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Volumn 4, Issue 3, 2014, Pages

Quantum speedup for active learning agents

Author keywords

Interdisciplinary physics; Quantum information; Quantum physics

Indexed keywords

INTELLIGENT AGENTS; QUANTUM OPTICS; QUANTUM THEORY;

EID: 84904537776     PISSN: None     EISSN: 21603308     Source Type: Journal    
DOI: 10.1103/PhysRevX.4.031002     Document Type: Article
Times cited : (251)

References (62)
  • 1
    • 0022421379 scopus 로고
    • Quantum Theory, The Church-Turing Principle and the Universal Quantum Computer
    • D. Deutsch, Quantum Theory, The Church-Turing Principle and the Universal Quantum Computer, Proc. R. Soc. A 400, 97 (1985)
    • (1985) Proc. R. Soc. A , vol.400 , pp. 97
    • Deutsch, D.1
  • 2
    • 0000119236 scopus 로고
    • Rapid Solution of Problems by Quantum Computation
    • D. Deutsch and R. Jozsa, Rapid Solution of Problems by Quantum Computation, Proc. R. Soc. A 439, 553 (1992)
    • (1992) Proc. R. Soc. A , vol.439 , pp. 553
    • Deutsch, D.1    Jozsa, R.2
  • 7
    • 84983710547 scopus 로고    scopus 로고
    • Quantum Learning and Universal Quantum Matching Machine
    • M. Sasaki and A. Carlini, Quantum Learning and Universal Quantum Matching Machine, Phys. Rev. A 66, 022303 (2002)
    • (2002) Phys. Rev. A , vol.66 , pp. 022303
    • Sasaki, M.1    Carlini, A.2
  • 10
    • 72049087760 scopus 로고    scopus 로고
    • The Speed of Quantum and Classical Learning for Performing the kth Root of Not
    • D. Manzano, M. Pawłowski, and Č. Brukner, The Speed of Quantum and Classical Learning for Performing the kth Root of Not, New J. Phys. 11, 113018 (2009)
    • (2009) New J. Phys. , vol.11 , pp. 113018
    • Manzano, D.1    Pawłowski, M.2    Brukner, Č.3
  • 11
  • 12
    • 84880558954 scopus 로고    scopus 로고
    • Quantum Speed-up for Unsupervised Learning
    • E. Aïmeur, G. Brassard, and S. Gambs, Quantum Speed-up for Unsupervised Learning, Mach. Learn. 90, 261 (2013)
    • (2013) Mach. Learn. , vol.90 , pp. 261
    • Aïmeur, E.1    Brassard, G.2    Gambs, S.3
  • 19
    • 84861122307 scopus 로고    scopus 로고
    • Projective Simulation for Artificial Intelligence
    • H. J. Briegel and G. De las Cuevas, Projective Simulation for Artificial Intelligence, Sci. Rep. 2, 400 (2012)
    • (2012) Sci. Rep. , vol.2 , pp. 400
    • Briegel, H.J.1    De Las Cuevas, G.2
  • 22
    • 84904564782 scopus 로고    scopus 로고
    • AIBO, adapted from, created by Rama, and licensed under the CC-BY-SA-2.0-FR
    • AIBO, adapted from http://commons.wikimedia.org/wiki/ Category:Aibo#mediaviewer/File:Aibo_img_0807.jpg, created by Rama, and licensed under the CC-BY-SA-2.0-FR
  • 25
    • 84904571933 scopus 로고    scopus 로고
    • Examples of such applications include the problems of navigation, or human-robot interaction. We note that the focus on such classical environments is by no means a restriction of our scheme. For a quantum environment, the actions that the agent can perform could, e.g., be quantum measurements (as components of his actuators), and percepts the measurement outcomes-such scenarios are certainly not without interest. The results we present in this work apply equally to such environments. However, we will not explore the applications of learning agents in quantum environments in this paper
    • Examples of such applications include the problems of navigation, or human-robot interaction. We note that the focus on such classical environments is by no means a restriction of our scheme. For a quantum environment, the actions that the agent can perform could, e.g., be quantum measurements (as components of his actuators), and percepts the measurement outcomes-such scenarios are certainly not without interest. The results we present in this work apply equally to such environments. However, we will not explore the applications of learning agents in quantum environments in this paper
  • 26
    • 84904542330 scopus 로고    scopus 로고
    • Even if we were to allow superpositions of actions, the amount of control the agent must have over the degrees of freedom of the environment, in order to apply quantum query algorithms, may be prohibitive. This problem constitutes one of the fundamental operative distinctions between quantum algorithms, where full control is assumed, and quantum agents, where such control is limited
    • Even if we were to allow superpositions of actions, the amount of control the agent must have over the degrees of freedom of the environment, in order to apply quantum query algorithms, may be prohibitive. This problem constitutes one of the fundamental operative distinctions between quantum algorithms, where full control is assumed, and quantum agents, where such control is limited
  • 27
    • 84904545182 scopus 로고    scopus 로고
