN =		{urn:nbn:de:0030-drops-135581},
  doi =		{10.4230/LIPIcs.ITCS.2021.19},
  annote =	{Keywords: Quantum computing, quantum cryptography, device-independence, self-testing, post-quantum cryptography}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2020.87
On the Complexity of Zero Gap MIP*

Authors: Hamoon Mousavi, Seyed Sajjad Nezhadi, and Henry Yuen

Published in: LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

Abstract
The class MIP^* is the set of languages decidable by multiprover interactive proofs with quantum entangled provers. It was recently shown by Ji, Natarajan, Vidick, Wright and Yuen that MIP^* is equal to RE, the set of recursively enumerable languages. In particular this shows that the complexity of approximating the quantum value of a non-local game G is equivalent to the complexity of the Halting problem. In this paper we investigate the complexity of deciding whether the quantum value of a non-local game G is exactly 1. This problem corresponds to a complexity class that we call zero gap MIP^*, denoted by MIP₀^*, where there is no promise gap between the verifier’s acceptance probabilities in the YES and NO cases. We prove that MIP₀^* extends beyond the first level of the arithmetical hierarchy (which includes RE and its complement coRE), and in fact is equal to Π₂⁰, the class of languages that can be decided by quantified formulas of the form ∀ y ∃ z R(x,y,z). Combined with the previously known result that MIP₀^{co} (the commuting operator variant of MIP₀^*) is equal to coRE, our result further highlights the fascinating connection between various models of quantum multiprover interactive proofs and different classes in computability theory.
Cite as

Hamoon Mousavi, Seyed Sajjad Nezhadi, and Henry Yuen. On the Complexity of Zero Gap MIP*. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 87:1-87:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{mousavi_et_al:LIPIcs.ICALP.2020.87,
  author =	{Mousavi, Hamoon and Nezhadi, Seyed Sajjad and Yuen, Henry},
  title =	{{On the Complexity of Zero Gap MIP*}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{87:1--87:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.87},
  URN =		{urn:nbn:de:0030-drops-124940},
  doi =		{10.4230/LIPIcs.ICALP.2020.87},
  annote =	{Keywords: Quantum Complexity, Multiprover Interactive Proofs, Computability Theory}
}
Document
DOI: 10.4230/LIPIcs.TQC.2020.8
Simpler Proofs of Quantumness

Authors: Zvika Brakerski, Venkata Koppula, Umesh Vazirani, and Thomas Vidick

Published in: LIPIcs, Volume 158, 15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020)

Abstract
A proof of quantumness is a method for provably demonstrating (to a classical verifier) that a quantum device can perform computational tasks that a classical device with comparable resources cannot. Providing a proof of quantumness is the first step towards constructing a useful quantum computer. There are currently three approaches for exhibiting proofs of quantumness: (i) Inverting a classically-hard one-way function (e.g. using Shor’s algorithm). This seems technologically out of reach. (ii) Sampling from a classically-hard-to-sample distribution (e.g. BosonSampling). This may be within reach of near-term experiments, but for all such tasks known verification requires exponential time. (iii) Interactive protocols based on cryptographic assumptions. The use of a trapdoor scheme allows for efficient verification, and implementation seems to require much less resources than (i), yet still more than (ii). In this work we propose a significant simplification to approach (iii) by employing the random oracle heuristic. (We note that we do not apply the Fiat-Shamir paradigm.) We give a two-message (challenge-response) proof of quantumness based on any trapdoor claw-free function. In contrast to earlier proposals we do not need an adaptive hard-core bit property. This allows the use of smaller security parameters and more diverse computational assumptions (such as Ring Learning with Errors), significantly reducing the quantum computational effort required for a successful demonstration.
Cite as

Zvika Brakerski, Venkata Koppula, Umesh Vazirani, and Thomas Vidick. Simpler Proofs of Quantumness. In 15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 158, pp. 8:1-8:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{brakerski_et_al:LIPIcs.TQC.2020.8,
  author =	{Brakerski, Zvika and Koppula, Venkata and Vazirani, Umesh and Vidick, Thomas},
  title =	{{Simpler Proofs of Quantumness}},
  booktitle =	{15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020)},
  pages =	{8:1--8:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-146-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{158},
  editor =	{Flammia, Steven T.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2020.8},
  URN =		{urn:nbn:de:0030-drops-120677},
  doi =		{10.4230/LIPIcs.TQC.2020.8},
  annote =	{Keywords: Proof of Quantumness, Random Oracle, Learning with Errors}
}
Document
DOI: 10.4230/LIPIcs.STACS.2020.20
Oracle Complexity Classes and Local Measurements on Physical Hamiltonians

