scholarly journals Research on Palmprint Identification Method Based on Quantum Algorithms

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Hui Li ◽  
Zhanzhan Zhang
Keyword(s):  
Fourier Transform ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Palmprint Recognition ◽  
Quantum Image ◽  
Grover Algorithm ◽  
Filtering Algorithm ◽  
Classical Algorithm ◽  
Set Operations ◽  
Speed Up

Quantum image recognition is a technology by using quantum algorithm to process the image information. It can obtain better effect than classical algorithm. In this paper, four different quantum algorithms are used in the three stages of palmprint recognition. First, quantum adaptive median filtering algorithm is presented in palmprint filtering processing. Quantum filtering algorithm can get a better filtering result than classical algorithm through the comparison. Next, quantum Fourier transform (QFT) is used to extract pattern features by only one operation due to quantum parallelism. The proposed algorithm exhibits an exponential speed-up compared with discrete Fourier transform in the feature extraction. Finally, quantum set operations and Grover algorithm are used in palmprint matching. According to the experimental results, quantum algorithm only needs to apply square ofNoperations to find out the target palmprint, but the traditional method needsNtimes of calculation. At the same time, the matching accuracy of quantum algorithm is almost 100%.

Algorithms With Superpolynomial Speed-Up

2006 ◽  
Author(s):  
Phillip Kaye ◽  
Raymond Laflamme ◽  
Michele Mosca
Keyword(s):  
Quantum Algorithms ◽  
Discrete Logarithm ◽  
Quantum Algorithm ◽  
Estimation Algorithm ◽  
Discrete Logarithm Problem ◽  
Phase Estimation ◽  
Post Process ◽  
Classical Algorithm ◽  
Speed Up ◽  
Hadamard Gate

In this chapter we examine one of two main classes of algorithms: quantum algorithms that solve problems with a complexity that is superpolynomially less than the complexity of the best-known classical algorithm for the same problem. That is, the complexity of the best-known classical algorithm cannot be bounded above by any polynomial in the complexity of the quantum algorithm. The algorithms we will detail all make use of the quantum Fourier transform (QFT). We start off the chapter by studying the problem of quantum phase estimation, which leads us naturally to the QFT. Section 7.1 also looks at using the QFT to find the period of periodic states, and introduces some elementary number theory that is needed in order to post-process the quantum algorithm. In Section 7.2, we apply phase estimation in order to estimate eigenvalues of unitary operators. Then in Section 7.3, we apply the eigenvalue estimation algorithm in order to derive the quantum factoring algorithm, and in Section 7.4 to solve the discrete logarithm problem. In Section 7.5, we introduce the hidden subgroup problem which encompasses both the order finding and discrete logarithm problem as well as many others. This chapter by no means exhaustively covers the quantum algorithms that are superpolynomially faster than any known classical algorithm, but it does cover the most well-known such algorithms. In Section 7.6, we briefly discuss other quantum algorithms that appear to provide a superpolynomial advantage. To introduce the idea of phase estimation, we begin by noting that the final Hadamard gate in the Deutsch algorithm, and the Deutsch–Jozsa algorithm, was used to get at information encoded in the relative phases of a state. The Hadamard gate is self-inverse and thus does the opposite as well, namely it can be used to encode information into the phases. To make this concrete, first consider H acting on the basis state |x⟩ (where x ∊ {0, 1}). It is easy to see that You can think about the Hadamard gate as having encoded information about the value of x into the relative phases between the basis states |0⟩ and |1⟩.

scholarly journals A panoply of quantum algorithms

2008 ◽  
Vol 8 (8&9) ◽  
pp. 834-859
Author(s):  
B. Furrow
Keyword(s):  
Quantum Physics ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Breadth First Search ◽  
Basic Tool ◽  
Grover’S Algorithm ◽  
Classical Algorithm ◽  
Grover's Algorithm ◽  
Programming Techniques ◽  
New Algorithms

This paper's aim is to explore improvements to, and applications of, a fundamental quantum algorithm invented by Grover\cite{grover}. Grover's algorithm is a basic tool that can be applied to a large number of problems in computer science, creating quantum algorithms that are polynomially faster than fastest known and fastest possible classical algorithms that solve the same problems. Our goal in this paper is to make these techniques readily accessible to those without a strong background in quantum physics: we achieve this by providing a set of tools, each of which makes use of Grover's algorithm or similar techniques, which can be used as subroutines in many quantum algorithms.}{The tools we provide are carefully constructed: they are easy to use, and in many cases they are asymptotically faster than the best tools previously available. The tools we build on include algorithms by Boyer, Brassard, Hoyer and Tapp, Buhrman, Cleve, de Witt and Zalka and Durr and Hoyer.}{After creating our tools, we create several new quantum algorithms, each of which is faster than the fastest known deterministic classical algorithm that accomplishes the same aim, and some of which are faster than the fastest possible deterministic classical algorithm. These algorithms solve problems from the fields of graph theory and computational geometry, and some employ dynamic programming techniques. We discuss a breadth-first search that is faster than $\Theta(\text{edges})$ (the classical limit) in a dense graph, maximum-points-on-a-line in $O(N^{3/2}\lg N)$ (faster than the fastest classical algorithm known), as well as several other algorithms that are similarly illustrative of solutions in some class of problem. Through these new algorithms we illustrate the use of our tools, working to encourage their use and the study of quantum algorithms in general.