    • In embodied agents, these physical processes may, e.g., realize some internal representation of the environment, which the agent itself has to develop as it interacts with the environment. For example, in the context of artificial neural networks, such internal models are known as selforganizing maps and, more specifically, sensorimotor maps [58,59]
    • In embodied agents, these physical processes may, e.g., realize some internal representation of the environment, which the agent itself has to develop as it interacts with the environment. For example, in the context of artificial neural networks, such internal models are known as selforganizing maps and, more specifically, sensorimotor maps [58,59]
  • 28
    • 84904563139 scopus 로고    scopus 로고
    • In the PS framework, one formally distinguishes between real percepts and actions s and a and their internal representations, denoted as ({eth}s{Thorn} and ({eth}a{Thorn}, which comprise clips. For our purposes, by abuse of notation, we will omit the mapping (. For more details, see Appendix C
    • In the PS framework, one formally distinguishes between real percepts and actions s and a and their internal representations, denoted as μ{eth}s{Thorn} and μ{eth}a{Thorn}, which comprise clips. For our purposes, by abuse of notation, we will omit the mapping μ. For more details, see Appendix C
  • 29
    • 84904560215 scopus 로고    scopus 로고
    • In the PS, the hopping probabilities themselves are encoded in the so-called h matrix, which is an unnormalized representation of the transition matrix [19]
    • In the PS, the hopping probabilities themselves are encoded in the so-called h matrix, which is an unnormalized representation of the transition matrix [19]
  • 30
    • 84904570959 scopus 로고    scopus 로고
    • Each agent is equipped with input and output couplers, which translate, through sensors and actuators (see Fig. 1), real percepts to the internal representations of percepts, and internal representations of actions to real actions
    • Each agent is equipped with input and output couplers, which translate, through sensors and actuators (see Fig. 1), real percepts to the internal representations of percepts, and internal representations of actions to real actions
  • 31
    • 84904541995 scopus 로고    scopus 로고
    • In this paper, we do not consider logarithmically contributing terms in the complexity analysis; thus, we use the Õ -level analysis of the limiting behavior (instead of the standard "big-O" O)
    • In this paper, we do not consider logarithmically contributing terms in the complexity analysis; thus, we use the Õ -level analysis of the limiting behavior (instead of the standard "big-O" O)
  • 35
    • 84904547704 scopus 로고    scopus 로고
    • The optimality claim holds provided that no additional mechanisms, except for diffusion and checking, are available to the agent
    • The optimality claim holds provided that no additional mechanisms, except for diffusion and checking, are available to the agent
  • 38
    • 53349157069 scopus 로고    scopus 로고
    • Quantum Simulations of Classical Annealing Processes
    • R. D. Somma, S. Boixo, H. Barnum, and E. Knill, Quantum Simulations of Classical Annealing Processes, Phys. Rev. Lett. 101, 130504 (2008)
    • (2008) Phys. Rev. Lett. , vol.101 , pp. 130504
    • Somma, R.D.1    Boixo, S.2    Barnum, H.3    Knill, E.4
  • 39
    • 55749115823 scopus 로고    scopus 로고
    • Speedup via Quantum Sampling
    • P. Wocjan and A. Abeyesinghe, Speedup via Quantum Sampling, Phys. Rev. A 78, 042336 (2008)
    • (2008) Phys. Rev. A , vol.78 , pp. 042336
    • Wocjan, P.1    Abeyesinghe, A.2
  • 40
    • 84904567355 scopus 로고    scopus 로고
    • *, so V can be constructed from U by conjugating it with the swap operator of the two registers. Here, we present the construction for the general case of irreducible, aperiodic Markov chains
    • *, so V can be constructed from U by conjugating it with the swap operator of the two registers. Here, we present the construction for the general case of irreducible, aperiodic Markov chains
  • 41
    • 84904574929 scopus 로고    scopus 로고
    • Here, we note that concrete applications of quantum walks specified by nonsymmetric Markov chains have, to our knowledge and aside from this work, only been studied in Refs. [60,61], by two of the authors and other collaborators, in a significantly different context
    • Here, we note that concrete applications of quantum walks specified by nonsymmetric Markov chains have, to our knowledge and aside from this work, only been studied in Refs. [60,61], by two of the authors and other collaborators, in a significantly different context
  • 42
    • 84904542178 scopus 로고    scopus 로고
    • For completeness, we note, as a technicality, following Ref. [24], that if ?s is always bounded below by a known constant (say, 3=4, as in Ref. [43]), the quantum agent can immediately measure the initial state and efficiently produce the desired output by iterating this process a constant number of times. However, in the scenarios we envision, ?s is very small
