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Documents authored by Vidick, Thomas

Document
DOI: 10.4230/LIPIcs.CCC.2026.4
Probabilistically Checking Quantum Proofs, with Interaction

Authors: Baocheng Sun and Thomas Vidick

Published in: LIPIcs, Volume 383, 41st Computational Complexity Conference (CCC 2026)

Abstract
The model of interactive oracle proofs (IOP) generalizes the notion of probabilistically checkable proof (PCP), in which a static proof is verified probabilistically by querying a small number of bits, to the interactive setting: a polynomial-time verifier interacts with an unbounded prover, but is restricted to only reading a small number of bits, in total, from the messages sent by the prover. IOPs provide a relaxed setting in which to study local probabilistic verification. They have proved instrumental in devising efficient methods for verification through subsequent compilation into non-interactive or succinct protoocls. We study a quantum analogue of interactive oracle proofs (qIOP) in which the verifier and communication are both allowed to be quantum; yet the verifier is restricted to perform measurements only on a small number of qubits received from the prover. Our main result is a qIOP for any language in QMA, in which the total communication is polynomial but the verifier only reads a polylogarithmic number of qubits in total. The protocol has completeness parameter exponentially close to 1 and soundness bounded away from 1 by a constant. In the absence of a quantum PCP theorem, this provides the first information-theoretically sound local and robust characterization of QMA, albeit interactive. Previous works in the information-theoretic setting either considered two isolated but entangled quantum provers or quantum verifiers whose effort in a single round is small but remains polynomial when aggregated across all rounds of the protocol. Our protocol combines the use of a quantum locally testable code (LTC) with classical techniques, notably probabilistically checkable proofs of proximity (PCPP). We avoid the necessity for complex multi-qubit tests employed in other settings by leveraging the local indistinguishability property of the quantum LTC.
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Baocheng Sun and Thomas Vidick. Probabilistically Checking Quantum Proofs, with Interaction. In 41st Computational Complexity Conference (CCC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 383, pp. 4:1-4:49, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{sun_et_al:LIPIcs.CCC.2026.4,
  author =	{Sun, Baocheng and Vidick, Thomas},
  title =	{{Probabilistically Checking Quantum Proofs, with Interaction}},
  booktitle =	{41st Computational Complexity Conference (CCC 2026)},
  pages =	{4:1--4:49},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-437-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{383},
  editor =	{Moshkovitz, Dana},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2026.4},
  URN =		{urn:nbn:de:0030-drops-270463},
  doi =		{10.4230/LIPIcs.CCC.2026.4},
  annote =	{Keywords: quantum complexity theory, quantum probabilistically checkable proofs, interactive oracle proofs, quantum locally testable codes, QMA}
}
Document
DOI: 10.4230/LIPIcs.CCC.2026.15
Derandomised Tensor Product Gap Amplification for Quantum Hamiltonians

Authors: Thiago Bergamaschi, Tony Metger, Thomas Vidick, and Tina Zhang

Published in: LIPIcs, Volume 383, 41st Computational Complexity Conference (CCC 2026)

Abstract
The quantum PCP conjecture asks whether it is QMA-hard to distinguish between high- and low-energy Hamiltonians even when the gap between "high" and "low" energy is large (constant). A natural proof strategy is gap amplification: start from the fact that high- and low-energy Hamiltonians are hard to distinguish if the gap is small (inverse polynomial) [Alexei Y. Kitaev et al., 2002] and amplify the Hamiltonians to increase the energy gap while preserving hardness. Such a gap amplification procedure is at the heart of Dinur’s proof of the classical PCP theorem [Dinur, 2007]. In this work, following Dinur’s model, we introduce a new quantum gap amplification procedure for Hamiltonians which uses random walks on expander graphs to derandomise (subsample the terms of) the tensor product amplification of a Hamiltonian. Curiously, our analysis relies on a new technique inspired by quantum de Finetti theorems, which have previously been used to rule out certain approaches to the quantum PCP conjecture [Fernando G. S. L. Brandão and Aram Wettroth Harrow, 2013].
Cite as

