Related papers: Experimentally demonstrating indefinite causal ord…
This paper summarizes a research program that has been underway for a decade. The objective is to find a fast and accurate scheme for solving quantum problems which does not involve a Monte Carlo algorithm. We use an alternative strategy…
We study the advantage of pure-state quantum computation without entanglement over classical computation. For the Deutsch-Jozsa algorithm we present the maximal subproblem that can be solved without entanglement, and show that the algorithm…
Recent work of Bravyi et al. and follow-up work by Bene Watts et al. demonstrates a quantum advantage for shallow circuits: constant-depth quantum circuits can perform a task which constant-depth classical (i.e., AC$^0$) circuits cannot.…
The measurement problem in quantum mechanics originates in the inability of the Schr\"odinger equation to predict definite outcomes of measurements. This is due to the lack of objectivity of the eigenstates of the measuring apparatus. Such…
We present two quantum interior point methods for semidefinite optimization problems, building on recent advances in quantum linear system algorithms. The first scheme, more similar to a classical solution algorithm, computes an inexact…
In this paper we discuss how we can design Hamiltonians to implement quantum algorithms, in particular we focus in Deutsch and Grover algorithms. As main result of this paper, we show how Hamiltonian inverse quantum engineering method allow…
We present a novel quantum algorithm for solving the unstructured search problem with one marked element. Our algorithm allows generating quantum circuits that use asymptotically fewer additional quantum gates than the famous Grover's…
A central problem in quantum computation is to understand which quantum circuits are useful for exponential speed-ups over classical computation. We address this question in the setting of query complexity and show that for almost any…
The performance of quantum computers today can be studied by analyzing the effect of errors in the result of simple quantum algorithms. The modeling and characterization of these errors is relevant to correct them, for example, with quantum…
We use Deutsch's algorithm as a stand in for more complex quantum algorithms in order to determine how quantum properties of an environment manifest themselves in results that can be obtained on quantum computers. We model pure dephasing in…
This paper presents a quantum algorithm for solving the fractional Poisson equation \((-\Delta)^s u = f\) with \(s \in (0,1)\) on bounded domains. The proposed approach combines rational approximation techniques with quantum linear system…
Quantum correlations have been pointed out as the most likely source of the speed-up in quantum computation. Here we analyzed the presence of quantum correlations in the implementation of Deutsch-Jozsa algorithm running in the DQC1 and DQCp…
We consider the problem of search of an unstructured list for a marked element, when one is given advice as to where this element might be located, in the form of a probability distribution. The goal is to minimise the expected number of…
Let $f$ denote length preserving function on words. A classical algorithm can be considered as $T$ iterated applications of black box representing $f$, beginning with input word $x$ of length $n$. It is proved that if $T=O(2^{n/(7+e)}), e…
We present a quantum algorithm which simulates the quantum kicked rotator model exponentially faster than classical algorithms. This shows that important physical problems of quantum chaos, localization and Anderson transition can be…
Quantum algorithms are known for providing more efficient solutions to certain computational tasks than any corresponding classical algorithm. Here we show that a single qudit is sufficient to implement an oracle based quantum algorithm,…
Randomized algorithms are crucial subroutines in quantum computing, but the requirement to execute many types of circuits on a real quantum device has been challenging to their extensive implementation. In this study, we propose an…
The discovery of causal relations from observed data has attracted significant interest from disciplines such as economics, social sciences, and biology. In practical applications, considerable knowledge of the underlying systems is often…
Indefinite causal order (ICO) has the potential to be a new resource for quantum information processing. In most of its experiments, ICO has been investigated in a photonic platform. Here we investigate ICO in a cavity quantum…
The oracle chooses a function out of a known set of functions and gives to the player a black box that, given an argument, evaluates the function. The player should find out a certain character of the function through function evaluation.…