Related papers: Efficient computation of permanents, with applicat…
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…
Consider the collection of all binary matrices having a specific sequence of row and column sums and consider sampling binary matrices uniformly from this collection. Practical algorithms for exact uniform sampling are not known, but there…
We describe a dynamic programming algorithm for exact counting and exact uniform sampling of matrices with specified row and column sums. The algorithm runs in polynomial time when the column sums are bounded. Binary or non-negative integer…
Recent experiments demonstrated quantum computational advantage in random circuit sampling and Gaussian boson sampling. However, it is unclear whether these experiments can lead to practical applications even after considerable research…
We present a deterministic algorithm, which, for any given 0< epsilon < 1 and an nxn real or complex matrix A=(a_{ij}) such that | a_{ij}-1| < 0.19 for all i, j computes the permanent of A within relative error epsilon in n^{O(ln n -ln…
The search for new, application-specific quantum computers designed to outperform any classical computer is driven by the ending of Moore's law and the quantum advantages potentially obtainable. Photonic networks are promising examples,…
We describe an algorithm for using a quantum computer to calculate mean values of observables and the partition function of a quantum system. Our algorithm includes two sub-algorithms. The first sub-algorithm is for calculating, with…
Matrix multiplication is a fundamental computation in many scientific disciplines. In this paper, we show that novel fast matrix multiplication algorithms can significantly outperform vendor implementations of the classical algorithm and…
The algorithm and complexity of approximating the permanent of a matrix is an extensively studied topic. Recently, its connection with quantum supremacy and more specifically BosonSampling draws special attention to the average-case…
The Cox process is a stochastic process which generalises the Poisson process by letting the underlying intensity function itself be a stochastic process. In this paper we present a fast Bayesian inference scheme for the permanental…
Big data is ubiquitous in practices, and it has also led to heavy computation burden. To reduce the calculation cost and ensure the effectiveness of parameter estimators, an optimal subset sampling method is proposed to estimate the…
We present a quantum algorithm for estimating the matrix determinant based on quantum spectral sampling. The algorithm estimates the logarithm of the determinant of an $n \times n$ positive sparse matrix to an accuracy $\epsilon$ in time…
A fundamental question in linear optical quantum computing is to understand the origin of the quantum supremacy in the physical system. It is found that the multimode linear optical transition amplitudes are calculated through the…
Multiphoton interference is at the very heart of quantum foundations and applications in quantum sensing and information processing. In particular, boson sampling experiments have the potential to demonstrate quantum computational supremacy…
The efficient preparation of input distributions is an important problem in obtaining quantum advantage in a wide range of domains. We propose a novel quantum algorithm for the efficient preparation of arbitrary normal distributions in…
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…
BosonSampling is a problem where a quantum computer offers a provable speedup over classical computers. Its main feature is that it can be solved with current linear optics technology, without the need for a full quantum computer. In this…
We investigate fully self-consistent multiscale quantum-classical algorithms on current generation superconducting quantum computers, in a unified approach to tackle the correlated electronic structure of large systems in both quantum…
Exact calculation and even multiplicative error estimation of matrix permanent are challenging for both classical and quantum computers. Regarding the permanents of random Gaussian matrices, the additive error estimation is closely linked…
The search for new, application-specific quantum computers designed to outperform any classical computer is driven by the ending of Moore's law and the quantum advantages potentially obtainable. Photonic networks are promising examples,…