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).

Classical and Quantum Algorithms for Assembling a Text from a Dictionary

2021 ◽  
Vol 24 (3) ◽  
pp. 207-221
Author(s):  
Kamil Khadiev ◽  
Vladislav Remidovskii
Keyword(s):  
Deoxyribonucleic Acid ◽  
Quantum Algorithms ◽  
Randomized Algorithm ◽  
Quantum Algorithm ◽  
Deterministic Algorithm ◽  
Constant Length ◽  
Running Time ◽  
Assembly Method ◽  
Speed Up ◽  
Quantum Speed Up

We study algorithms for solving the problem of assembling a text (long string) from a dictionary (a sequence of small strings). The problem has an application in bioinformatics and has a connection with the sequence assembly method for reconstructing a long deoxyribonucleic-acid (DNA) sequence from small fragments. The problem is assembling a string t of length n from strings s1,...,sm. Firstly, we provide a classical (randomized) algorithm with running time Õ(nL0.5 + L) where L is the sum of lengths of s1,...,sm. Secondly, we provide a quantum algorithm with running time Õ(nL0.25 + √mL). Thirdly, we show the lower bound for a classical (randomized or deterministic) algorithm that is Ω(n+L). So, we obtain the quadratic quantum speed-up with respect to the parameter L; and our quantum algorithm have smaller running time comparing to any classical (randomized or deterministic) algorithm in the case of non-constant length of strings in the dictionary.

scholarly journals Quantum algorithm for multivariate polynomial interpolation

2018 ◽  
Vol 474 (2209) ◽  
pp. 20170480 ◽  
Author(s):  
Jianxin Chen ◽  
Andrew M. Childs ◽  
Shih-Han Hung
Keyword(s):  
Open Problem ◽  
Polynomial Interpolation ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Query Complexity ◽  
Large Field ◽  
Multivariate Polynomial ◽  
Multivariate Polynomial Interpolation ◽  
Special Cases ◽  
Speed Up

How many quantum queries are required to determine the coefficients of a degree- d polynomial in n variables? We present and analyse quantum algorithms for this multivariate polynomial interpolation problem over the fields F q , R and C . We show that k C and 2 k C queries suffice to achieve probability 1 for C and R , respectively, where k C = ⌈ ( 1 / ( n + 1 ) ) ( n + d d ) ⌉ except for d =2 and four other special cases. For F q , we show that ⌈( d /( n + d ))( n + d d ) ⌉ queries suffice to achieve probability approaching 1 for large field order q . The classical query complexity of this problem is ( n + d d ) , so our result provides a speed-up by a factor of n +1, ( n +1)/2 and ( n + d )/ d for C , R and F q , respectively. Thus, we find a much larger gap between classical and quantum algorithms than the univariate case, where the speedup is by a factor of 2. For the case of F q , we conjecture that 2 k C queries also suffice to achieve probability approaching 1 for large field order q , although we leave this as an open problem.

scholarly journals Quantum advantage with shallow circuits

Science ◽  
2018 ◽  
Vol 362 (6412) ◽  
pp. 308-311 ◽  
Author(s):  
Sergey Bravyi ◽  
David Gosset ◽  
Robert König
Keyword(s):  
Quadratic Forms ◽  
Nearest Neighbor ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Quantum Nonlocality ◽  
Binary Quadratic Forms ◽  
Time Period ◽  
Speed Up ◽  
Active Debate ◽  
Near Term

Quantum effects can enhance information-processing capabilities and speed up the solution of certain computational problems. Whether a quantum advantage can be rigorously proven in some setting or demonstrated experimentally using near-term devices is the subject of active debate. We show that parallel quantum algorithms running in a constant time period are strictly more powerful than their classical counterparts; they are provably better at solving certain linear algebra problems associated with binary quadratic forms. Our work gives an unconditional proof of a computational quantum advantage and simultaneously pinpoints its origin: It is a consequence of quantum nonlocality. The proposed quantum algorithm is a suitable candidate for near-future experimental realizations, as it requires only constant-depth quantum circuits with nearest-neighbor gates on a two-dimensional grid of qubits (quantum bits).

scholarly journals EXACT QUANTUM FOURIER TRANSFORMS AND DISCRETE LOGARITHM ALGORITHMS

