Related papers: A Quadratic Lower Bound for Simulation
We introduce symmetric arithmetic circuits, i.e. arithmetic circuits with a natural symmetry restriction. In the context of circuits computing polynomials defined on a matrix of variables, such as the determinant or the permanent, the…
An abstract indefinite least squares problem with a quadratic constraint is considered. This is a quadratic programming problem with one quadratic equality constraint, where neither the objective nor the constraint are convex functions.…
We show that Nechiporuk's method for proving lower bounds for Boolean formulas can be extended to the quantum case. This leads to an $\Omega(n^2 / \log^2 n)$ lower bound for quantum formulas computing an explicit function. The only known…
Contextuality has been conjectured to be a super-classical resource for quantum computation, analogous to the role of non-locality as a super-classical resource for communication. We show that the presence of contextuality places a lower…
There has been a great deal of recent interest in methods for performing lifted inference; however, most of this work assumes that the first-order model is given as input to the system. Here, we describe lifted inference algorithms that…
Quantum simulation uses a well-known quantum system to predict the behavior of another quantum system. Certain limitations in this technique arise, however, when applied to specific problems, as we demonstrate with a theoretical and…
We consider the time and space required for quantum computers to solve a wide variety of problems involving matrices, many of which have only been analyzed classically in prior work. Our main results show that for a range of linear algebra…
We study sequential prediction of real-valued, arbitrary and unknown sequences under the squared error loss as well as the best parametric predictor out of a large, continuous class of predictors. Inspired by recent results from…
We present a formalism that captures the process of proving quantum superiority to skeptics as an interactive game between two agents, supervised by a referee. Bob, is sampling from a classical distribution on a quantum device that is…
Many real life optimization problems contain both hard and soft constraints, as well as qualitative conditional preferences. However, there is no single formalism to specify all three kinds of information. We therefore propose a framework,…
Practical model building processes are often time-consuming because many different models must be trained and validated. In this paper, we introduce a novel algorithm that can be used for computing the lower and the upper bounds of model…
Quantum particle simulations have largely been based on time-independent, split-operator schemes in which kinetic and potential operators are interwoven to provide accurate approximations to system dynamics. These simulations can be very…
We study symmetric arithmetic circuits and improve on lower bounds given by Dawar and Wilsenach (ArXiv 2020). Their result showed an exponential lower bound of the permanent computed by symmetric circuits. We extend this result to show a…
The problem if a given configuration of a pushdown automaton (PDA) is bisimilar with some (unspecified) finite-state process is shown to be decidable. The decidability is proven in the framework of first-order grammars, which are given by…
As simulations of quantum systems cross the limits of classical computability, both quantum and classical approaches become hard to verify. Scaling predictions are therefore based on local structure and asymptotic assumptions, typically…
We define formally decohered quantum computers (using density matrices), and present a simulation of them by a probabalistic classical Turing Machine. We study the slowdown of the simulation for two cases: (1) sequential quantum computers,…
Bisimulation equivalence (or bisimilarity) of first-order grammars is decidable, as follows from the decidability result by Senizergues (1998, 2005) that has been given in an equivalent framework of equational graphs with finite out-degree,…
Discrete translational symmetry plays a fundamental role in condensed matter physics and lattice gauge theories, enabling the analysis of systems that would otherwise be intractable. Despite this, many open problems remain. Quantum…
This paper initiates the study of quantum algorithms for matroid property problems. It is shown that quadratic quantum speedup is possible for the calculation problem of finding the girth or the number of circuits (bases, flats,…
We show that there is a language in $\mathsf{S}_2\mathsf{E}/_1$ (symmetric exponential time with one bit of advice) with circuit complexity at least $2^n/n$. In particular, the above also implies the same near-maximum circuit lower bounds…