14 research outputs found
Upper bounds on quantum query complexity inspired by the Elitzur-Vaidman bomb tester
Inspired by the Elitzur-Vaidman bomb testing problem [arXiv:hep-th/9305002],
we introduce a new query complexity model, which we call bomb query complexity
. We investigate its relationship with the usual quantum query complexity
, and show that .
This result gives a new method to upper bound the quantum query complexity:
we give a method of finding bomb query algorithms from classical algorithms,
which then provide nonconstructive upper bounds on .
We subsequently were able to give explicit quantum algorithms matching our
upper bound method. We apply this method on the single-source shortest paths
problem on unweighted graphs, obtaining an algorithm with quantum
query complexity, improving the best known algorithm of [arXiv:quant-ph/0606127]. Applying this method to the maximum bipartite
matching problem gives an algorithm, improving the best known
trivial upper bound.Comment: 32 pages. Minor revisions and corrections. Regev and Schiff's proof
that P(OR) = \Omega(N) remove
Quantum-accelerated constraint programming
Constraint programming (CP) is a paradigm used to model and solve constraint
satisfaction and combinatorial optimization problems. In CP, problems are
modeled with constraints that describe acceptable solutions and solved with
backtracking tree search augmented with logical inference. In this paper, we
show how quantum algorithms can accelerate CP, at both the levels of inference
and search. Leveraging existing quantum algorithms, we introduce a
quantum-accelerated filtering algorithm for the global
constraint and discuss its applicability to a broader family of global
constraints with similar structure. We propose frameworks for the integration
of quantum filtering algorithms within both classical and quantum backtracking
search schemes, including a novel hybrid classical-quantum backtracking search
method. This work suggests that CP is a promising candidate application for
early fault-tolerant quantum computers and beyond.Comment: published in Quantu
Quantum Query Algorithms
Elektroniskā versija nesatur pielikumusLELDE LĀCE
KVANTU VAICĀJOŠIE ALGORITMI
ANOTĀCIJA
Kvantu skaitļošana ir datorzinātņu apakšnozare, kurā tiek izmantotas kvantu mehānikas īpatnības, lai efektīvāk risinātu skaitļošanas uzdevumus. Šajā darbā tiek aplūkoti kvantu vaicājošie algoritmi Bula funkciju rēķināšanai.
Darba sākumā tiek pierādīti kvantu algoritmu apakšējie novērtējumi dažādām funkcijām, kas apraksta grafu problēmas. Promocijas darba galvenais uzdevums ir izveidot efektīvus kvantu vaicājošos algoritmus. Ir nodefinēts kā veidot precīzus kvantu vaicājošos algoritmus ar sarežģītību n-1, 2n/3 un n/2. Darba turpinājumā tiek analizēti nedeterminētie kvantu algoritmi ar vienu jautājumu, to veidošanas iespējas un īpašības. Promocijas darbā tiek definēts jauns kvantu vaicājošo algoritmu veids - kvantu vaicājošie algoritmi ar pēcatlasi un tiek pierādīta šo algoritmu saistība ar nedeterminētajiem kvantu vaicājošajiem algoritmiem.LELDE LĀCE
QUANTUM QUERY ALGORITHMS
ANNOTATION
Quantum computing is the subfield of computer science that aims to employ effects of quantum mechanics to efficiently perform computational tasks. The main research object of this work is quantum query model to compute Boolean functions.
At first we prove higher lower bounds of quantum query algorithms for some of graph problems. Main purpose of the research is to find quantum query algorithms with complexity lower than deterministic one. The work presents a set of new exact quantum algorithms with quantum query complexity n-1, 2n/3 and n/2. We construct some nondeterministic quantum query algorithms with complexity 1 for Boolean functions with 2, 4 and 2n variables and study some properties of these functions. We propose definition of postselection quantum query algorithm and we propose one method how to make postselection quantum query algorithms
Control and Verification of Quantum Mechanical Systems
Quantum information science uses the distinguishing features of quantum mechanics for novel information processing tasks, ranging from metrology to computation. This manuscript explores multiple topics in this field. We discuss implementations of hybrid quantum systems composed of trapped ions and superconducting circuits, protocols for detecting signatures of entanglement in small and many-body systems, and a proposal for ground state preparation in quantum Hamiltonian simulators