Related papers: High-dimensional quantum Schur transforms
This Ph.D. thesis provides a comprehensive review of the state-of-the-art in the field of Variational Quantum Algorithms and Quantum Machine Learning, including numerous original contributions. The first chapters are devoted to a brief…
An alternative quantum algorithm for the discrete logarithm problem is presented. The algorithm uses two quantum registers and two Fourier transforms whereas Shor's algorithm requires three registers and four Fourier transforms. A crucial…
We present quantum algorithms to efficiently perform discriminant analysis for dimensionality reduction and classification over an exponentially large input data set. Compared with the best-known classical algorithms, the quantum algorithms…
For the unsorted database quantum search with the unknown fraction $\lambda$ of target items, there are mainly two kinds of methods, i.e., fixed-point or trail-and-error. (i) In terms of the fixed-point method, Yoder et al. [Phys. Rev.…
In quantum key distribution (QKD), protocols are tailored to adopt desirable experimental attributes, including high key rates, operation in high noise levels, and practical security considerations. The round-robin differential phase shift…
High-dimensional quantum systems are a valuable resource for quantum information processing. They can be used to encode error-correctable logical qubits, which has been demonstrated using continuous-variable states in microwave cavities or…
We consider the quantum complexity of estimating matrix elements of unitary irreducible representations of groups. For several finite groups including the symmetric group, quantum Fourier transforms yield efficient solutions to this…
In this work, we develop a highly efficient representation of functions and differential operators based on Fourier analysis. Using this representation, we create a variational hybrid quantum algorithm to solve static, Schr\"odinger-type,…
The quantum Oppenheimer-Snyder model for higher-dimensional spacetimes is studied. The higher-dimensional quantum-corrected Schwarzschild black hole is obtained by the junction condition. It turns out that quantum bounces always occur in…
Quantum models of computation are widely believed to be more powerful than classical ones. Efforts center on proving that, for a given problem, quantum algorithms are more resource efficient than any classical one. All this, however,…
The Quantum Fourier Transform (QFT) is a key component of many important quantum algorithms, most famously as being the essential ingredient in Shor's algorithm for factoring products of primes. Given its remarkable capability, one would…
In this paper the authors introduce a new notion called the quantum wreath product, which is the algebra $B \wr_Q \mathcal{H}(d)$ produced from a given algebra $B$, a positive integer $d$, and a choice $Q=(R,S,\rho,\sigma)$ of parameters.…
A quantum algorithm for approximating efficiently 3--manifold topological invariants in the framework of SU(2) Chern-Simons-Witten (CSW) topological quantum field theory at finite values of the coupling constant k is provided. The model of…
In the Hamiltonian formulation, Quantum Field Theory calculations scale exponentially with spatial volume, making real-time simulations intractable on classical computers and motivating quantum computation approaches. In Hamiltonian…
In the paper, we show that the transformations between modified Jacobi and Bernstein bases of the constrained space of polynomials of degree at most $n$ can be performed with the complexity $O(n^2)$. As a result, the algorithm of degree…
Shor's algorithms for factorization and discrete logarithms on a quantum computer employ Fourier transforms preceding a final measurement. It is shown that such a Fourier transform can be carried out in a semi-classical way in which a…
Many quantum information tasks use inputs of the form $\rho^{\otimes m}$, which naturally induce permutation and unitary symmetries. We classify all quantum channels that respect both symmetries - i.e. unitary-equivariant and…
We study the dimensional aspect of the geometry of quantum spaces. Introducing a physically motivated notion of the scaling dimension, we study in detail the model based on a fuzzy torus. We show that for a natural choice of a deformed…
Quantum computers are able to outperform classical algorithms. This was long recognized by the visionary Richard Feynman who pointed out in the 1980s that quantum mechanical problems were better solved with quantum machines. It was only in…
Twirling, i.e. averaging over symmetry actions, is a standard tool for reducing quantum states and channels to a symmetry-invariant form. We study channel twirling from the perspective of the channel-state duality and provide a constructive…