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1
June 2014
CCC '14: Proceedings of the 2014 IEEE 29th Conference on Computational Complexity
Publisher: IEEE Computer Society
We introduce and study a new model of interactive proofs: AM(k), or ArthurMerlin with k noncommunicating Merlins. Unlike with the betterknown MIP, here the assumption is that each Merlin receives an independent random challenge from Arthur. One motivation for this model (which we explore in detail) comes from the close ...
Keywords:
ArthurMerlin, Exponential Time Hypothesis, free games, multiprover, PCP, QMA(2), quasipolynomial time
2
August 2012
Communications of the ACM: Volume 55 Issue 8, August 2012
Publisher: ACM
Bibliometrics:
Citation Count: 2
Downloads (6 Weeks): 11, Downloads (12 Months): 107, Downloads (Overall): 7,275
Imagine money you can carry and spend without a trace.
3
May 2012
STOC '12: Proceedings of the fortyfourth annual ACM symposium on Theory of computing
Publisher: ACM
Bibliometrics:
Citation Count: 6
Downloads (6 Weeks): 0, Downloads (12 Months): 33, Downloads (Overall): 577
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Forty years ago, Wiesner pointed out that quantum mechanics raises the striking possibility of money that cannot be counterfeited according to the laws of physics. We propose the first quantum money scheme that is (1) publickeymeaning that anyone can verify a banknote as genuine, not only the bank that printed ...
Keywords:
multivariate polynomials, nocloning theorem, quantum computing, quantum cryptography, quantum money
4
July 2011
ICALP'11: Proceedings of the 38th international colloquim conference on Automata, languages and programming  Volume Part I
Publisher: SpringerVerlag
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 a surprising result that we prove: a quantum finite automaton with just two states ...
Keywords:
quantum computation, rootfinding, PSPACE, BQP, finite automata, finiteprecision arithmetic
5
June 2011
CSR'11: Proceedings of the 6th international conference on Computer science: theory and applications
Publisher: SpringerVerlag
In a sampling problem, we are given an input x ∈ {0, 1} n , and asked to sample approximately from a probability distribution D x over poly ( n )bit strings. In a search problem, we are given an input x ∈ {0, 1} n , and asked to ...
6
June 2011
STOC '11: Proceedings of the fortythird annual ACM symposium on Theory of computing
Publisher: ACM
Bibliometrics:
Citation Count: 15
Downloads (6 Weeks): 18, Downloads (12 Months): 201, Downloads (Overall): 1,545
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We give new evidence that quantum computers  moreover, rudimentary quantum computers built entirely out of linearoptical elements  cannot be efficiently simulated by classical computers. In particular, we define a model of computation in which identical photons are generated, sent through a linearoptical network, then nonadaptively measured to count ...
Keywords:
#p, BGP, bosons, linear optics, permanent, polynomial hierarchy, random selfreducibility, sampling
7
December 2010
Communications of the ACM: Volume 53 Issue 12, December 2010
Publisher: ACM
Bibliometrics:
Citation Count: 0
Downloads (6 Weeks): 3, Downloads (12 Months): 55, Downloads (Overall): 32,969
8
June 2010
STOC '10: Proceedings of the fortysecond ACM symposium on Theory of computing
Publisher: ACM
Bibliometrics:
Citation Count: 2
Downloads (6 Weeks): 1, Downloads (12 Months): 8, Downloads (Overall): 209
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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 to simulate rho on all quantum circuits of fixed polynomial size. ...
Keywords:
advice, boosting, compression, karplipton theorem, learning, local hamiltonians, nonuniform computation, quantum computation
9
June 2010
STOC '10: Proceedings of the fortysecond ACM symposium on Theory of computing
Publisher: ACM
Bibliometrics:
Citation Count: 15
Downloads (6 Weeks): 5, Downloads (12 Months): 57, Downloads (Overall): 372
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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 this question to topics in circuit complexity, pseudorandomness, and Fourier analysis. First, we show that there ...
