scholarly journals Control Theoretical Expression of Quantum Systems And Lower Bound of Finite Horizon Quantum Algorithms

2007 ◽  
Author(s):  
Masahiro Yanagisawa
Keyword(s):  
Lower Bound ◽  
Quantum Algorithms ◽  
Quantum Systems ◽  
Finite Horizon ◽  
Theoretical Expression

scholarly journals Selective Phase Rotation Quantum Gate Entangler

2009 ◽  
Vol 16 (04) ◽  
pp. 407-412
Author(s):  
Hoshang Heydari
Keyword(s):  
Integral Transform ◽  
Quantum Algorithms ◽  
Quantum Systems ◽  
Quantum Gate ◽  
Multipartite Quantum Systems ◽  
Phase Rotation ◽  
Quantum Integral ◽  
Qubit States

We construct a quantum gate entangler for multi-qubit states based on a selective phase rotation transform. In particular, we establish a relation between the quantum integral transform and the quantum gate entangler in terms of universal controlled gates for multi-qubit states. Our result gives an effective way of constructing topological and geometrical quantum gate entanglers for multipartite quantum systems, which could also lead to a construction of geometrical quantum algorithms.

scholarly journals Using quantum computing to create efficient algorithms

2021 ◽  
Vol 2056 (1) ◽  
pp. 012059
Author(s):  
I N Balaba ◽  
G S Deryabina ◽  
I A Pinchuk ◽  
I V Sergeev ◽  
S B Zabelina
Keyword(s):  
Quantum Mechanics ◽  
Quantum Computing ◽  
Computational Model ◽  
Exponential Growth ◽  
Quantum Algorithms ◽  
Quantum Systems ◽  
Efficient Algorithms ◽  
Historical Overview ◽  
Computing Model ◽  
Computational Strategy

Abstract The article presents a historical overview of the development of the mathematical idea of a quantum computing model - a new computational strategy based on the postulates of quantum mechanics and having advantages over the traditional computational model based on the Turing machine; clarified the features of the operation of multi-qubit quantum systems, which ensure the creation of efficient algorithms; the principles of quantum computing are outlined and a number of efficient quantum algorithms are described that allow solving the problem of exponential growth of the complexity of certain problems.

scholarly journals Algorithms for Quantum Systems - Quantum Algorithms

2005 ◽  
pp. 1-13
Author(s):  
Th. Beth ◽  
M. Grassl ◽  
D. Janzing ◽  
M. Rötteler ◽  
P. Wocjan ◽  
...  
Keyword(s):  
Quantum Algorithms ◽  
Quantum Systems

scholarly journals COMPLEMENTARITY IN GENERIC OPEN QUANTUM SYSTEMS

2010 ◽  
Vol 24 (24) ◽  
pp. 2485-2509 ◽  
Author(s):  
SUBHASHISH BANERJEE ◽  
R. SRIKANTH
Keyword(s):  
Lower Bound ◽  
Uniform Distribution ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Atomic Systems ◽  
Information Theoretic ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
The Difference ◽  
Positive Operator Valued Measure

We develop a unified, information theoretic interpretation of the number-phase complementarity that is applicable both to finite-dimensional (atomic) and infinite-dimensional (oscillator) systems, with number treated as a discrete Hermitian observable and phase as a continuous positive operator valued measure (POVM). The relevant uncertainty principle is obtained as a lower bound on entropy excess, X, the difference between the entropy of one variable, typically the number, and the knowledge of its complementary variable, typically the phase, where knowledge of a variable is defined as its relative entropy with respect to the uniform distribution. In the case of finite-dimensional systems, a weighting of phase knowledge by a factor μ (> 1) is necessary in order to make the bound tight, essentially on account of the POVM nature of phase as defined here. Numerical and analytical evidence suggests that μ tends to 1 as the system dimension becomes infinite. We study the effect of non-dissipative and dissipative noise on these complementary variables for an oscillator as well as atomic systems.

