scholarly journals Quantum Computer Can Not Speed Up Iterated Applications of a Black Box

1999 ◽  
pp. 152-159
Author(s):  
Y. Ozhigov
Keyword(s):  
Quantum Computer ◽  
Black Box ◽  
Speed Up

scholarly journals Temporal concatenation for Markov decision processes

2021 ◽  
pp. 1-28
Author(s):  
Ruiyang Song ◽  
Kuang Xu
Keyword(s):  
Markov Decision Processes ◽  
Large Scale ◽  
Optimal Solution ◽  
Upper Bounds ◽  
Black Box ◽  
Decision Processes ◽  
Optimal Solutions ◽  
Wide Range ◽  
Markov Decision ◽  
Speed Up

We propose and analyze a temporal concatenation heuristic for solving large-scale finite-horizon Markov decision processes (MDP), which divides the MDP into smaller sub-problems along the time horizon and generates an overall solution by simply concatenating the optimal solutions from these sub-problems. As a “black box” architecture, temporal concatenation works with a wide range of existing MDP algorithms. Our main results characterize the regret of temporal concatenation compared to the optimal solution. We provide upper bounds for general MDP instances, as well as a family of MDP instances in which the upper bounds are shown to be tight. Together, our results demonstrate temporal concatenation's potential of substantial speed-up at the expense of some performance degradation.

scholarly journals A random walk approach to quantum algorithms

2006 ◽  
Vol 364 (1849) ◽  
pp. 3407-3422 ◽  
Author(s):  
Vivien M Kendon
Keyword(s):  
Random Walk ◽  
Quantum Dynamics ◽  
Quantum Computer ◽  
Quantum Algorithms ◽  
Quantum Walk ◽  
Quantum Random Walk ◽  
Small Quantum ◽  
Starting Point ◽  
Quantum Version ◽  
Speed Up

The development of quantum algorithms based on quantum versions of random walks is placed in the context of the emerging field of quantum computing. Constructing a suitable quantum version of a random walk is not trivial; pure quantum dynamics is deterministic, so randomness only enters during the measurement phase, i.e. when converting the quantum information into classical information. The outcome of a quantum random walk is very different from the corresponding classical random walk owing to the interference between the different possible paths. The upshot is that quantum walkers find themselves further from their starting point than a classical walker on average, and this forms the basis of a quantum speed up, which can be exploited to solve problems faster. Surprisingly, the effect of making the walk slightly less than perfectly quantum can optimize the properties of the quantum walk for algorithmic applications. Looking to the future, even with a small quantum computer available, the development of quantum walk algorithms might proceed more rapidly than it has, especially for solving real problems.

scholarly journals CoVEGI: Cooperative Verification via Externally Generated Invariants

2021 ◽  
pp. 108-129
Author(s):  
Jan Haltermann ◽  
Heike Wehrheim
Keyword(s):  
Software Verification ◽  
Black Box ◽  
Loop Invariant ◽  
Invariant Generation ◽  
Smt Solving ◽  
The Core ◽  
Verification Tool ◽  
Verification Methods ◽  
Speed Up ◽  
Verification Tools

AbstractSoftware verification has recently made enormous progress due to the development of novel verification methods and the speed-up of supporting technologies like SMT solving. To keep software verification tools up to date with these advances, tool developers keep on integrating newly designed methods into their tools, almost exclusively by re-implementing the method within their own framework. While this allows for a conceptual re-use of methods, it nevertheless requires novel implementations for every new technique.In this paper, we employ cooperative verification in order to avoid re-implementation and enable usage of novel tools as black-box components in verification. Specifically, cooperation is employed for the core ingredient of software verification which is invariant generation. Finding an adequate loop invariant is key to the success of a verification run. Our framework named CoVEGI allows a master verification tool to delegate the task of invariant generation to one or several specialized helper invariant generators. Their results are then utilized within the verification run of the master verifier, allowing in particular for crosschecking the validity of the invariant. We experimentally evaluate our framework on an instance with two masters and three different invariant generators using a number of benchmarks from SV-COMP 2020. The experiments show that the use of CoVEGI can increase the number of correctly verified tasks without increasing the used resources.

