Related papers: Sculpting Quantum Speedups
We consider the bipartite boolean quadric polytope (BQP) with multiple-choice constraints and analyse its combinatorial properties. The well-studied BQP is defined as the convex hull of all quadric incidence vectors over a bipartite graph.…
We study the forrelation problem: given a pair of $n$-bit Boolean functions $f$ and $g$, estimate the correlation between $f$ and the Fourier transform of $g$. This problem is known to provide the largest possible quantum speedup in terms…
Simulating quantum circuits using classical computers lets us analyse the inner workings of quantum algorithms. The most complete type of simulation, strong simulation, is believed to be generally inefficient. Nevertheless, several…
Quantum data access and quantum processing can make certain classically intractable learning tasks feasible. However, quantum capabilities will only be available to a select few in the near future. Thus, reliable schemes that allow…
Quantum computation is frequently mischaracterized as the simultaneous execution of exponentially many classical computations. This article offers a conceptual clarification of why this ``branchwise parallelism'' picture is misleading,…
In this work, we develop a framework aiming at designing quantum algorithms for combinatorial optimization problems while providing theoretical guarantees on their approximation ratios. The principal innovative aspect of our work is the…
We identify a sub-class of BQP that captures certain structural commonalities among many quantum algorithms including Shor's algorithms. This class does not contain all of BQP (e.g. Grover's algorithm does not fall into this class). Our…
Quantum algorithms have the potential to provide exponential speedups over some of the best known classical algorithms. These speedups may enable quantum devices to solve currently intractable problems such as those in the fields of…
Due to the significant progress made in the implementation of quantum hardware, efficient methods and tools to design corresponding algorithms become increasingly important. Many of these tools rely on functional representations of certain…
It is known that for some languages quantum finite automata are more efficient than classical counterparts. Particularly, a QFA recognizing the language $MOD_p$ has an exponential advantage over the classical finite automata. However, the…
Imagine coating buildings and bridges with smart particles (also coined smart paint) that monitor structural integrity and sense and report on traffic and wind loads, leading to technology that could do such inspection jobs faster and…
As research on building scalable quantum computers advances, it is important to be able to certify their correctness. Due to the exponential hardness of classically simulating quantum computation, straight-forward verification through…
Quantum computers may achieve speedups over their classical counterparts for solving linear algebra problems. However, in some cases -- such as for low-rank matrices -- dequantized algorithms demonstrate that there cannot be an exponential…
Quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given in a black box and the aim is to compute function value for arbitrary input using as few queries as possible. We concentrate on quantum…
Optimization problems become fundamentally challenging as the number of variables increases. Because the volume of the search space grows exponentially, classical algorithms frequently fail to locate the global minimum of non-convex…
Polylogarithmic time delineates a relevant notion of feasibility on several classical computational models such as Boolean circuits or parallel random access machines. As far as the quantum paradigm is concerned, this notion yields the…
Recently, increased computational power and data availability, as well as algorithmic advances, have led machine learning techniques to impressive results in regression, classification, data-generation and reinforcement learning tasks.…
In our thesis, we try to shed more light onto the complexity of quantum complexity classes by refining the related part of the hierarchy. First, we review the basic concepts of quantum computing in general. Then, inspired by BQP, we define…
It has been shown that the apparent advantage of some quantum machine learning algorithms may be efficiently replicated using classical algorithms with suitable data access -- a process known as dequantization. Existing works on…
The Traveling Salesman Problem (TSP) is a classical NP-hard problem that plays a crucial role in combinatorial optimization. In this paper, we are interested in the quantum search framework for the TSP because it has robust theoretical…