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63
Quantum Programming Language
, 2007
"... This work would not be realized without support of many people who helped me both proffessionally and personally. I would like to thank my supervisor, Jozef Gruska, for his guidance, support and advices during my PhD studies. I would like also to express my thanks to Lukáˇs Boháč, Jan Bouda, Simon G ..."
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Gay, Philippe Jorrand, Rajagopal Nagarajan, Nick Papanikolaou, Simon Perdrix, Igor Peterlík, Libor ˇ Skarvada, Josef ˇ Sprojcar and Tomoyuki Yamakami for their enthusiasm and invaluable comments on LanQ and related discussions. I would like to particularly thank to Rajagopal Nagarajan and Nick
Quantum MerlinArthur Proof Systems: Are Multiple Merlins More Helpful to Arthur?
, 2008
"... This paper introduces quantum “multipleMerlin”Arthur proof systems in which Arthur receives multiple quantum proofs that are unentangled with each other. Although classical multiproof systems are obviously equivalent to classical singleproof systems (i.e., usual MerlinArthur proof systems), it ..."
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Cited by 40 (7 self)
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This paper introduces quantum “multipleMerlin”Arthur proof systems in which Arthur receives multiple quantum proofs that are unentangled with each other. Although classical multiproof systems are obviously equivalent to classical singleproof systems (i.e., usual MerlinArthur proof systems), it is unclear whether or not quantum multiproof systems collapse to quantum singleproof systems (i.e., usual quantum MerlinArthur proof systems). This paper presents a necessary and sufficient condition under which the number of quantum proofs is reducible to two. It is also proved that, in the case of perfect soundness, using multiple quantum proofs
Quantum measurements for hidden subgroup problems with optimal sample
 Quantum Information and Computation
, 2008
"... One of the central issues in the hidden subgroup problem is to bound the sample complexity, i.e., the number of identical samples of coset states sufficient and necessary to solve the problem. In this paper, we present general bounds for the sample complexity of the identification and decision versi ..."
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Cited by 16 (2 self)
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One of the central issues in the hidden subgroup problem is to bound the sample complexity, i.e., the number of identical samples of coset states sufficient and necessary to solve the problem. In this paper, we present general bounds for the sample complexity of the identification and decision versions of the hidden subgroup problem. As a consequence of the bounds, we show that the sample complexity for both of the decision and identification versions isΘ(logH / log p) for a candidate setH of hidden subgroups in the case that the candidate subgroups have the same prime order p, which implies that the decision version is at least as hard as the identification version in this case. In particular, it does so for the important instances such as the dihedral and the symmetric hidden subgroup problems. Moreover, the upper bound of the identification is attained by the pretty good measurement, which shows that the pretty good measurements can identify any hidden subgroup of an arbitrary group with at most O(logH) samples. 1
Quantum Minimal One Way Information: Relative Hardness and Quantum Advantage of Combinatorial Tasks
, 2005
"... Abstract. Twoparty oneway quantum communication has been extensively studied in the recent literature. We target the size of minimal information that is necessary for a feasible party to finish a given combinatorial task, such as distinction of instances, using oneway communication from another p ..."
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Abstract. Twoparty oneway quantum communication has been extensively studied in the recent literature. We target the size of minimal information that is necessary for a feasible party to finish a given combinatorial task, such as distinction of instances, using oneway communication from another party. This type of complexity measure has been studied under various names: advice complexity, Kolmogorov complexity, distinguishing complexity, and instance complexity. We present a general framework focusing on underlying combinatorial takes to study these complexity measures using quantum information processing. We introduce the key notions of relative hardness and quantum advantage, which provide the foundations for taskbased quantum minimal oneway information complexity theory.
A foundation of programming a multitape quantum Turing machine
 in Proceedings of the 24th International Symposium on Mathematical Foundation of Computer Science, Lecture Notes in Computer Science
, 1999
"... Abstract. The notion of quantum Turing machines is a basis of quantum complexity theory. We discuss a general model of multitape, multihead Quantum Turing machines with multi final states that also allow tape heads to stay still. 1 ..."
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Cited by 17 (12 self)
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Abstract. The notion of quantum Turing machines is a basis of quantum complexity theory. We discuss a general model of multitape, multihead Quantum Turing machines with multi final states that also allow tape heads to stay still. 1
Computational indistinguishability between quantum states and its cryptographic application
 Advances in Cryptology – EUROCRYPT 2005
, 2005
"... We introduce a computational problem of distinguishing between two specific quantum states as a new cryptographic problem to design a quantum cryptographic scheme that is “secure ” against any polynomialtime quantum adversary. Our problem QSCDff is to distinguish between two types of random coset s ..."