Hidden symmetry detection on a quantum computer

2007 ◽  
Vol 7 (1&2) ◽  
pp. 83-92
Author(s):  
R. Schutzhold ◽  
W.G. Unruh
Keyword(s):  
Quantum Computer ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Quantum Computers ◽  
Self Similarity ◽  
Hidden Subgroup Problem ◽  
Hidden Symmetry ◽  
Speed Up ◽  
Subgroup Problem ◽  
Discrete Scale

The fastest quantum algorithms (for the solution of classical computational tasks) known so far are basically variations of the hidden subgroup problem with {$f(U[x])=f(x)$}. Following a discussion regarding which tasks might be solved efficiently by quantum computers, it will be demonstrated by means of a simple example, that the detection of more general hidden (two-point) symmetries {$V\{f(x),f(U[x])\}=0$} by a quantum algorithm can also admit an exponential speed-up. E.g., one member of this class of symmetries {$V\{f(x),f(U[x])\}=0$} is discrete self-similarity (or discrete scale invariance).

scholarly journals Quantum-inspired algorithms for multivariate analysis: from interpolation to partial differential equations

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 431
Author(s):  
Juan José García-Ripoll
Keyword(s):  
Fourier Transforms ◽  
Quantum Computer ◽  
Large Family ◽  
Monte Carlo Integration ◽  
Quantum Computers ◽  
Matrix Product ◽  
Fourier Sampling ◽  
Tensor Network ◽  
Speed Up ◽  
Similar Task

In this work we study the encoding of smooth, differentiable multivariate functions in quantum registers, using quantum computers or tensor-network representations. We show that a large family of distributions can be encoded as low-entanglement states of the quantum register. These states can be efficiently created in a quantum computer, but they are also efficiently stored, manipulated and probed using Matrix-Product States techniques. Inspired by this idea, we present eight quantum-inspired numerical analysis algorithms, that include Fourier sampling, interpolation, differentiation and integration of partial derivative equations. These algorithms combine classical ideas – finite-differences, spectral methods – with the efficient encoding of quantum registers, and well known algorithms, such as the Quantum Fourier Transform. When these heuristic methods work, they provide an exponential speed-up over other classical algorithms, such as Monte Carlo integration, finite-difference and fast Fourier transforms (FFT). But even when they don't, some of these algorithms can be translated back to a quantum computer to implement a similar task.

scholarly journals Quantum Random Numbers Generated by a Cloud Superconducting Quantum Computer

2020 ◽  
pp. 17-37
Author(s):  
Kentaro Tamura ◽  
Yutaka Shikano
Keyword(s):  
Random Number ◽  
Quantum Computer ◽  
Statistical Tests ◽  
Random Number Generator ◽  
Random Number Generation ◽  
Black Box ◽  
Random Numbers ◽  
Number Generator ◽  
Random Number Generators ◽  
Simple Indicator

Abstract A cloud quantum computer is similar to a random number generator in that its physical mechanism is inaccessible to its users. In this respect, a cloud quantum computer is a black box. In both devices, its users decide the device condition from the output. A framework to achieve this exists in the field of random number generation in the form of statistical tests for random number generators. In the present study, we generated random numbers on a 20-qubit cloud quantum computer and evaluated the condition and stability of its qubits using statistical tests for random number generators. As a result, we observed that some qubits were more biased than others. Statistical tests for random number generators may provide a simple indicator of qubit condition and stability, enabling users to decide for themselves which qubits inside a cloud quantum computer to use.

scholarly journals Implementasi Metode SAW dalam Penilaian Kinerja Tenaga Harian Lepas

Jurnal Teknik ◽  
2021 ◽  
Vol 19 (1) ◽  
pp. 85-95
Author(s):  
Khairil ◽  
Hari Aspriyono
Keyword(s):  
Performance Appraisal ◽  
Employee Performance ◽  
Unified Modeling Language ◽  
Black Box ◽  
Unified Modeling ◽  
Testing Stage ◽  
Long Time ◽  
Black Box Testing ◽  
Speed Up ◽  
Simple Additive Weighting

The performance assessment of Civil Servants at the Bengkulu Province Communication, Informatics, and Statistics Service (Diskominkotik) process has utilized an e-performance application. However, the assessment of daily workers' performance is not included, which means evaluating their performance and competence would take a long time. This study aims to determine daily workers to get the best performance rewards using the Simple Additive Weighting (SAW) method. The research method used was the waterfall method, supported by data from observations, interviews, and questionnaires. Unified Modeling Language (UML) was used to analyze and design the system and in the coding stage, Microsoft Visual Studio 2010 software connected to a MySQL database was used, and in the testing stage, a Black-box testing approach was employed. The results showed that the implementation of the SAW method in the decision support system application could speed up the process of evaluating the performance of daily workers at Bengkulu Province Diskominkotik. Furthermore, daily workers’ performance appraisal became more objective because it involves the participation of many parties so that the results of the best daily worker employee performance appraisal can be accepted by various parties.

