Browsing by Author "Aaronson, Scott"
Now showing items 120 of 26

Advice coins for classical and quantum computation
Aaronson, Scott; Drucker, Andrew Donald (Springer Berlin / Heidelberg, 201106)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, 201411)BosonSampling, which we proposed three years ago, is a scheme for using linearoptical 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, 201601)BosonSampling is an intermediate model of quantum computation where linearoptical 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, 201001)Publickey 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 publickey quantum money ... 
Closed timelike curves make quantum and classical computing equivalent
Aaronson, Scott; Watrous, John (Royal Society of London, 200902)While closed timelike curves (CTCs) are not known to exist, studying their consequences has led to nontrivial 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 computersmoreover, rudimentary quantum computers built entirely out of linearoptical elementscannot be efficiently simulated by classical computers. In particular, we define a model ... 
Doubly infinite separation of quantum information and communication
Liu, ZiWen; Perry, Christopher; Zhu, Yechao; Koh, Dax Enshan; Aaronson, Scott (American Physical Society, 201601)We prove the existence of (oneway) 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, 201106)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 DagstuhlLeibnizZentrum fuer Informatik, 201606)When analyzing the computational complexity of wellknown 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), 201506)We achieve essentially the largest possible separation between quantum and classical query complexities. We do so using a propertytesting 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, 201006)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 twoqubit 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, 201406)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 CollisionFreeness
Aaronson, Scott (HassoPlattnerInstitut für Softwaresystemtechnik GmbH, 201101)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 linearoptical proof that the permanent is #Phard
Aaronson, Scott (Royal Society, The, 201112)One of the crown jewels of complexity theory is Valiant's theorem that computing the permanent of an n×n matrix is #Phard. Here we show that, by using the model of linearoptical quantum computing—and in particular, a ... 
The need for structure in quantum speedups
Aaronson, Scott; Ambainis, Andris (Electronic Colloquium on Computational Complexity, 200901)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 blackbox model where most ... 
On perfect completeness for QMA
Aaronson, Scott (Association for Computing Machinery (ACM), 200901)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 oneway communication complexity of group membership
Le Gall, Francois; Tani, Seiichiro; Russell, Alexander; Aaronson, Scott (200902)This paper studies the oneway 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; RahimiKeshari, Saleh; e.a. (American Association for the Advancement of Science (AAAS), 201212)Quantum computers are unnecessary for exponentially efficient computation or simulation if the Extended ChurchTuring thesis is correct. The thesis would be strongly contradicted by physical devices that efficiently perform ... 
Quantum CopyProtection and Quantum Money
Aaronson, Scott (Institute of Electrical and Electronics Engineers, 200909)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 ...