Authors: Sevag Gharibian, Stephen Piddock, and Justin Yirka

Published in: LIPIcs, Volume 154, 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)

Abstract
The canonical hard problems for NP and its quantum analogue, Quantum Merlin-Arthur (QMA), are MAX-k-SAT and the k-local Hamiltonian problem (k-LH), the quantum generalization of MAX-k-SAT, respectively. In recent years, however, an arguably even more physically motivated problem than k-LH has been formalized - the problem of simulating local measurements on ground states of local Hamiltonians (APX-SIM). Perhaps surprisingly, [Ambainis, CCC 2014] showed that APX-SIM is likely harder than QMA. Indeed, [Ambainis, CCC 2014] showed that APX-SIM is P^{QMA[log]}-complete, for P^{QMA[log]} the class of languages decidable by a P machine making a logarithmic number of adaptive queries to a QMA oracle. In this work, we show that APX-SIM is P^{QMA[log]}-complete even when restricted to physically motivated Hamiltonians, obtaining as intermediate steps a variety of related complexity-theoretic results. Specifically, we first give a sequence of results which together yield P^{QMA[log]}-hardness for APX-SIM on well-motivated Hamiltonians such as the 2D Heisenberg model: - We show that for NP, StoqMA, and QMA oracles, a logarithmic number of adaptive queries is equivalent to polynomially many parallel queries. Formally, P^{NP[log]}=P^{||NP}, P^{StoqMA[log]}=P^{||StoqMA}, and P^{QMA[log]}=P^{||QMA}. (The result for NP was previously shown using a different proof technique.) These equalities simplify the proofs of our subsequent results. - Next, we show that the hardness of APX-SIM is preserved under Hamiltonian simulations (à la [Cubitt, Montanaro, Piddock, 2017]) by studying a seemingly weaker problem, ∀-APX-SIM. As a byproduct, we obtain a full complexity classification of APX-SIM, showing it is complete for P, P^{||NP},P^{||StoqMA}, or P^{||QMA} depending on the Hamiltonians employed. - Leveraging the above, we show that APX-SIM is P^{QMA[log]}-complete for any family of Hamiltonians which can efficiently simulate spatially sparse Hamiltonians. This implies APX-SIM is P^{QMA[log]}-complete even on physically motivated models such as the 2D Heisenberg model. Our second focus considers 1D systems: We show that APX-SIM remains P^{QMA[log]}-complete even for local Hamiltonians on a 1D line of 8-dimensional qudits. This uses a number of ideas from above, along with replacing the "query Hamiltonian" of [Ambainis, CCC 2014] with a new "sifter" construction.
Cite as

Sevag Gharibian, Stephen Piddock, and Justin Yirka. Oracle Complexity Classes and Local Measurements on Physical Hamiltonians. In 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 154, pp. 20:1-20:37, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{gharibian_et_al:LIPIcs.STACS.2020.20,
  author =	{Gharibian, Sevag and Piddock, Stephen and Yirka, Justin},
  title =	{{Oracle Complexity Classes and Local Measurements on Physical Hamiltonians}},
  booktitle =	{37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)},
  pages =	{20:1--20:37},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-140-5},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{154},
  editor =	{Paul, Christophe and Bl\"{a}ser, Markus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2020.20},
  URN =		{urn:nbn:de:0030-drops-118818},
  doi =		{10.4230/LIPIcs.STACS.2020.20},
  annote =	{Keywords: Quantum Merlin Arthur (QMA), simulation of local measurement, local Hamiltonian, oracle complexity class, physical Hamiltonians}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.ITCS.2020
LIPIcs, Volume 151, ITCS'20, Complete Volume

Authors: Thomas Vidick

Published in: LIPIcs, Volume 151, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)

Abstract
LIPIcs, Volume 151, ITCS'20, Complete Volume
Cite as

11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@Proceedings{vidick:LIPIcs.ITCS.2020,
  title =	{{LIPIcs, Volume 151, ITCS'20, Complete Volume}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Vidick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020},
  URN =		{urn:nbn:de:0030-drops-117829},
  doi =		{10.4230/LIPIcs.ITCS.2020},
  annote =	{Keywords: Mathematics of computing; Theory of computation}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.ITCS.2020.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Thomas Vidick

Published in: LIPIcs, Volume 151, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)

Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as

11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 0:i-0:xvi, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{vidick:LIPIcs.ITCS.2020.0,
  author =	{Vidick, Thomas},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{0:i--0:xvi},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Vidick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.0},
  URN =		{urn:nbn:de:0030-drops-116855},
  doi =		{10.4230/LIPIcs.ITCS.2020.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2020.1
Hardness Amplification of Optimization Problems

Authors: Elazar Goldenberg and Karthik C. S.

