scholarly journals Efficient verification of anticoncentrated quantum states

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Ryan S. Bennink
Keyword(s):  
Quantum State ◽  
Quantum Circuits ◽  
Collision Probability ◽  
Simple Quantum ◽  
Significant Step ◽  
Approximate Cost ◽  
Efficient Verification ◽  
Pure Target ◽  
Sophisticated Version ◽  
Better Than

AbstractI present a method for estimating the fidelity F(μ, τ) between a preparable quantum state μ and a classically specified pure target state $$\tau =\left|\tau \right\rangle \left\langle \tau \right|$$ τ = τ τ , using simple quantum circuits and on-the-fly classical calculation (or lookup) of selected amplitudes of $$\left|\tau \right\rangle$$ τ . The method is sample efficient for anticoncentrated states (including many states that are hard to simulate classically), with approximate cost 4ϵ−2(1 − F)dpcoll where ϵ is the desired precision of the estimate, d is the dimension of the Hilbert space, and pcoll is the collision probability of the target distribution. This scaling is exponentially better than that of any method based on classical sampling. I also present a more sophisticated version of the method that uses any efficiently preparable and well-characterized quantum state as an importance sampler to further reduce the number of copies of μ needed. Though some challenges remain, this work takes a significant step toward scalable verification of complex states produced by quantum processors.

How significant are the known collision and element distinctness quantum algorithms?

2004 ◽  
Vol 4 (3) ◽  
pp. 201-206
Author(s):  
L. Grover ◽  
T. Rudolph
Keyword(s):  
Search Algorithm ◽  
Quantum Algorithms ◽  
Search Space ◽  
Space Complexity ◽  
Quantum Search ◽  
Quantum Search Algorithm ◽  
Time Space ◽  
Simple Quantum ◽  
Structured Problems ◽  
Better Than

Quantum search is a technique for searching $N$ possibilities for a desired target in $O(\sqrt{N})$ steps. It has been applied in the design of quantum algorithms for several structured problems. Many of these algorithms require significant amount of quantum hardware. In this paper we propose the criterion that an algorithm which requires $O(S)$ hardware should be considered significant if it produces a speedup of better than $O\left(\sqrt{S}\right)$ over a simple quantum search algorithm. This is because a speedup of $O\left(\sqrt{S}\right)$ can be trivially obtained by dividing the search space into $S$ separate parts and handing the problem to $S$ independent processors that do a quantum search (in this paper we drop all logarithmic factors when discussing time/space complexity). Known algorithms for collision and element distinctness exactly saturate the criterion.

Machine invention of quantum computing circuits by means of genetic programming

2008 ◽  
Vol 22 (3) ◽  
pp. 275-283 ◽  
Author(s):  
Lee Spector ◽  
Jon Klein
Keyword(s):  
Quantum Computing ◽  
Genetic Programming ◽  
Quantum Computer ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Practical Significance ◽  
Programming System ◽  
Computer Simulator ◽  
Classical Quantum ◽  
Better Than

AbstractWe demonstrate the use of genetic programming in the automatic invention of quantum computing circuits that solve problems of potential theoretical and practical significance. We outline a developmental genetic programming scheme for such applications; in this scheme the evolved programs, when executed, build quantum circuits and the resulting quantum circuits are then tested for “fitness” using a quantum computer simulator. Using the PushGP genetic programming system and the QGAME quantum computer simulator we demonstrate the invention of a new, better than classical quantum circuit for the two-oracle AND/OR problem.

scholarly journals Performance Analysis for Uniform and Binomial Distribution on Contention Window using DSRC and Wi-Fi Direct Standard

2015 ◽  
Vol 5 (6) ◽  
pp. 1452
Author(s):  
Nurain Izzati Shuhaimi ◽  
Heriansyah Heriansyah ◽  
Tutun Juhana ◽  
Adit Kurniawan
Keyword(s):  
Performance Analysis ◽  
Binomial Distribution ◽  
Wireless Networking ◽  
The Other ◽  
Contention Window ◽  
Collision Probability ◽  
Average Throughput ◽  
Potential Competitor ◽  
And Behavior ◽  
Better Than

In this paper, we present a mathematical analysis on the performance and behavior of uniformly distributed and non-uniformly distributed backoff timer based on binomial algorithm by using two standards which is the conventional DSRC and the latest Wi-Fi Direct. DSRC is a well-known technology being considered as the most promising wireless standard in VANET. On the other hand, as the latest wireless networking standard, the potential of Wi-Fi Direct technology should be concerned. We evaluates these standards using uniform and binomial distribution for contention window under mathematical modelling in order to analyze the average throughput and collision probability performance. The results show that binomial distribution in Wi-Fi Direct standard is 7.05% and 97.13% better than uniform distribution, in terms of average throughput and collision probability, respectively. Thus we can defer that Wi-Fi Direct is feasible to be used as an alternative standard since it has been considered as potential competitor of DSRC in VANET.

