Related papers: Quantum algorithm for the Boolean hidden shift pro…
A quantum computer directly manipulates information stored in the state of quantum mechanical systems. The available operations have many attractive features but also underly severe restrictions, which complicate the design of quantum…
Quantum algorithms can deliver asymptotic speedups over their classical counterparts. However, there are few cases where a substantial quantum speedup has been worked out in detail for reasonably-sized problems, when compared with the best…
The Bin Packing Problem (BPP) stands out as a paradigmatic combinatorial optimization problem in logistics. Quantum and hybrid quantum-classical algorithms are expected to show an advantage over their classical counterparts in obtaining…
Quantum algorithms speeding up classical counterparts are proposed for the problems: 1. Recognition of eigenvalues with fixed precision. Given a quantum circuit generating unitary mapping $U$ and a complex number the problem is to determine…
We associate to each Boolean function a polynomial whose evaluations represents the distances from all possible Boolean affine functions. Both determining the coefficients of this polynomial from the truth table of the Boolean function and…
In machine learning, fewer features reduce model complexity. Carefully assessing the influence of each input feature on the model quality is therefore a crucial preprocessing step. We propose a novel feature selection algorithm based on a…
We present a quantum algorithm for finding the minimum of a function based on multistep quantum computation and apply it for optimization problems with continuous variables, in which the variables of the problem are discretized to form the…
Quantum Fourier transformation is important in many quantum algorithms. In this paper, we generalize quantum Fourier transformation over the Abelian group $\mathbb{Z}_N$ from two different points to get more efficient unitary…
Simulating noninteracting fermion systems is a common task in computational many-body physics. In absence of translational symmetries, modeling free fermions on $N$ modes usually requires poly$(N)$ computational resources. While often…
We introduce a quantum algorithm to perform the Laplace transform on quantum computers. Already, the quantum Fourier transform (QFT) is the cornerstone of many quantum algorithms, but the Laplace transform or its discrete version has not…
We report an experimental demonstration of a one-way implementation of a quantum algorithm solving Simon's Problem - a black box period-finding problem which has an exponential gap between the classical and quantum runtime. Using an…
Random classical linear codes are widely believed to be hard to decode. While slightly sub-exponential time algorithms exist when the coding rate vanishes sufficiently rapidly, all known algorithms at constant rate require exponential time.…
We present four quantum algorithms for solving a multidimensional drift-diffusion equation. They rely on a quantum linear system solver, a quantum Hamiltonian simulation, a quantum random walk, and the quantum Fourier transform. We compare…
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…
Motivated by the need to uncover some underlying mathematical structure of optimal quantum computation, we carry out a systematic analysis of a wide variety of quantum algorithms from the majorization theory point of view. We conclude that…
In a recent paper, Kuperberg described the first subexponential time algorithm for solving the dihedral hidden subgroup problem. The space requirement of his algorithm is super-polynomial. We describe a modified algorithm whose running time…
Several classes of quantum circuits have been shown to provide a quantum computational advantage under certain assumptions. The study of ever more restricted classes of quantum circuits capable of quantum advantage is motivated by possible…
We propose a quantum algorithm to solve systems of nonlinear algebraic equations. In the ideal case the complexity of the algorithm is linear in the number of variables $n$, which means our algorithm's complexity is less than $O(n^{3})$ of…
We provide a polynomial-time classical algorithm for noisy quantum circuits. The algorithm computes the expectation value of any observable for any circuit, with a small average error over input states drawn from an ensemble (e.g. the…
The quantum Fourier transform and quantum wavelet transform have been cornerstones of quantum information processing. However, for non-stationary signals and anomaly detection, the Hilbert transform can be a more powerful tool, yet no prior…