scholarly journals Exact quantum lower bound for Grover's problem

2009 ◽  
Vol 9 (5&6) ◽  
pp. 533-540
Author(s):  
C. Dohotaru ◽  
P. Hoyer
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Elementary Mathematics ◽  
Quantum Algorithms ◽  
Grover’S Algorithm ◽  
Exact Bound ◽  
Amount Of Information ◽  
Oracle Query ◽  
Grover's Algorithm ◽  
Query Model

One of the most important quantum algorithms ever discovered is Grover's algorithm for searching an unordered set. We give a new lower bound in the query model which proves that Grover's algorithm is exactly optimal. Similar to existing methods for proving lower bounds, we bound the amount of information we can gain from a single oracle query, but we bound this information in terms of angles. This allows our proof to be simple, self-contained, based on only elementary mathematics, capturing our intuition, while obtaining at the same time an exact bound.

scholarly journals Variational Quantum Algorithms for the Steady States of Open Quantum Systems

2021 ◽  
Vol 38 (8) ◽  
pp. 080301
Author(s):  
Huan-Yu Liu ◽  
Tai-Ping Sun ◽  
Yu-Chun Wu ◽  
Guo-Ping Guo
Keyword(s):  
Quantum Algorithms ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Steady States ◽  
Open Quantum

scholarly journals Quantum algorithms for search with wildcards and combinatorial group testing

2014 ◽  
Vol 14 (5&6) ◽  
pp. 439-453
Author(s):  
Andris Ambainis ◽  
Ashley Montanaro
Keyword(s):  
Lower Bound ◽  
Quantum Algorithms ◽  
Group Testing ◽  
Quantum Algorithm ◽  
Quantum Walk ◽  
Combinatorial Problems ◽  
Special Items ◽  
State Discrimination ◽  
Combinatorial Group Testing ◽  
Combinatorial Group

We consider two combinatorial problems. The first we call ``search with wildcards'': given an unknown $n$-bit string $x$, and the ability to check whether any subset of the bits of $x$ is equal to a provided query string, the goal is to output $x$. We give a nearly optimal $O(\sqrt{n} \log n)$ quantum query algorithm for search with wildcards, beating the classical lower bound of $\Omega(n)$ queries. Rather than using amplitude amplification or a quantum walk, our algorithm is ultimately based on the solution to a state discrimination problem. The second problem we consider is combinatorial group testing, which is the task of identifying a subset of at most $k$ special items out of a set of $n$ items, given the ability to make queries of the form ``does the set $S$ contain any special items?''\ for any subset $S$ of the $n$ items. We give a simple quantum algorithm which uses $O(k)$ queries to solve this problem, as compared with the classical lower bound of $\Omega(k \log(n/k))$ queries.

scholarly journals Quantum Processes: A Novel Optimization for Quantum Simulation

2013 ◽  
Vol 14 (3) ◽  
pp. 399
Author(s):  
Adriano Maron ◽  
Renata Reiser ◽  
Maurício Pilla ◽  
Adenauer Yamin
Keyword(s):  
Performance Evaluation ◽  
Theoretical Model ◽  
Execution Time ◽  
Quantum Algorithms ◽  
Quantum Systems ◽  
Sequential Simulation ◽  
Quantum Processes ◽  
Execution Environment ◽  
Temporal And Spatial ◽  
High Processing

The simulation of quantum algorithms in classic computers is a task which requires high processing and storing capabilities, limiting the size of quantum systems supported by the simulators. However, optimizations for reduction of temporal and spatial complexities are promising and expanding the capabilities of some simulators. The main contribution of this work consists in designing optimizations by the description of quantum transformations using Quantum Processes and Partial Quantum Processes conceived in the qGM theoretical model. These processes, when computed on the VPE-qGM execution environment, result in lower execution time and better performance, allowing the simulation of more complex quantum algorithms. The performance evaluation of this proposal was carried out by benchmarks used in similar works and included the sequential simulation of quantum algorithms up to 24 qubits. The results show a great improvement when compared to the previous version of the environment and indicate possibilities of advances in this research.

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