2005
DOI: 10.1016/j.tcs.2004.12.031
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Quantum branching programs and space-bounded nonuniform quantum complexity

Abstract: In this paper, the space complexity of nonuniform quantum algorithms is investigated using the model of quantum branching programs (QBPs). In order to clarify the relationship between QBPs and nonuniform quantum Turing machines, simulations between these two models are presented which allow to transfer upper and lower bound results. Exploiting additional insights about the connection between the running time and the precision of amplitudes, it is shown that nonuniform quantum Turing machines with algebraic amp… Show more

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Cited by 36 publications
(39 citation statements)
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References 42 publications
(106 reference statements)
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“…Polylogarithmic Memory We start by analyzing the model with polylogarithmic size of memory. Let us apply the Black Hats Method from Section 3 to a Boolean function R ν,l,m,u : {0, 1} n → {0, 1} from [24]: Let |1 , . .…”
Section: Quantum Vs Classical Algorithmsmentioning
confidence: 99%
See 1 more Smart Citation
“…Polylogarithmic Memory We start by analyzing the model with polylogarithmic size of memory. Let us apply the Black Hats Method from Section 3 to a Boolean function R ν,l,m,u : {0, 1} n → {0, 1} from [24]: Let |1 , . .…”
Section: Quantum Vs Classical Algorithmsmentioning
confidence: 99%
“…Otherwise the function is undefined. It is known from [24] that there is a quantum OBDD that computes R ν,l,m,u using linear width. At the same time, any deterministic or probabilistic OBDD requires exponential width.…”
Section: Quantum Vs Classical Algorithmsmentioning
confidence: 99%
“…And it can be seen as nonuniform automata (see for example [AG05]). In the last decades quantum OBDDs came into play [AGK01], [NHK00], [SS05a], [Sau06].…”
Section: Introductionmentioning
confidence: 99%
“…Authors presented quantum OBDD of width O(log p) for this function (another quantum OBDD of same width is presented in [AV08]) and proved that any deterministic OBDD has width at least p. However explicit function M OD p presents a gap for OBDD of at most linear width. For bigger width it was shown that Boolean function P ERM has not deterministic OBDD of width less than 2 √ n/2 /( √ n/2) 3/2 [KMW91] and M. Sauerhoff and D. Sieling [SS05b] constructed quantum OBDD of width O(n 2 log n). F. Ablayev, A. Khasianov and A. Vasiliev [AKV08] presented the quantum OBDD of width O(n log n) for P ERM .…”
Section: Introductionmentioning
confidence: 99%
“…For example, it was shown that randomized OBDDs can be exponentially more efficient than deterministic and nondeterministic OBDDs [6], and, quantum OBDDs can be exponentially more effcient than deterministic and stable probabilistic OBDD and that this bound is tight [3]. In [17] some simple functions were presented such that unitary OBDDs (the known most restricted quantum OBDD) need exponential size for computing these functions with bounded error, while ⋆ Some parts of this work was done during Gainutdinova's visit to National Laboratory for Scientific Computing (Brazil) in June 2015 supported by CAPES with grant 88881.030338/2013-01. ⋆⋆ Partially supported by CAPES with grant 88881.030338/2013-01 and ERC Advanced Grant MQC.…”
Section: Introductionmentioning
confidence: 99%