Thiago Bergamaschi, Tony Metger, Thomas Vidick, and Tina Zhang. Derandomised Tensor Product Gap Amplification for Quantum Hamiltonians. In 41st Computational Complexity Conference (CCC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 383, pp. 15:1-15:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bergamaschi_et_al:LIPIcs.CCC.2026.15,
  author =	{Bergamaschi, Thiago and Metger, Tony and Vidick, Thomas and Zhang, Tina},
  title =	{{Derandomised Tensor Product Gap Amplification for Quantum Hamiltonians}},
  booktitle =	{41st Computational Complexity Conference (CCC 2026)},
  pages =	{15:1--15:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-437-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{383},
  editor =	{Moshkovitz, Dana},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2026.15},
  URN =		{urn:nbn:de:0030-drops-270572},
  doi =		{10.4230/LIPIcs.CCC.2026.15},
  annote =	{Keywords: quantum PCP conjecture, gap amplification, local Hamiltonians, tensor product amplification, expander random walks, quantum de Finetti theorems}
}
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.
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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.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
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.
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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.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
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.
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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.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
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.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
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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.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.CCC.2018.20
Retracted: Two-Player Entangled Games are NP-Hard

Authors: Anand Natarajan and Thomas Vidick

Published in: LIPIcs, Volume 102, 33rd Computational Complexity Conference (CCC 2018)

Abstract
The article, published on June 4th, 2018 in the CCC 2018 proceedings, has been retracted by agreement between the authors, the editor(s), and the publisher Schloss Dagstuhl / LIPIcs. The retraction has been agreed due to an error in the proof of the main result. This error is carried over from an error in the referenced paper “Three-player entangled XOR games are NP-hard to approximate” by Thomas Vidick (SICOMP ’16). That paper was used in an essential way to obtain the present result, and the error cannot be addressed through an erratum. See Retraction Notice on the last page of the PDF. We show that it is NP-hard to approximate, to within an additive constant, the maximum success probability of players sharing quantum entanglement in a two-player game with classical questions of logarithmic length and classical answers of constant length. As a corollary, the inclusion NEXP subseteq MIP^*, first shown by Ito and Vidick (FOCS'12) with three provers, holds with two provers only. The proof is based on a simpler, improved analysis of the low-degree test of Raz and Safra (STOC'97) against two entangled provers.
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Anand Natarajan and Thomas Vidick. Retracted: Two-Player Entangled Games are NP-Hard. In 33rd Computational Complexity Conference (CCC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 102, pp. 20:1-20:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{natarajan_et_al:LIPIcs.CCC.2018.20,
  author =	{Natarajan, Anand and Vidick, Thomas},
  title =	{{Retracted: Two-Player Entangled Games are NP-Hard}},
  booktitle =	{33rd Computational Complexity Conference (CCC 2018)},
  pages =	{20:1--20:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-069-9},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{102},
  editor =	{Servedio, Rocco A.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2018.20},
  URN =		{urn:nbn:de:0030-drops-88696},
  doi =		{10.4230/LIPIcs.CCC.2018.20},
  annote =	{Keywords: low-degree testing, entangled nonlocal games, multi-prover interactive proof systems}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2017.22
Parallel Repetition via Fortification: Analytic View and the Quantum Case