    • s is very small
  • 44
    • 84904549753 scopus 로고    scopus 로고
    • We note that some of the only logarithmically contributing terms, which appear in a more detailed analysis omitted here, can be further avoided using more complicated constructions, as has, for instance, been done in Ref. [24]
    • We note that some of the only logarithmically contributing terms, which appear in a more detailed analysis omitted here, can be further avoided using more complicated constructions, as has, for instance, been done in Ref. [24]
  • 45
    • 84859353883 scopus 로고    scopus 로고
    • Photonic Quantum Simulators
    • A. Aspuru-Guzik and P. Walther, Photonic Quantum Simulators, Nat. Phys. 8, 285 (2012)
    • (2012) Nat. Phys. , vol.8 , pp. 285
    • Aspuru-Guzik, A.1    Walther, P.2
  • 46
    • 84859312162 scopus 로고    scopus 로고
    • Quantum Simulations with Trapped Ions
    • R. Blatt and C. F. Roos, Quantum Simulations with Trapped Ions, Nat. Phys. 8, 277 (2012)
    • (2012) Nat. Phys. , vol.8 , pp. 277
    • Blatt, R.1    Roos, C.F.2
  • 48
    • 0000459353 scopus 로고    scopus 로고
    • The Lack of A Priori Distinctions between Learning Algorithms
    • D. H. Wolpert, The Lack of A Priori Distinctions between Learning Algorithms, Neural Comput. 8, 1341 (1996)
    • (1996) Neural Comput , vol.8 , pp. 1341
    • Wolpert, D.H.1
  • 49
    • 84904580627 scopus 로고    scopus 로고
    • Optimization with Randomized Search Heuristics-The (a)nfl Theorem, Realistic Scenarios, and Difficult Functions
    • S. Droste, T. Jansen, and I. Wegener, Optimization with Randomized Search Heuristics-The (a)nfl Theorem, Realistic Scenarios, and Difficult Functions, Theor. Comput. Sci. 287, 2002 (1997)
    • (1997) Theor. Comput. Sci. , vol.287 , pp. 2002
    • Droste, S.1    Jansen, T.2    Wegener, I.3
  • 50
    • 84904571746 scopus 로고    scopus 로고
    • We acknowledge that the interpretation of these results in the sense of their practical impact on the field is not without controversy. Nonetheless, the validity of the mathematical statements is not contested. See Ref. [62] for more details
    • We acknowledge that the interpretation of these results in the sense of their practical impact on the field is not without controversy. Nonetheless, the validity of the mathematical statements is not contested. See Ref. [62] for more details
  • 51
    • 84904570793 scopus 로고    scopus 로고
    • That is, a comparison can be made with no further assumptions on the environment beyond the trivial ones -that the percept and action sets are compatible with the environment and that the environment provides a rewarding scheme
    • That is, a comparison can be made with no further assumptions on the environment beyond the trivial ones -that the percept and action sets are compatible with the environment and that the environment provides a rewarding scheme
  • 54
    • 84864253463 scopus 로고    scopus 로고
    • On Creative Machines and the Physical Origins of Freedom
    • H. J. Briegel, On Creative Machines and the Physical Origins of Freedom, Sci. Rep. 2, 522 (2012)
    • (2012) Sci. Rep. , vol.2 , pp. 522
    • Briegel, H.J.1
  • 55
    • 38549152759 scopus 로고    scopus 로고
    • Quantum Algorithms for the Triangle Problem
    • F. Magniez, M. Santha, and M. Szegedy, Quantum Algorithms for the Triangle Problem, SIAM J. Comput. 37, 413 (2007)
    • (2007) SIAM J. Comput. , vol.37 , pp. 413
    • Magniez, F.1    Santha, M.2    Szegedy, M.3
  • 57
    • 84904555007 scopus 로고    scopus 로고
    • Additionally, the quality of the approximation can be, probabilistically, arbitrarily raised by one round of the phase-estimation algorithm for the walk operator, provided that no phase is detected. Should this process fail, the unsearching process is repeated
    • Additionally, the quality of the approximation can be, probabilistically, arbitrarily raised by one round of the phase-estimation algorithm for the walk operator, provided that no phase is detected. Should this process fail, the unsearching process is repeated
  • 59
    • 33646454112 scopus 로고    scopus 로고
    • A Sensorimotor Map: Modulating Lateral Interactions for Anticipation and Planning
    • M. Toussaint, A Sensorimotor Map: Modulating Lateral Interactions for Anticipation and Planning, Neural Comput. 18, 1132 (2006)
    • (2006) Neural Comput , vol.18 , pp. 1132
    • Toussaint, M.1
  • 62
    • 84904570841 scopus 로고    scopus 로고
    • An introduction to discussions regarding the no free lunch theorems, and their interpretations, can be found at
    • An introduction to discussions regarding the no free lunch theorems, and their interpretations, can be found at http:// no-free-lunch.org/


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.