2004 ◽  
Vol 02 (01) ◽  
pp. 91-100 ◽  
Author(s):  
MICHELE MOSCA ◽  
CHRISTOF ZALKA
Keyword(s):  
Fourier Transform ◽  
Fourier Transforms ◽  
Quantum Algorithms ◽  
Discrete Logarithm ◽  
Quantum Algorithm ◽  
Quantum Fourier Transform ◽  
The Family ◽  
The Fourier Transform ◽  
Quantum Fourier Transforms ◽  
Amplitude Amplification

We show how the Quantum Fast Fourier Transform (QFFT) can be made exact for arbitrary orders (first showing it for large primes). Most quantum algorithms only need a good approximation of the quantum Fourier transform of order 2n to succeed with high probability, and this QFFT can in fact be done exactly. Kitaev1 showed how to approximate the Fourier transform for any order. Here we show how his construction can be made exact by using the technique known as "amplitude amplification". Although unlikely to be of any practical use, this construction allows one to make Shor's discrete logarithm quantum algorithm exact. Thus we have the first example of an exact non black box fast quantum algorithm, thereby giving more evidence that "quantum" need not be probabilistic. We also show that in a certain sense the family of circuits for the exact QFFT is uniform. Namely, the parameters of the gates can be approximated efficiently.

scholarly journals Quantum algorithms and lower bounds for convex optimization

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 221 ◽  
Author(s):  
Shouvanik Chakrabarti ◽  
Andrew M. Childs ◽  
Tongyang Li ◽  
Xiaodi Wu
Keyword(s):  
Convex Body ◽  
Convex Optimization ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Quantum Computers ◽  
Semidefinite Programs ◽  
Membership Queries ◽  
Speed Up ◽  
General Convex ◽  
Quantum Complexity

While recent work suggests that quantum computers can speed up the solution of semidefinite programs, little is known about the quantum complexity of more general convex optimization. We present a quantum algorithm that can optimize a convex function over an n-dimensional convex body using O~(n) queries to oracles that evaluate the objective function and determine membership in the convex body. This represents a quadratic improvement over the best-known classical algorithm. We also study limitations on the power of quantum computers for general convex optimization, showing that it requires Ω~(n) evaluation queries and Ω(n) membership queries.

scholarly journals Solving Burgers’ equation with quantum computing

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Furkan Oz ◽  
Rohit K. S. S. Vuppala ◽  
Kursat Kara ◽  
Frank Gaitan
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Burgers Equation ◽  
Exact Analytical Solution ◽  
Quantum Algorithms ◽  
Turbulence Models ◽  
Quantum Algorithm ◽  
Spatial Dimensions ◽  
Speed Up ◽  
Computational Fluid Dynamics Cfd

AbstractComputational fluid dynamics (CFD) simulations are a vital part of the design process in the aerospace industry. Although reliable CFD results can be obtained with turbulence models, direct numerical simulation of complex bodies in three spatial dimensions (3D) is impracticable due to the massive amount of computational elements. For instance, a 3D direct numerical simulation of a turbulent boundary-layer over the wing of a commercial jetliner that resolves all relevant length scales using a serial CFD solver on a modern digital computer would take approximately 750 million years or roughly 20% of the earth’s age. Over the past 25 years, quantum computers have become the object of great interest worldwide as powerful quantum algorithms have been constructed for several important, computationally challenging problems that provide enormous speed-up over the best-known classical algorithms. In this paper, we adapt a recently introduced quantum algorithm for partial differential equations to Burgers’ equation and develop a quantum CFD solver that determines its solutions. We used our quantum CFD solver to verify the quantum Burgers’ equation algorithm to find the flow solution when a shockwave is and is not present. The quantum simulation results were compared to: (i) an exact analytical solution for a flow without a shockwave; and (ii) the results of a classical CFD solver for flows with and without a shockwave. Excellent agreement was found in both cases, and the error of the quantum CFD solver was comparable to that of the classical CFD solver.

scholarly journals Learning DNFs under product distributions via mu--biased quantum Fourier sampling

2019 ◽  
Vol 19 (15&16) ◽  
pp. 1261-1278
Author(s):  
Varun Kanade ◽  
Andrea Rocchetto ◽  
Simone Severini
Keyword(s):  
Fourier Transform ◽  
Uniform Distribution ◽  
Polynomial Time ◽  
Quantum Algorithm ◽  
Classical Algorithm ◽  
Product Distributions ◽  
Fourier Sampling

We show that DNF formulae can be quantum PAC-learned in polynomial time under product distributions using a quantum example oracle. The current best classical algorithm runs in superpolynomial time. Our result extends the work by Bshouty and Jackson (1998) that proved that DNF formulae are efficiently learnable under the uniform distribution using a quantum example oracle. Our proof is based on a new quantum algorithm that efficiently samples the coefficients of a μ–biased Fourier transform.

Sign in / Sign up

Export Citation Format

Share Document