Related papers: What can quantum optics say about computational co…
We consider the quantum complexity of computing Schatten $p$-norms and related quantities, and find that the problem of estimating these quantities is closely related to the one clean qubit model of computation. We show that the problem of…
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…
We develop a general formulation of quantum statistical mechanics in terms of probability currents that satisfy continuity equations in the multi-particle position space, for closed and open systems with a fixed number of particles. The…
The quest for quantum computers is motivated by their potential for solving problems that defy existing, classical, computers. The theory of computational complexity, one of the crown jewels of computer science, provides a rigorous…
We introduce and study the computational problem of determining statistical similarity between probability distributions. For distributions $P$ and $Q$ over a finite sample space, their statistical similarity is defined as…
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…
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…
Recently much effort has been made towards the introduction of non-Hermitian random matrix models respecting $PT$-symmetry. Here we show that there is a one-to-one correspondence between complex $PT$-symmetric matrices and split-complex and…
Probabilistic computing excels in approximating combinatorial problems and modelling uncertainty. However, using conventional deterministic hardware for probabilistic models is challenging: (pseudo) random number generation introduces…
We introduce a general method for the construction of quasiprobability representations for arbitrary notions of quantum coherence. Our technique yields a nonnegative probability distribution for the decomposition of any classical state.…
According to the statistical interpretation of quantum theory, quantum computers form a distinguished class of probabilistic machines (PMs) by encoding n qubits in 2n pbits (random binary variables). This raises the possibility of a…
The quantum density matrix generalises the classical concept of probability distribution to quantum theory. It gives the complete description of a quantum state as well as the observable quantities that can be extracted from it. Its…
Given a collection $\{\lambda_1, \dots, \lambda_n\} $ of real numbers, there is a canonical probability distribution on the set of real symmetric or complex Hermitian matrices with eigenvalues $\lambda_1,\ldots,\lambda_n$. In this paper, we…
We extend algorithmic information theory to quantum mechanics, taking a universal semicomputable density matrix (``universal probability'') as a starting point, and define complexity (an operator) as its negative logarithm. A number of…
By using a generalization of the optical tomography technique we describe the dynamics of a quantum system in terms of equations for a purely classical probability distribution which contains complete information about the system.
Approximation algorithms for classical constraint satisfaction problems are one of the main research areas in theoretical computer science. Here we define a natural approximation version of the QMA-complete local Hamiltonian problem and…
It is usually believed that a picture of Quantum Mechanics in terms of true probabilities cannot be given due to the uncertainty relations. Here we discuss a tomographic approach to quantum states that leads to a probability representation…
Given a multiparticle quantum state, one may ask whether it can be represented as a thermal state of some Hamiltonian with k-particle interactions only. The distance from the exponential family defined by these thermal states can be…
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…
We introduce an algorithm for the classical simulation of Gaussian boson sampling that is quadratically faster than previously known methods. The complexity of the algorithm is exponential in the number of photon pairs detected, not the…