相关论文: A common algebraic description for probabilistic a…

Semi-supervised symmetric non-negative matrix factorization (SNMF) utilizes the available supervisory information (usually in the form of pairwise constraints) to improve the clustering ability of SNMF. The previous methods introduce the…

Quantum Process Tomography (QPT) is a powerful tool to characterize quantum operations, but it requires considerable resources making it impractical for more than 2-qubit systems. This work proposes an alternative approach that requires…

We present an approach to computing probabilities in quantum field theory for a wide class of source-detector models. The approach works directly with probabilities and not with squared matrix elements, and the resulting probabilities can…

The polynomial-time computability of the permanent over fields of characteristic 3 for k-semi-unitary matrices (i.e. square matrices such that the differences of their Gram matrices and the corresponding identity matrices are of rank k) in…

We present a randomized quantum algorithm for polynomial factorization over finite fields. For polynomials of degree $n$ over a finite field $\F_q$, the average-case complexity of our algorithm is an expected $O(n^{1 + o(1)} \log^{2 +…

In the last three decades, the $k$-SUM hypothesis has emerged as a satisfying explanation of long-standing time barriers for a variety of algorithmic problems. Yet to this day, the literature knows of only few proven consequences of a…

The ability of fully reconstructing quantum maps is a fundamental task of quantum information, in particular when coupling with the environment and experimental imperfections of devices are taken into account. In this context we carry out a…

The general adversary bound is a semi-definite program (SDP) that lower-bounds the quantum query complexity of a function. We turn this lower bound into an upper bound, by giving a quantum walk algorithm based on the dual SDP that has query…

It is shown that a class of separately frustration-free (SFF) Hamiltonians can be Monte Carlo simulated efficiently on a classical computing machine, because such an SFF Hamiltonian corresponds to a Gibbs wavefunction whose nodal structure…

The schemes for fault-tolerant postselected quantum computation given in [Knill, Fault-Tolerant Postselected Quantum Computation: Schemes, http://arxiv.org/abs/quant-ph/0402171] are analyzed to determine their error-tolerance. The analysis…

Exact solution to many problems in mathematical physics and quantum field theory often can be expressed in terms of an algebraic curve equipped with a meromorphic differential. Typically, the geometry of the curve can be seen most clearly…

We argue that the complex numbers are an irreducible object of quantum probability. This can be seen in the measurements of geometric phases that have no classical probabilistic analogue. Having complex phases as primitive ingredient…

Let $\R$ be a real closed field, $ {\mathcal Q} \subset \R[Y_1,...,Y_\ell,X_1,...,X_k], $ with $ \deg_{Y}(Q) \leq 2, \deg_{X}(Q) \leq d, Q \in {\mathcal Q}, #({\mathcal Q})=m$, and $ {\mathcal P} \subset \R[X_1,...,X_k] $ with $\deg_{X}(P)…

We found that the actual computational time-cost of the QFT is O(n 2^n) for large n in a quantum computer using nuclear spins. The computational cost of a quantum algorithm has usually been estimated as the sum of the universal gates…

A simple and flexible scheme for high-dimensional linear quantum operations on optical transverse spatial modes is demonstrated. The quantum Fourier transformation (QFT) and quantum state tomography (QST) via symmetric informationally…

The quantum Fourier transform (QFT) has emerged as the primary tool in quantum algorithms which achieve exponential advantage over classical computation and lies at the heart of the solution to the abelian hidden subgroup problem, of which…

Number partitioning is one of the classical NP-hard problems of combinatorial optimization. It has applications in areas like public key encryption and task scheduling. The random version of number partitioning has an "easy-hard" phase…

Probabilistic machine learning models are distinguished by their ability to integrate prior knowledge of noise statistics, smoothness parameters, and training data uncertainty. A common approach involves modeling data with Gaussian…

In this paper, a method via sparse-sparse iteration for computing a sparse incomplete factorization of the inverse of a symmetric positive definite matrix is proposed. The resulting factorized sparse approximate inverse is used as a…

The so-called "threshold" theorem says that, once the error rate per qubit per gate is below a certain value, indefinitely long quantum computation becomes feasible, even if all of the qubits involved are subject to relaxation processes,…