COLLECTIVE REMOTE STATE PREPARATION

2008 ◽  
Vol 06 (05) ◽  
pp. 1051-1066 ◽  
Author(s):  
NGUYEN BA AN ◽  
JAEWAN KIM
Keyword(s):  
Success Probability ◽  
The State ◽  
Remote State Preparation ◽  
The Other ◽  
Quantum Circuits ◽  
State Preparation ◽  
Remote Location ◽  
Simple Quantum ◽  
Classical Knowledge ◽  
Analytical Expressions

We show that any M ≥ 2 distant parties who independently share the complete classical knowledge of a secret qubit state can collectively prepare the state at another remote location. Two distinct schemes for such a task are proposed: one via a single (M + 1)-partite GHZ-type state and the other via M EPR-type pairs. Analytical expressions of the total success probability are derived explicitly for both the schemes. Of interest is the M-dependence of both the success probability and the receiver's action. We also construct simple quantum circuits for the two-qubit operators whose execution is necessary to accomplish the schemes.

scholarly journals Structure optimization for parameterized quantum circuits

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 391
Author(s):  
Mateusz Ostaszewski ◽  
Edward Grant ◽  
Marcello Benedetti
Keyword(s):  
Ground State ◽  
Heisenberg Model ◽  
Quantum Computer ◽  
Structure Optimization ◽  
Hydrogen Gas ◽  
Quantum Circuits ◽  
Quantum Computers ◽  
Computational Overhead ◽  
Parameter Values ◽  
Better Than

We propose an efficient method for simultaneously optimizing both the structure and parameter values of quantum circuits with only a small computational overhead. Shallow circuits that use structure optimization perform significantly better than circuits that use parameter updates alone, making this method particularly suitable for noisy intermediate-scale quantum computers. We demonstrate the method for optimizing a variational quantum eigensolver for finding the ground states of Lithium Hydride and the Heisenberg model in simulation, and for finding the ground state of Hydrogen gas on the IBM Melbourne quantum computer.

scholarly journals Further Considerations on the Sephardim of the Petite Côte

2005 ◽  
Vol 32 ◽  
pp. 165-183 ◽  
Author(s):  
Tobias Green
Keyword(s):  
Seventeenth Century ◽  
West Africa ◽  
Guinea Coast ◽  
Documentary Sources ◽  
Significant Step ◽  
Extended Lifespan ◽  
First Time ◽  
Better Than ◽  
Area Of Study

The publication in these pages of an article by Peter Mark and José da Silva Horta on the Sephardic communities of the Petite Côte in the early seventeenth century represents a significant step forward in our understanding of the Jewish presence in west Africa. Using previously unreferenced material, Mark and Horta have filled out for the first time the nature of this community, and in particular provided valuable evidence as to the group's connections with Lisbon and Amsterdam.This type of assiduous documentary research has long been needed for this topic. Although some Africanists have referred to the Jewish presence there, such references have tended to draw on the same few documentary sources. So though the work of Jean Boulegue, Antonio Carreira, and Nize Isabel de Moraes has been important in drawing the attention of Africanists to the Jewish presence in Senegambia, one can say that, in general, historians of the upper Guinea coast have not systematized the place of the Sephardim in discourses related to their area of study.Meanwhile, there is almost a complete absence of reference to the Jewish presence in west Africa among historians of the Sephardim. There are perhaps two overriding explanations for this lacuna. For one thing, these communities were comparatively small and did not have an extended lifespan, and it is of course natural that historians of the Sephardim should concentrate on the most important communities of the diaspora. For another, we suspect that the absence of their commentary on this subject is not entirely unrelated to fears as to what might be uncovered, since it is notorious that one of the major activities of Europeans in Africa at this time was slaving. The implication of a significant number of Sephardim being involved in this activity would not sit comfortably with the traditional interpretation of many historians of the Sephardim that their subjects were, essentially, victims of persecution, and that, where they were slave owners, they treated their charges much better than did Christians.

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