Related papers: Efficient computation of permanents, with applicat…
We construct a quantum-inspired classical algorithm for computing the permanent of Hermitian positive semidefinite matrices, by exploiting a connection between these mathematical structures and the boson sampling model. Specifically, the…
It is known that computing the permanent of the matrix $1+A$, where $A$ is a finite-rank matrix, requires a number of operations polynomial in the matrix size. Motivated by the boson-sampling proposal of restricted quantum computation, I…
Universal quantum computers promise a dramatic speed-up over classical computers but a full-size realization remains challenging. However, intermediate quantum computational models have been proposed that are not universal, but can solve…
Computing the distribution of permanents of random matrices has been an outstanding open problem for several decades. In quantum computing, "anti-concentration" of this distribution is an unproven input for the proof of hardness of the task…
Considering the problem of sampling from the output photon-counting probability distribution of a linear-optical network for input Gaussian states, we obtain results that are of interest from both quantum theory and the computational…
Boson sampling has been theoretically proposed and experimentally demonstrated to show quantum computational advantages. However, it still lacks the deep understanding of the practical applications of boson sampling. Here we propose that…
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…
The research in parallel machine scheduling in combinatorial optimization suggests that the desirable parallel efficiency could be achieved when the jobs are sorted in the non-increasing order of processing times. In this paper, we find…
BosonSampling is an intermediate model of quantum computation where linear-optical networks are used to solve sampling problems expected to be hard for classical computers. Since these devices are not expected to be universal for quantum…
Since its introduction Boson Sampling has been the subject of intense study in the world of quantum computing. The task is to sample independently from the set of all $n \times n$ submatrices built from possibly repeated rows of a larger $m…
In 2011, Aaronson gave a striking proof, based on quantum linear optics, showing that the problem of computing the permanent of a matrix is #P-hard. Aaronson's proof led naturally to hardness of approximation results for the permanent, and…
We give new evidence that quantum computers -- moreover, rudimentary quantum computers built entirely out of linear-optical elements -- cannot be efficiently simulated by classical computers. In particular, we define a model of computation…
It is predicted that quantum computers will dramatically outperform their conventional counterparts. However, large-scale universal quantum computers are yet to be built. Boson sampling is a rudimentary quantum algorithm tailored to the…
Gaussian boson sampling is a model of photonic quantum computing that has attracted attention as a platform for building quantum devices capable of performing tasks that are out of reach for classical devices. There is therefore significant…
We propose a computationally efficient method to solve the dynamics of operators of bosonic quantum systems coupled to their environments. The method maps the operator under interest to a set of complex-valued functions, and its adjoint…
A universal quantum computer of large scale is not available yet, however, intermediate models of quantum computation would still permit demonstrations of a quantum computational advantage over classical computing and could challenge the…
Boson Sampling is a computational task strongly believed to be hard for classical computers, but efficiently solvable by orchestrated bosonic interference in a specialised quantum computer. Current experimental schemes, however, are still…
Boson-Sampling is a classically computationally hard problem that can - in principle - be efficiently solved with quantum linear optical networks. Very recently, a rush of experimental activity has ignited with the aim of developing such…
Random point patterns are ubiquitous in nature, and statistical models such as point processes, i.e., algorithms that generate stochastic collections of points, are commonly used to simulate and interpret them. We propose an application of…
Evaluating the permanent of a matrix is a fundamental computation that emerges in many domains, including traditional fields like computational complexity theory, graph theory, many-body quantum theory and emerging disciplines like machine…