Related papers: Permanents in linear optical networks
Matrix permanents arise naturally in the context of linear optical networks fed with nonclassical states of light. In this letter we tie the computational complexity of a class of multi-dimensional integrals to the permanents of large…
In order to find the outcome probabilities of quantum mechanical systems like the optical networks underlying Boson sampling, it is necessary to be able to compute the permanents of unitary matrices, a computationally hard task. Here we…
In this paper, we strengthen the connection between qubit-based quantum circuits and photonic quantum computation. Within the framework of circuit-based quantum computation, the sum-over-paths interpretation of quantum probability…
Unitary transformations are routinely modeled and implemented in the field of quantum optics. In contrast, nonunitary transformations that can involve loss and gain require a different approach. In this theory work, we present a universal…
Particular complexity of linear quantum optical networks is deserved recently certain attention due to possible implications for theory of quantum computation. Two relevant models of bosons are discussed in presented work. Symmetric product…
Linear optical networks are devices that turn classical incident modes by a linear transformation into outgoing ones. In general, the quantum version of such transformations may mix annihilation and creation operators. We derive a simple…
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…
We present a finite-order system of recurrence relations for a permanent of circulant matrices containing a band of k any-value diagonals on top of a uniform matrix (for k = 1, 2, and 3) as well as the method for deriving such recurrence…
Linear optical elements are pivotal instruments in the manipulation of classical and quantum states of light. The vast progress in integrated quantum photonic technology enables the implementation of large numbers of such elements on chip…
Linear optical computing (LOC) with thermal light has recently gained attention because the problem is connected to the permanent of a Hermitian positive semidefinite matrix (HPSM), which is of importance in the computational complexity…
We establish a formal bridge between qubit-based and photonic quantum computing. We do this by defining a functor from the ZX calculus to linear optical circuits. In the process we provide a compositional theory of quantum linear optics…
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…
We study the time and space complexity of matrix permanents over rings and semirings.
The paper addresses the calculation of correlation functions of permanental polynomials of matrices with random entries. By exploiting a convenient contour integral representation of the matrix permanent some explicit results are provided…
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…
The permanent is pivotal to both complexity theory and combinatorics. In quantum computing, the permanent appears in the expression of output amplitudes of linear optical computations, such as in the Boson Sampling model. Taking advantage…
We explore some properties of a recent representation of permanental vectors which expresses them as sums of independent vectors with components that are independent gamma random variables.
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…
We show that the permanent of a matrix can be written as the expectation value of a function of random variables each with zero mean and unit variance. This result is used to show that Glynn's theorem and a simplified MacMahon theorem…
Linear optical circuits of growing complexity are playing an increasing role in emerging photonic quantum technologies. Individual photonic devices are typically described by a unitary matrix containing amplitude and phase information, the…