Related papers: Expressiveness of Commutative Quantum Circuits: A …
A fundamental challenge in probabilistic modeling is to balance expressivity and inference efficiency. Tractable probabilistic models (TPMs) aim to directly address this tradeoff by imposing constraints that guarantee efficient inference of…
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…
What makes a class of quantum circuits efficiently classically simulable on average? I present a framework that applies harmonic analysis of groups to circuits with a structure encoded by group parameters. Expanding the circuits in a…
We have proved new estimates for the coherent control errors of quantum circuits used in quantum computing. These estimates essentially take into account the commutator properties of the Hamiltonians and are based on the formulas of the…
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…
Quantum computers can be used for supervised learning by treating parametrised quantum circuits as models that map data inputs to predictions. While a lot of work has been done to investigate practical implications of this approach, many…
We propose an implementation of a quantum walk on a circle on an optomechanical system by encoding the walker on the phase space of a radiation field and the coin on a two-level state of a mechanical resonator. The dynamics of the system is…
We apply results from Baryshnikov, Brady, Bressler and Pemantle (2008) to compute limiting probability profiles for various quantum random walks in one and two dimensions. Using analytic machinery we show some features of the limit…
On the basis of extensive numerical studies it is argued that there are strong analogies between the probabilistic behavior of quantum systems defined by Hermitian Hamiltonians and the deterministic behavior of classical mechanical systems…
This is an investigation of the limits of quantum circuit simulation with Schrodinger's formulation and low precision arithmetic. The goal is to estimate how much memory can be saved in simulations that involve random, maximally entangled…
Quantum circuits generating probability distributions has applications in several areas. Areas like finance require quantum circuits that can generate distributions that mimic some given data pattern. Hamiltonian simulations require…
The study of quantum circuits composed of commuting gates is particularly useful to understand the delicate boundary between quantum and classical computation. Indeed, while being a restricted class, commuting circuits exhibit genuine…
When random walks on a square lattice are biased horizontally to move solely to the right, the probability distribution of their algebraic area can be exactly obtained. We explicitly map this biased classical random system on a non…
We make and generalize the observation that summing of probability amplitudes of a discrete-time quantum walk over partitions of the walking graph consistent with the step operator results in a unitary evolution on the reduced graph which…
In the worldline formalism, scalar Quantum Electrodynamics on a 2-dimensional lattice is related to the areas of closed loops on this lattice. We exploit this relationship in order to determine the general structure of the moments of the…
It was recently shown that a generalization of quantum Turing machines (QTMs), in which potentials are associated with elementary steps or transitions of the computation, generates potential distributions along computation paths of states…
In this paper, we study the properties of lackadaisical quantum walks on a line. This model is first proposed in~\cite{wong2015grover} as a quantum analogue of lazy random walks where each vertex is attached $\tau$ self-loops. We derive an…
A representation of the continuum fermionic propagator as a sum of directed random walks on a lattice is presented. Also a random walk representation for the lattice fermionic propagators is developed for the case of the naive, the Wilson,…
An analytical solution for a quantum wave impedance in a case of piesewise constant potential was derived. It is in fact an analytical depiction of a well-known iterative method of a quantum wave impedance determination. The expression for…
The general matrix representation of a beam splitter array is presented. Each beam splitter has a transmission/reflection coefficient that determines the behavior of these individual devices and, in consequence, the whole system response.…