Related papers: A Satisfiability Algorithm for AC$^0$
We study the scaling of the convergence of several statistical properties of a recently introduced random unitary circuit ensemble towards their limits given by the circular unitary ensemble (CUE). Our study includes the full distribution…
We present a wait-free algorithm for proper coloring the n nodes of the asynchronous cycle $C_n$, where each crash-prone node starts with its (unique) identifier as input. The algorithm is independent of $n \geq 3$, and runs in…
We prove that any polynomial-time $\alpha(n)$-approximation algorithm for the $n$-vertex metric asymmetric Traveling Salesperson Problem yields a polynomial-time $O(\alpha(C))$-approximation algorithm for the mixed and windy Capacitated Arc…
The imputation of missing data is a common procedure in data analysis that consists in predicting missing values of incomplete data points. In this work we analyse a variational quantum circuit for the imputation of missing data. We…
In arXiv:1710.08163 a generalization of Boolean circuits to arbitrary finite algebras had been introduced and applied to sketch P versus NP-complete borderline for circuits satisfiability over algebras from congruence modular varieties.…
In this paper, we consider the problem of scheduling an application on a parallel computational platform. The application is a particular task graph, either a linear chain of tasks, or a set of independent tasks. The platform is made of…
Over a decade after its proposal, the idea of using quantum computers to sample hard distributions has remained a key path to demonstrating quantum advantage. Yet a severe drawback remains: verification seems to require classical…
We show that the CNF satisfiability problem (SAT) can be solved in time $O^*(1.1199^{(d-2)n})$, where $d$ is either the maximum number of occurrences of any variable or the average number of occurrences of all variables if no variable…
Classical simulation of noisy quantum circuits is essential for understanding quantum computing experiments. It enables scalable error characterization, analysis of how noise impacts quantum algorithms, and optimized implementations of…
We present a quantum circuit optimization technique that takes into account the variability in error rates that is inherent across present day noisy quantum computing platforms. This method can be run post qubit routing or post-compilation,…
Variational quantum algorithms are believed to be promising for solving computationally hard problems and are often comprised of repeated layers of quantum gates. An example thereof is the quantum approximate optimization algorithm (QAOA),…
Randomized benchmarking (RB) is a widely used method for estimating the average fidelity of gates implemented on a quantum computing device. The stochastic error of the average gate fidelity estimated by RB depends on the sampling strategy…
The paper introduces a novel algorithm for computing the output admissible set of linear discrete-time systems subject to input saturation. The proposed method takes advantage of the piecewise-affine dynamics to propagate the output…
Approximate circuits trading the power consumption for the quality of results play a key role in the development of energy-aware systems. Designing complex approximate circuits is, however, a very difficult and computationally demanding…
We study optimization problems that are neither approximable in polynomial time (at least with a constant factor) nor fixed parameter tractable, under widely believed complexity assumptions. Specifically, we focus on Maximum Independent…
The taxing computational effort that is involved in solving some high-dimensional statistical problems, in particular problems involving non-convex optimization, has popularized the development and analysis of algorithms that run…
We describe a new efficient algorithm to approximate z-rotations by ancilla-free Clifford+V circuits, up to a given precision epsilon. Our algorithm is optimal in the presence of an oracle for integer factoring: it outputs the shortest…
We consider the problem of solving integer programs of the form $\min \{\,c^\intercal x\ \colon\ Ax=b, x\geq 0\}$, where $A$ is a multistage stochastic matrix in the following sense: the primal treedepth of $A$ is bounded by a parameter…
Variational quantum algorithms have been advocated as promising candidates to solve combinatorial optimization problems on near-term quantum computers. Their methodology involves transforming the optimization problem into a quadratic…
Classical circuit complexity characterizes parallel computation in purely combinatorial terms, ignoring the physical constraints that govern real hardware. The standard classes $\mathbf{NC}$, $\mathbf{AC}$, and $\mathbf{TC}$ treat unlimited…