Quantum algorithm for measuring the eigenvalues of UÄU-1 for a black-box unitary transformation U

2002 ◽  
Vol 2 (3) ◽  
pp. 192-197
Author(s):  
D. Janzing ◽  
T. Beth
Keyword(s):  
Energy Spectrum ◽  
Quantum System ◽  
Autocorrelation Function ◽  
Unitary Transformation ◽  
Quantum Computer ◽  
Quantum Algorithm ◽  
Black Box ◽  
Phase Estimation

Estimating the eigenvalues of a unitary transformation U by standard phase estimation requires the implementation of controlled-U-gates which are not available if U is only given as a black box. We show that a simple trick allows to measure eigenvalues of U\otimesU^\deggar even in this case. Running the algorithm several times allows therefore to estimate the autocorrelation function of the density of eigenstates of U. This can be applied to find periodicities in the energy spectrum of a quantum system with unknown Hamiltonian if it can be coupled to a quantum computer.

A Fast Convergence Scheme for Coupled Energy Domains Simulation of MEMS

2006 ◽  
Author(s):  
J. Guo ◽  
Q. M. Querin
Keyword(s):  
Relaxation Method ◽  
Black Box ◽  
Fast Convergence ◽  
Newton Methods ◽  
Mems Devices ◽  
Numerical Techniques ◽  
Acceleration Technique ◽  
Speed Up ◽  
Convergence Performance ◽  
Better Than

Due to the massive demands from industry, the black-box based coupled energy domains simulation plays a more and more important role in the design of MEMS devices, and many numerical techniques have been developed so far for it. This paper presents a fast convergence scheme for coupled energy domains simulation of MEMS. This scheme is based on the relaxation approach but employs the Steffensen's acceleration technique to speed up the convergence procedure. In this paper, the details of this scheme are described as well as the relaxation and the multilevel Newton methods. The numerical examples show that the proposed scheme has equivalent convergence performance, sometimes even more efficient, as the multilevel Newton method, and much better than the relaxation method, especially for strong coupled or nonlinear situations, while keeping the advantage of easy programming.

Quantum Computational Complexity Theory and Lower Bounds

2006 ◽  
Author(s):  
Phillip Kaye ◽  
Raymond Laflamme ◽  
Michele Mosca
Keyword(s):  
Computational Complexity ◽  
Lower Bounds ◽  
Quantum Computer ◽  
Black Box ◽  
Box Model ◽  
Quantum Computers ◽  
Complexity Classes ◽  
Integer Multiplication ◽  
Classical Computer ◽  
Quantum Complexity

We have seen in the previous chapters that quantum computers seem to be more powerful than classical computers for certain problems. There are limits on the power of quantum computers, however. Since a classical computer can simulate a quantum computer, a quantum computer can only compute the same set of functions that a classical computer can. The advantage of using a quantum computer is that the amount of resources needed by a quantum algorithm might be much less than what is needed by the best classical algorithm. In Section 9.1 we briefly define some classical and quantum complexity classes and give some relationships between them. Most of the interesting questions relating classical and quantum complexity classes remain open. For example, we do not yet know if a quantum computer is capable of efficiently solving an NP-complete problem (defined later). One can prove upper bounds on the difficulty of a problem by providing an algorithm that solves that problem, and proving that it will work within in a given running time. But how does one prove a lower bound on the computational complexity of a problem? For example, if we wish to find the product of two n-bit numbers, computing the answer requires outputting roughly 2n bits and that requires Ω(n) steps (in any computing model with finite-sized gates). The best-known upper bound for integer multiplication is O(n log n log log n) steps. It has proved extremely difficult to derive non-trivial lower bounds on the computational complexity of a problem. Most of the known non-trivial lower bounds are in the ‘black-box’ model (for both classical and quantum computing), where we only query the input via a ‘black-box’ of a specific form. We discuss the black-box model in more detail in Section 9.2. We then sketch several approaches for proving black-box lower bounds. The first technique has been called the ‘hybrid method’ and was used to prove that quantum searching requires Ω(√n) queries to succeed with constant probability. The second technique is called the ‘polynomial method’. We then describe a technique based on ‘block sensitivity’, and conclude with a technique known as the ‘adversary method’.

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