Authors: Mohammad Bavarian, Thomas Vidick, and Henry Yuen

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

Abstract
In a recent work, Moshkovitz [FOCS'14] presented a transformation n two-player games called "fortification", and gave an elementary proof of an (exponential decay) parallel repetition theorem for fortified two-player projection games. In this paper, we give an analytic reformulation of Moshkovitz's fortification framework, which was originally cast in combinatorial terms. This reformulation allows us to expand the scope of the fortification method to new settings. First, we show any game (not just projection games) can be fortified, and give a simple proof of parallel repetition for general fortified games. Then, we prove parallel repetition and fortification theorems for games with players sharing quantum entanglement, as well as games with more than two players. This gives a new gap amplification method for general games in the quantum and multiplayer settings, which has recently received much interest. An important component of our work is a variant of the fortification transformation, called "ordered fortification", that preserves the entangled value of a game. The original fortification of Moshkovitz does not in general preserve the entangled value of a game, and this was a barrier to extending the fortification framework to the quantum setting.
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Mohammad Bavarian, Thomas Vidick, and Henry Yuen. Parallel Repetition via Fortification: Analytic View and the Quantum Case. In 8th Innovations in Theoretical Computer Science Conference (ITCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 67, pp. 22:1-22:33, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{bavarian_et_al:LIPIcs.ITCS.2017.22,
  author =	{Bavarian, Mohammad and Vidick, Thomas and Yuen, Henry},
  title =	{{Parallel Repetition via Fortification: Analytic View and the Quantum Case}},
  booktitle =	{8th Innovations in Theoretical Computer Science Conference (ITCS 2017)},
  pages =	{22:1--22:33},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-029-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{67},
  editor =	{Papadimitriou, Christos H.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2017.22},
  URN =		{urn:nbn:de:0030-drops-81670},
  doi =		{10.4230/LIPIcs.ITCS.2017.22},
  annote =	{Keywords: Parallel repetition, quantum entanglement, non-local games}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2017.46
Rigorous Rg Algorithms and Area Laws for Low Energy Eigenstates In 1D

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

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

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

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

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@InProceedings{arad_et_al:LIPIcs.ITCS.2017.46,
  author =	{Arad, Itai and Landau, Zeph and Vazirani, Umesh V. and Vidick, Thomas},
  title =	{{Rigorous Rg Algorithms and Area Laws for Low Energy Eigenstates In 1D}},
  booktitle =	{8th Innovations in Theoretical Computer Science Conference (ITCS 2017)},
  pages =	{46:1--46:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-029-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{67},
  editor =	{Papadimitriou, Christos H.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2017.46},
  URN =		{urn:nbn:de:0030-drops-81920},
  doi =		{10.4230/LIPIcs.ITCS.2017.46},
  annote =	{Keywords: Hamiltonian complexity, area law, gapped ground states, algorithm}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2017.48
Overlapping Qubits

Authors: Rui Chao, Ben W. Reichardt, Chris Sutherland, and Thomas Vidick

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

Abstract
An ideal system of n qubits has 2^n dimensions. This exponential grants power, but also hinders characterizing the system's state and dynamics. We study a new problem: the qubits in a physical system might not be independent. They can "overlap," in the sense that an operation on one qubit slightly affects the others. We show that allowing for slight overlaps, n qubits can fit in just polynomially many dimensions. (Defined in a natural way, all pairwise overlaps can be <= epsilon in n^{O(1/epsilon^2)} dimensions.) Thus, even before considering issues like noise, a real system of n qubits might inherently lack any potential for exponential power. On the other hand, we also provide an efficient test to certify exponential dimensionality. Unfortunately, the test is sensitive to noise. It is important to devise more robust tests on the arrangements of qubits in quantum devices.
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Rui Chao, Ben W. Reichardt, Chris Sutherland, and Thomas Vidick. Overlapping Qubits. In 8th Innovations in Theoretical Computer Science Conference (ITCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 67, pp. 48:1-48:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{chao_et_al:LIPIcs.ITCS.2017.48,
  author =	{Chao, Rui and Reichardt, Ben W. and Sutherland, Chris and Vidick, Thomas},
  title =	{{Overlapping Qubits}},
  booktitle =	{8th Innovations in Theoretical Computer Science Conference (ITCS 2017)},
  pages =	{48:1--48:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-029-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{67},
  editor =	{Papadimitriou, Christos H.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2017.48},
  URN =		{urn:nbn:de:0030-drops-81826},
  doi =		{10.4230/LIPIcs.ITCS.2017.48},
  annote =	{Keywords: Quantum computing, Qubits, Dimension test}
}
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