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Cited by 14 (6 self)
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We introduce a computational problem of distinguishing between two specific quantum states as a new cryptographic problem to design a quantum cryptographic scheme that is “secure ” against any polynomialtime quantum adversary. Our problem QSCDff is to distinguish between two types of random coset states with a hidden permutation over the symmetric group of finite degree. This naturally generalizes the commonlyused distinction problem between two probability distributions in computational cryptography. As our major contribution, we show three cryptographic properties: (i) QSCDff has the trapdoor property; (ii) the averagecase hardness of QSCDff coincides with its worstcase hardness; and (iii) QSCDff is computationally at least as hard in the worst case as the graph automorphism problem. These cryptographic properties enable us to construct a quantum publickey cryptosystem, which is likely to withstand any chosen plaintext attack of a polynomialtime quantum adversary. We further discuss a generalization of QSCDff, called QSCDcyc, and introduce a multibit encryption scheme relying on the cryptographic properties of QSCDcyc.
Polynomial time quantum computation with advice
 Inform. Proc. Lett., 90:195–204, 2003. ECCC
"... Abstract. Advice is supplementary information that enhances the computational power of an underlying computation. This paper focuses on advice that is given in the form of a pure quantum state. The notion of advised quantum computation has a direct connection to nonuniform quantum circuits and tall ..."
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Cited by 12 (2 self)
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Abstract. Advice is supplementary information that enhances the computational power of an underlying computation. This paper focuses on advice that is given in the form of a pure quantum state. The notion of advised quantum computation has a direct connection to nonuniform quantum circuits and tally languages. The paper examines the influence of such advice on the behaviors of an underlying polynomialtime quantum computation with boundederror probability and shows a power and a limitation of advice. Key Words: computational complexity, quantum circuit, advice function 1
A Tight Relationship between Generic Oracles and Type2 Complexity Theory
, 1997
"... We show that any two complexity classes satisfying some general conditions are distinct relative to a generic oracle iff the corresponding type2 classes are distinct. ..."
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Cited by 7 (1 self)
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We show that any two complexity classes satisfying some general conditions are distinct relative to a generic oracle iff the corresponding type2 classes are distinct.
Sets Computable in Polynomial Time on Average
, 1995
"... . In this paper, we discuss the complexity and properties of the sets which are computable in polynomialtime on average. This study is motivated by Levin's question of whether all sets in NP are solvable in polynomialtime on average for every reasonable (i.e., polynomialtime computable) d ..."
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Cited by 8 (3 self)
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. In this paper, we discuss the complexity and properties of the sets which are computable in polynomialtime on average. This study is motivated by Levin's question of whether all sets in NP are solvable in polynomialtime on average for every reasonable (i.e., polynomialtime computable) distribution on the instances. Let PPcomp denote the class of all those sets which are computable in polynomialtime on average for every polynomialtime computable distribution on the instances. It is known that P ( PPcomp ( E. In this paper, we show that PPcomp is not contained in DTIME(2 cn ) for any constant c and that it lacks some basic structural properties: for example, it is not closed under manyone reducibility or for the existential operator. From these results, it follows that PPcomp contains Pimmune sets but no Pbiimmune sets; it is not included in P=cn for any constant c; and it is different from most of the wellknown complexity classes, such as UP, NP, BPP, and ...
Exponential separation of quantum and classical online space complexity
 In 18th ACM SPAA
, 2006
"... Abstract. Although quantum algorithms realizing an exponential time speedup over the best known classical algorithms exist, no quantum algorithm is known performing computation using less space resources than classical algorithms. In this paper, we study, for the first time explicitly, spacebounde ..."
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Cited by 8 (0 self)
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Abstract. Although quantum algorithms realizing an exponential time speedup over the best known classical algorithms exist, no quantum algorithm is known performing computation using less space resources than classical algorithms. In this paper, we study, for the first time explicitly, spacebounded quantum algorithms for computational problems where the input is given not as a whole, but bit by bit. We show that there exist such problems that a quantum computer can solve using exponentially less work space than a classical computer. More precisely, we introduce a very natural and simple model of a spacebounded quantum online machine and prove an exponential separation of classical and quantum online space complexity, in the boundederror setting and for a total language. The language we consider is inspired by a communication problem (the disjointness function) that Buhrman, Cleve and Wigderson used to show an almost quadratic separation of quantum and classical boundederror communication complexity. We prove that, in the framework of online space complexity, the separation becomes exponential. 1
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