Related papers: Direct dialling of Haar random unitary matrices
We consider the problem of efficiently simulating random quantum states and random unitary operators, in a manner which is convincing to unbounded adversaries with black-box oracle access. This problem has previously only been considered…
The paper discusses progress in understanding statistical properties of complex eigenvalues (and corresponding eigenvectors) of weakly non-unitary and non-Hermitian random matrices. Ensembles of this type emerge in various physical…
In linear optics, photons are scattered in a network through passive optical elements including beamsplitters and phase shifters, leading to many intriguing applications in physics, such as Mach-Zehnder interferometry, Hong-Ou-Mandel…
Photonic circuits, engineered to couple optical modes according to a specific map, serve as processors for classical and quantum light. The number of components typically scales with that of processed modes, thus correlating system size,…
The paper deals with distribution of singular values of product of random matrices arising in the analysis of deep neural networks. The matrices resemble the product analogs of the sample covariance matrices, however, an important…
The aim of this paper is to endow the well-known family of hypercubic quantization hashing methods with theoretical guarantees. In hypercubic quantization, applying a suitable (random or learned) rotation after dimensionality reduction has…
The properties of coherence and polarization of light has been the subject of intense investigations and form the basis of many technological applications. These concepts which historically have been treated independently can now be…
We review and extend, in a self-contained way, the mathematical foundations of numerical simulation methods that are based on the use of random states. The power and versatility of this simulation technology is illustrated by calculations…
We present an efficient way of heralding photonic qubit signals using linear optics devices. First we show that one can obtain asymptotically perfect heralding and unit success probability with growing resources. Second, we show that even…
We describe a general-purpose framework to design quantum algorithms relying upon an efficient handling of arrays. The corner-stone of the framework is the direct embedding of information into quantum amplitudes, thus avoiding the need to…
This thesis reports advances in the theory of design, characterization and simulation of multi-photon multi-channel interferometers. I advance the design of interferometers through an algorithm to realize an arbitrary discrete unitary…
We develop an abstract look at linear optical networks from the viewpoint of combinatorics and permanents. In particular we show that calculation of matrix elements of unitarily transformed photonic multi-mode states is intimately linked to…
Circulant matrices are an important family of operators, which have a wide range of applications in science and engineering related fields. They are in general non-sparse and non-unitary. In this paper, we present efficient quantum circuits…
This article introduces an algorithm to draw random discrete uniform variables within a given range of size n from a source of random bits. The algorithm aims to be simple to implement and optimal both with regards to the amount of random…
In this note we extend kernel function approximation results for neural networks with Gaussian-distributed weights to single-layer networks initialized using Haar-distributed random orthogonal matrices (with possible rescaling). This is…
Randomness is one of the most important resources in modern information science, since encryption founds upon the trust in random numbers. Since it is impossible to prove if an existing random bit string is truly random, it is relevant that…
One of the most promising applications of quantum computing is simulating quantum many-body systems. However, there is still a need for methods to efficiently investigate these systems in a native way, capturing their full complexity. Here,…
The quantum random walk has drawn special interests because its remarkable features to the classical counterpart could lead to new quantum algorithms. In this paper, we propose a feasible scheme to implement quantum random walks on a line…
Random quantum circuits are proficient information scramblers and efficient generators of randomness, rapidly approximating moments of the unitary group. We study the convergence of local random quantum circuits to unitary $k$-designs.…
Random unitaries are a central object of study in quantum information, with applications to quantum computation, quantum many-body physics, and quantum cryptography. Recent work has constructed unitary designs and pseudorandom unitaries…