Published in: LIPIcs, Volume 151, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)

Abstract
In this paper, we prove a general hardness amplification scheme for optimization problems based on the technique of direct products. We say that an optimization problem Π is direct product feasible if it is possible to efficiently aggregate any k instances of Π and form one large instance of Π such that given an optimal feasible solution to the larger instance, we can efficiently find optimal feasible solutions to all the k smaller instances. Given a direct product feasible optimization problem Π, our hardness amplification theorem may be informally stated as follows: If there is a distribution D over instances of Π of size n such that every randomized algorithm running in time t(n) fails to solve Π on 1/α(n) fraction of inputs sampled from D, then, assuming some relationships on α(n) and t(n), there is a distribution D' over instances of Π of size O(n⋅α(n)) such that every randomized algorithm running in time t(n)/poly(α(n)) fails to solve Π on 99/100 fraction of inputs sampled from D'. As a consequence of the above theorem, we show hardness amplification of problems in various classes such as NP-hard problems like Max-Clique, Knapsack, and Max-SAT, problems in P such as Longest Common Subsequence, Edit Distance, Matrix Multiplication, and even problems in TFNP such as Factoring and computing Nash equilibrium.
Cite as

Elazar Goldenberg and Karthik C. S.. Hardness Amplification of Optimization Problems. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 1:1-1:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{goldenberg_et_al:LIPIcs.ITCS.2020.1,
  author =	{Goldenberg, Elazar and Karthik C. S.},
  title =	{{Hardness Amplification of Optimization Problems}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{1:1--1:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Vidick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.1},
  URN =		{urn:nbn:de:0030-drops-116863},
  doi =		{10.4230/LIPIcs.ITCS.2020.1},
  annote =	{Keywords: hardness amplification, average case complexity, direct product, optimization problems, fine-grained complexity, TFNP}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2020.2
Smooth and Strong PCPs

Authors: Orr Paradise

Published in: LIPIcs, Volume 151, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)

Abstract
Probabilistically checkable proofs (PCPs) can be verified based only on a constant amount of random queries, such that any correct claim has a proof that is always accepted, and incorrect claims are rejected with high probability (regardless of the given alleged proof). We consider two possible features of PCPs: - A PCP is strong if it rejects an alleged proof of a correct claim with probability proportional to its distance from some correct proof of that claim. - A PCP is smooth if each location in a proof is queried with equal probability. We prove that all sets in NP have PCPs that are both smooth and strong, are of polynomial length, and can be verified based on a constant number of queries. This is achieved by following the proof of the PCP theorem of Arora, Lund, Motwani, Sudan and Szegedy (JACM, 1998), providing a stronger analysis of the Hadamard and Reed - Muller based PCPs and a refined PCP composition theorem. In fact, we show that any set in NP has a smooth strong canonical PCP of Proximity (PCPP), meaning that there is an efficiently computable bijection of NP witnesses to correct proofs. This improves on the recent construction of Dinur, Gur and Goldreich (ITCS, 2019) of PCPPs that are strong canonical but inherently non-smooth. Our result implies the hardness of approximating the satisfiability of "stable" 3CNF formulae with bounded variable occurrence, where stable means that the number of clauses violated by an assignment is proportional to its distance from a satisfying assignment (in the relative Hamming metric). This proves a hypothesis used in the work of Friggstad, Khodamoradi and Salavatipour (SODA, 2019), suggesting a connection between the hardness of these instances and other stable optimization problems.
Cite as

Orr Paradise. Smooth and Strong PCPs. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 2:1-2:41, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{paradise:LIPIcs.ITCS.2020.2,
  author =	{Paradise, Orr},
  title =	{{Smooth and Strong PCPs}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{2:1--2:41},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Vidick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.2},
  URN =		{urn:nbn:de:0030-drops-116875},
  doi =		{10.4230/LIPIcs.ITCS.2020.2},
  annote =	{Keywords: Interactive and probabilistic proof systems, Probabilistically checkable proofs, Hardness of approximation}
}
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