Related papers: Quantum-like representation algorithm for trichoto…
We present a constructive method to translate small quantum circuits into their optical analogues, using linear components of present-day quantum optics technology only. These optical circuits perform precisely the computation that the…
It is well known in quantum optics that any process involving the preparation of a multimode gaussian state, followed by a gaussian operation and gaussian measurements, can be efficiently simulated by classical computers. Here, we provide…
Using the known possibility to associate the completely positive maps with density matrices and recent results on expressing the density matrices with sets of classical probability distributions of dichotomic random variables we construct…
I present here some results on the statistical behaviour of large random matrices in an ensemble where the probability distribution is not a function of the eigenvalues only. The perturbative expansion can be cast in a closed form and the…
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…
The quasiprobability representation of quantum states addresses two main concerns, the identification of nonclassical features and the decomposition of the density operator. While the former aspect is a main focus of current research, the…
We give a review of the tomographic probability representation of quantum mechanics. We present the formalism of quantum states and quantum observables using the formalism of standard probability distributions and classical-like random…
Originally, quantum probability theory was developed to analyze statistical phenomena in quantum systems, where classical probability theory does not apply, because the lattice of measurable sets is not necessarily distributive. On the…
Extracting information from weak optical signals is a critical challenge across a broad range of technologies. Conventional imaging techniques, constrained to integrating over detected signals and classical post-processing, are limited in…
The measurement problem and the role of observers have plagued quantum mechanics since its conception. Attempts to resolve these have introduced anthropomorphic or non-realist notions into physics. A shift of perspective based upon process…
Quantum mechanics relates probability of an observable event to the absolute square of the corresponding probability amplitude. It may, therefore, seem that the information about the amplitudes' phases must be irretrievably lost in the…
Equilibrium statistical mechanics provides powerful tools to understand physics at the macroscale. Yet, the question remains how this can be justified based on a microscopic quantum description. Here, we extend the ideas of pure state…
In this paper, we review some features of quantum annealing and related topics from viewpoints of statistical physics, condensed matter physics, and computational physics. We can obtain a better solution of optimization problems in many…
In this paper we present two flavors of a quantum extension to the lambda calculus. The first one, $\lambda_\rho$, follows the approach of classical control/quantum data, where the quantum data is represented by density matrices. We provide…
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…
Consider a graph whose vertices are populated by identical objects, together with an algorithm for the time-evolution of the number of objects placed at each of the vertices. The discrete dynamics of these objects can be observed and…
We present a quantum algorithm based on repeated measurement to solve initial-value problems for nonlinear ordinary differential equations (ODEs), which may be generated from partial differential equations in plasma physics. We map a…
As data volume grows extensively, data profiling helps to extract metadata of large-scale data. However, one kind of metadata, order statistics, is difficult to be computed because they are not mergeable or incremental. Thus, the limitation…
We introduce a family of identities that express general linear non-unitary evolution operators as a linear combination of unitary evolution operators, each solving a Hamiltonian simulation problem. This formulation can exponentially…
We prove that quantum computation is polynomially equivalent to classical probabilistic computation with an oracle for estimating the value of simple sums, quadratically signed weight enumerators. The problem of estimating these sums can be…