Keywords:
constantdepth circuits, fourier analysis, linialnisan conjecture, quantum complexity classes
10
February 2009
ACM Transactions on Computation Theory (TOCT): Volume 1 Issue 1, February 2009
Publisher: ACM
Bibliometrics:
Citation Count: 29
Downloads (6 Weeks): 3, Downloads (12 Months): 49, Downloads (Overall): 1,362
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Any proof of P ≠ NP will have to overcome two barriers: relativization and natural proofs . Yet over the last decade, we have seen circuit lower bounds (e.g., that PP does not have linearsize circuits) that overcome both barriers simultaneously. So the question arises of whether there is a third barrier ...
Keywords:
Lowdegree polynomials, arithmetization, interactive proofs, oracles, communication complexity, query complexity
11
January 2009
Quantum Information & Computation: Volume 9 Issue 1, January 2009
Publisher: Rinton Press, Incorporated
Whether the class QMA (Quantum Merlin Arthur) is equal to QMA 1 , 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 give a "quantum oracle" relative to which QMA ...
12
October 2008
FOCS '08: Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Publisher: IEEE Computer Society
N/A
Keywords:
quantum, polynomial method
13
June 2008
CCC '08: Proceedings of the 2008 IEEE 23rd Annual Conference on Computational Complexity
Publisher: IEEE Computer Society
The class QMA(k), introduced by Kobayashi et al., consists of all languages that can be verified using k unentangled quantum proofs. Many of the simplest questions about this class have remained embarrassingly open: for example, can we give any evidence that k quantum proofs are more powerful than one? Can ...
Keywords:
quantum computing, entanglement, QMA, additivity, 3SAT, PCP Theorem
14
May 2008
STOC '08: Proceedings of the fortieth annual ACM symposium on Theory of computing
Publisher: ACM
Bibliometrics:
Citation Count: 19
Downloads (6 Weeks): 0, Downloads (12 Months): 8, Downloads (Overall): 474
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Any proof of P!=NP will have to overcome two barriers: relativization and natural proofs. Yet over the last decade, we have seen circuit lower bounds (for example, that PP does not have linearsize circuits) that overcome both barriers simultaneously. So the question arises of whether there is a third barrier ...
Keywords:
arithmetization, communication complexity, interactive proofs, lowdegree polynomials, oracles, query complexity
15
May 2008
Journal of Computer and System Sciences: Volume 74 Issue 3, May, 2008
Publisher: Academic Press, Inc.
Given a Boolean function f, we study two natural generalizations of the certificate complexity C(f): the randomized certificate complexity RC(f) and the quantum certificate complexity QC(f). Using Ambainis' adversary method, we exactly characterize QC(f) as the square root of RC(f). We then use this result to prove the new relation ...
Keywords:
Adversary method, Black box, Block sensitivity, Boolean function, Decision tree, MerlinArthur, Quantum computing, Query complexity
16
December 2007
ACM SIGACT News: Volume 38 Issue 4, December 2007
Publisher: ACM
Bibliometrics:
Citation Count: 0
Downloads (6 Weeks): 0, Downloads (12 Months): 9, Downloads (Overall): 102
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17
September 2007
CSR'07: Proceedings of the Second international conference on Computer Science: theory and applications
Publisher: SpringerVerlag
18
June 2007
CCC '07: Proceedings of the TwentySecond Annual IEEE Conference on Computational Complexity
Publisher: IEEE Computer Society
This paper studies whether quantum proofs are more powerful than classical proofs, or in complexity terms, whether QMA = QCMA. We prove three results about this question. First, we give a "quantum oracle separation" between QMA and QCMA. More concretely, we show that any quantum algorithm needs \Omega \left( {\sqrt ...
19
July 2006
CCC '06: Proceedings of the 21st Annual IEEE Conference on Computational Complexity
Publisher: IEEE Computer Society
Theoretical computer scientists have been debating the role of oracles since the 1970's. This paper illustrates both that oracles can give us nontrivial insights about the barrier problems in circuit complexity, and that they need not prevent us from trying to solve those problems.
20
July 2006
CCC '06: Proceedings of the 21st Annual IEEE Conference on Computational Complexity
Publisher: IEEE Computer Society
This paper introduces a new technique for removing existential quantifiers over quantum states. Using this technique, we show that there is no way to pack an exponential number of bits into a polynomialsize quantum state, in such a way that the value of any one of those bits can later ...

