Related papers: An Efficient Deterministic Quantum Algorithm for t…
The quantum image segmentation algorithm is to divide a quantum image into several parts, but most of the existing algorithms use more quantum resource(qubit) or cannot process the complex image. In this paper, an improved two-threshold…
Composition is something we take for granted in classical algorithms design, and in particular, we take it as a basic axiom that composing ``efficient'' algorithms should result in an ``efficient'' algorithm -- even using this intuition to…
In the quest for quantum advantage, a central question is under what conditions can classical algorithms achieve a performance comparable to quantum algorithms--a concept known as dequantization. Random Fourier features (RFFs) have…
Recent results by Harrow et. al. and by Ta-Shma, suggest that quantum computers may have an exponential advantage in solving a wealth of linear algebraic problems, over classical algorithms. Building on the quantum intuition of these…
The search problem is to find a state satisfying certain properties out of a given set. Grover's algorithm drives a quantum computer from a prepared initial state to the target state and solves the problem quadratically faster than a…
As a compact representation of joint probability distributions over a dependence graph of random variables, and a tool for modelling and reasoning in the presence of uncertainty, Bayesian networks are of great importance for artificial…
One of the most basic computational problems is the task of finding a desired item in an ordered list of N items. While the best classical algorithm for this problem uses log_2 N queries to the list, a quantum computer can solve the problem…
Almost all of the most successful quantum algorithms discovered to date exploit the ability of the Fourier transform to recover subgroup structure of functions, especially periodicity. The fact that Fourier transforms can also be used to…
The fast Fourier transform (FFT) is one of the most successful numerical algorithms of the 20th century and has found numerous applications in many branches of computational science and engineering. The FFT algorithm can be derived from a…
We present a number of quantum computing patterns that build on top of fundamental algorithms, that can be applied to solving concrete, NP-hard problems. In particular, we introduce the concept of a quantum dictionary as a summation of…
Vector set orthogonal normalization and matrix QR decomposition are fundamental problems in matrix analysis with important applications in many fields. We know that Gram-Schmidt process is a widely used method to solve these two problems.…
Quantum algorithms for Hamiltonian simulation and linear differential equations more generally have provided promising exponential speed-ups over classical computers on a set of problems with high real-world interest. However, extending…
Faster algorithms, novel cryptographic mechanisms, and alternative methods of communication become possible when the model underlying information and computation changes from a classical mechanical model to a quantum mechanical one. Quantum…
Quantum computers are becoming more mainstream. As more programmers are starting to look at writing quantum programs, they face an inevitable task of debugging their code. How should the programs for quantum computers be debugged? In this…
We construct an efficient quantum algorithm to compute the quantum Schur-Weyl transform for any value of the quantum parameter $q \in [0,\infty]$. Our algorithm is a $q$-deformation of the Bacon-Chuang-Harrow algorithm, in the sense that it…
Quantum computers can solve specific complex tasks for which no reasonable-time classical algorithm is known. Quantum computers do however also offer inherent security of data, as measurements destroy quantum states. Using shared entangled…
Current quantum computers can only solve optimization problems of a very limited size. For larger problems, decomposition methods are required in which the original problem is broken down into several smaller sub-problems. These are then…
Current asymmetric cryptography is based on the principle that while classical computers can efficiently multiply large integers, the inverse operation, factorization, is significantly more complex. For sufficiently large integers, this…
Quantum algorithms based on quantum kernel methods have been investigated previously [1]. A quantum advantage is derived from the fact that it is possible to construct a family of datasets for which, only quantum processing can recognise…
In the last couple of decades, the world has seen several stunning instances of quantum algorithms that provably outperform the best classical algorithms. For most problems, however, it is currently unknown whether quantum algorithms can…