Now showing items 1-20 of 26

    • Advice coins for classical and quantum computation 

      Aaronson, Scott; Drucker, Andrew Donald (Springer Berlin / Heidelberg, 2011-06)
      We study the power of classical and quantum algorithms equipped with nonuniform advice, in the form of a coin whose bias encodes useful information. This question takes on particular importance in the quantum case, due to ...
    • Bosonsampling Is Far from Uniform 

      Aaronson, Scott; Arkhipov, Aleksandr (Rinton Press, 2014-11)
      BosonSampling, which we proposed three years ago, is a scheme for using linear-optical networks to solve sampling problems that appear to be intractable for a classical computer. In a recent manuscript, Gogolin et al. ...
    • BosonSampling with lost photons 

      Aaronson, Scott; Brod, Daniel J. (American Physical Society, 2016-01)
      BosonSampling is an intermediate model of quantum computation where linear-optical networks are used to solve sampling problems expected to be hard for classical computers. Since these devices are not expected to be universal ...
    • BQP and the Polynomial Hierarchy 

      Aaronson, Scott (Association for Computing Machinery, 2010)
      The relationship between BQP and PH has been an open problem since the earliest days of quantum computing. We present evidence that quantum computers can solve problems outside the entire polynomial hierarchy, by relating ...
    • Breaking and making quantum money: toward a new quantum cryptographic protocol 

      Lutomirski, Andrew Michael; Gosset, David Nicholas; Hassidim, Avinatan; Farhi, Edward; Shor, Peter W.; e.a. (Institute for Computer Science, 2010-01)
      Public-key quantum money is a cryptographic protocol in which a bank can create quantum states which anyone can verify but no one except possibly the bank can clone or forge. There are no secure public-key quantum money ...
    • Closed timelike curves make quantum and classical computing equivalent 

      Aaronson, Scott; Watrous, John (Royal Society of London, 2009-02)
      While closed timelike curves (CTCs) are not known to exist, studying their consequences has led to non-trivial insights into general relativity, quantum information and other areas. In this paper, we show that, if CTCs ...
    • The Computational Complexity of Linear Optics 

      Aaronson, Scott; Arkhipov, Aleksandr (Association for Computing Machinery, 2011)
      We give new evidence that quantum computers---moreover, rudimentary quantum computers built entirely out of linear-optical elements---cannot be efficiently simulated by classical computers. In particular, we define a model ...
    • Doubly infinite separation of quantum information and communication 

      Liu, Zi-Wen; Perry, Christopher; Zhu, Yechao; Koh, Dax Enshan; Aaronson, Scott (American Physical Society, 2016-01)
      We prove the existence of (one-way) communication tasks with a subconstant versus superconstant asymptotic gap, which we call “doubly infinite,” between their quantum information and communication complexities. We do so ...
    • The equivalence of sampling and searching 

      Aaronson, Scott (Springer Berlin/Heidelberg, 2011-06)
      In a sampling problem, we are given an input x\in\left\{ 0,1\right\} ^{n} , and asked to sample approximately from a probability distribution \mathcal{D}_{x}strings. In a search problem, we are given an input x\in\left\{ ...
    • The fewest clues problem 

      Fermi, Ma; Schvartzman, Ariel; Waingarten, Erik; Demaine, Erik D; Aaronson, Scott (Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik, 2016-06)
      When analyzing the computational complexity of well-known puzzles, most papers consider the algorithmic challenge of solving a given instance of (a generalized form of) the puzzle. We take a different approach by analyzing ...
    • Forrelation: A Problem That Optimally Separates Quantum from Classical Computing 

      Aaronson, Scott; Ambainis, Andris (Association for Computing Machinery (ACM), 2015-06)
      We achieve essentially the largest possible separation between quantum and classical query complexities. We do so using a property-testing problem called Forrelation, where one needs to decide whether one Boolean function ...
    • A Full Characterization of Quantum Advice 

      Aaronson, Scott; Drucker, Andrew Donald (Association for Computing Machinery, 2010-06)
      We prove the following surprising result: given any quantum state rho on n qubits, there exists a local Hamiltonian H on poly(n) qubits (e.g., a sum of two-qubit interactions), such that any ground state of H can be used ...
    • Generation of universal linear optics by any beam splitter 

      Aaronson, Scott; Bouland, Adam Michael (American Physical Society, 2014-06)
      In 1994, Reck et al. showed how to realize any unitary transformation on a single photon using a product of beam splitters and phase shifters. Here we show that any single beam splitter that nontrivially mixes two modes ...
    • Impossibility of Succinct Quantum Proofs for Collision-Freeness 

      Aaronson, Scott (Hasso-Plattner-Institut für Softwaresystemtechnik GmbH, 2011-01)
      We show that any quantum algorithm to decide whether a function f:\left[n\right] \rightarrow\left[ n\right] is a permutation or far from a permutation\ must make \Omega\left( n^{1/3}/w\right) queries to f, even if the ...
    • A linear-optical proof that the permanent is #P-hard 

      Aaronson, Scott (Royal Society, The, 2011-12)
      One of the crown jewels of complexity theory is Valiant's theorem that computing the permanent of an n×n matrix is #P-hard. Here we show that, by using the model of linear-optical quantum computing—and in particular, a ...
    • The need for structure in quantum speedups 

      Aaronson, Scott; Ambainis, Andris (Electronic Colloquium on Computational Complexity, 2009-01)
      Is there a general theorem that tells us when we can hope for exponential speedups from quantum algorithms, and when we cannot? In this paper, we make two advances toward such a theorem, in the black-box model where most ...
    • On perfect completeness for QMA 

      Aaronson, Scott (Association for Computing Machinery (ACM), 2009-01)
      Whether the class QMA (Quantum Merlin Arthur) is equal to QMA1, or QMA with onesided error, has been an open problem for years. This note helps to explain why the problem is difficult, by using ideas from real analysis to ...
    • The one-way communication complexity of group membership 

      Le Gall, Francois; Tani, Seiichiro; Russell, Alexander; Aaronson, Scott (2009-02)
      This paper studies the one-way communication complexity of the subgroup membership problem, a classical problem closely related to basic questions in quantum computing. Here Alice receives, as input, a subgroup H of a ...
    • Photonic Boson Sampling in a Tunable Circuit 

      Dove, Justin Michael; Aaronson, Scott; Broome, Matthew A.; Fedrizzi, Alessandro; Rahimi-Keshari, Saleh; e.a. (American Association for the Advancement of Science (AAAS), 2012-12)
      Quantum computers are unnecessary for exponentially efficient computation or simulation if the Extended Church-Turing thesis is correct. The thesis would be strongly contradicted by physical devices that efficiently perform ...
    • Quantum Copy-Protection and Quantum Money 

      Aaronson, Scott (Institute of Electrical and Electronics Engineers, 2009-09)
      Forty years ago, Wiesner proposed using quantum states to create money that is physically impossible to counterfeit, something that cannot be done in the classical world. However, Wiesner's scheme required a central bank ...