114 research outputs found
On the query complexity of perfect gate discrimination
No full text© Giulio Chiribella, Giacomo Mauro D'Ariano, and Martin Roetteler;. We investigate the problem of finding the minimum number of queries needed to perfectly identify an unknown quantum gate within a finite set of alternatives, considering both deterministic strategies. For unambiguous gate discrimination, where errors are not tolerated but inconclusive outcomes are allowed, we prove that parallel strategies are sufficient to identify the unknown gate with minimum number of queries and we use this fact to provide upper and lower bounds on the query complexity. In addition, we introduce the notion of generalized t-designs, which includes unitary t-designs and group representations as special cases. For gates forming a generalized t-design we prove that there is no difference between perfect probabilistic and perfect deterministic gate discrimination. Hence, evaluating of the query complexity of perfect discrimination is reduced to the easier problem of evaluating the query complexity of unambiguous discrimination.link_to_subscribed_fulltex
Quantum Algorithms for Abelian Difference Sets and Applications to Dihedral Hidden Subgroups
No full textDifference sets are basic combinatorial structures that have applications in signal processing, coding theory, and cryptography. We consider the problem of identifying a shifted version of the characteristic function of a (known) difference set and present a general algorithm that can be used to tackle any hidden shift problem for any difference set in any abelian group. We discuss special cases of this framework which include a) Paley difference sets based on quadratic residues in finite fields which allow to recover the shifted Legendre function quantum algorithm, b) Hadamard difference sets which allow to recover the shifted bent function quantum algorithm, and c) Singer difference sets which allow us to define instances of the dihedral hidden subgroup problem which can be efficiently solved on a quantum computer
Quantum Linear Network Coding as One-way Quantum Computation
No full textNetwork coding is a technique to maximize communication rates within a network, in communication protocols for simultaneous multi-party transmission of information. Linear network codes are examples of such protocols in which the local computations performed at the nodes in the network are limited to linear transformations of their input data (represented as elements of a ring, such as the integers modulo 2). The quantum linear network coding protocols of Kobayashi et al. coherently simulate classical linear network codes, using supplemental classical communication. We demonstrate that these protocols correspond in a natural way to measurement-based quantum computations with graph states over qudits having a structure directly related to the network
Improved reversible and quantum circuits for Karatsuba-based integer multiplication
No full textInteger arithmetic is the underpinning of many quantum algorithms, with applications ranging from Shor's algorithm over HHL for matrix inversion to Hamiltonian simulation algorithms. A basic objective is to keep the required resources to implement arithmetic as low as possible. This applies in particular to the number of qubits required in the implementation as for the foreseeable future this number is expected to be small. We present a reversible circuit for integer multiplication that is inspired by Karatsuba's recursive method. The main improvement over circuits that have been previously reported in the literature is an asymptotic reduction of the amount of space required from O(n^1.585) to O(n^1.427). This improvement is obtained in exchange for a small constant increase in the number of operations by a factor less than 2 and a small asymptotic increase in depth for the parallel version. The asymptotic improvement are obtained from analyzing pebble games on complete ternary trees
Quantum Programming Languages (Dagstuhl Seminar 18381)
No full textThis report documents the program and the outcomes of Dagstuhl Seminar
18381 "Quantum Programming Languages", which brought together researchers from quantum computing and classical programming languages
Quantum Cryptanalysis (Dagstuhl Seminar 15371)
No full textThis report documents the program and the outcomes of Dagstuhl Seminar 15371 "Quantum Cryptanalysis". In this seminar, participants explored the impact that quantum algorithms will have on cryptology once a large-scale quantum computer becomes available. Research highlights in this seminar included both computational resource requirement and availability estimates for meaningful quantum cryptanalytic attacks against conventional cryptography, as well as the security of proposed quantum-safe cryptosystems against emerging quantum cryptanalytic attacks
Easy and Hard Functions for the Boolean Hidden Shift Problem
No full textWe study the quantum query complexity of the Boolean hidden shift problem. Given oracle access to f(x+s) for a known Boolean function f, the task is to determine the n-bit string s. The quantum query complexity of this problem depends strongly on f. We demonstrate that the easiest instances of this problem correspond to bent functions, in the sense that an exact one-query algorithm exists if and only if the function is bent. We partially characterize the hardest instances, which include delta functions. Moreover, we show that the problem is easy for random functions, since two queries suffice. Our algorithm for random functions is based on performing the pretty good measurement on several copies of a certain state; its analysis relies on the Fourier transform. We also use this approach to improve the quantum rejection sampling approach to the Boolean hidden shift problem
Self-testing graph states
No full text10.1007/978-3-642-54429-3-7Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)6745 LNCS104-12
Efficient Decoupling Schemes Based on Hamilton Cycles
No full textDecoupling the interactions in a spin network governed by a pair-interaction
Hamiltonian is a well-studied problem. Combinatorial schemes for decoupling and
for manipulating the couplings of Hamiltonians have been developed which use
selective pulses. In this paper we consider an additional requirement on these
pulse sequences: as few {\em different} control operations as possible should
be used. This requirement is motivated by the fact that optimizing each
individual selective pulse will be expensive, i. e., it is desirable to use as
few different selective pulses as possible. For an arbitrary -dimensional
system we show that the ability to implement only two control operations is
sufficient to turn off the time evolution. In case of a bipartite system with
local control we show that four different control operations are sufficient.
Turning to networks consisting of several -dimensional nodes which are
governed by a pair-interaction Hamiltonian, we show that decoupling can be
achieved if one is able to control a number of different control operations
which is logarithmic in the number of nodes.Comment: 4 pages, 1 figure, uses revtex
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