Related papers: BQP $=$ PSPACE
A restricted path integral method is proposed to simulate a type of quantum system or Hamiltonian called a sum of controlled few-fermions on a classical computer using Monte Carlo without a numerical sign problem. Then a universality is…
Many computer vision problems can be formulated as binary quadratic programs (BQPs). Two classic relaxation methods are widely used for solving BQPs, namely, spectral methods and semidefinite programming (SDP), each with their own…
Quantum computers are predicted to outperform classical ones for solving partial differential equations, perhaps exponentially. Here we consider a prototypical PDE - the heat equation in a rectangular region - and compare in detail the…
The so-called welded tree problem provides an example of a black-box problem that can be solved exponentially faster by a quantum walk than by any classical algorithm. Given the name of a special ENTRANCE vertex, a quantum walk can find…
We consider quantum algorithms for the unique sink orientation problem on cubes. This problem is widely considered to be of intermediate computational complexity. This is because there no known polynomial algorithm (classical or quantum)…
In a previous paper, we have shown that any Boolean formula can be encoded as a linear programming problem in the framework of Bayesian probability theory. When applied to NP-complete algorithms, this leads to the fundamental conclusion…
For decades it is known that Quantum Computers might serve as a tool to solve a very specific kind of problems that have long thought to be incalculable. Some of those problems are of a combinatorial nature, with the quantum advantage…
Quantum computing has demonstrated the potential to solve computationally intensive problems more efficiently than classical methods. Many software engineering tasks, such as test case selection, static analysis, code clone detection, and…
We study multiplayer quantitative reachability games played on a finite directed graph, where the objective of each player is to reach his target set of vertices as quickly as possible. Instead of the well-known notion of Nash equilibrium…
Quality diversity (QD) algorithms have been shown to be very successful when dealing with problems in areas such as robotics, games and combinatorial optimization. They aim to maximize the quality of solutions for different regions of the…
The prevailing view is that quantum phenomena can be harnessed to tackle certain problems beyond the reach of classical approaches. Quantifying this capability as a quantum-classical separation and demonstrating it on current quantum…
We explain the mechanism of the quantum speed-up - quantum algorithms requiring fewer computation steps than their classical equivalent - for a family of algorithms. Bob chooses a function and gives to Alice the black box that computes it.…
In this paper, we give a quantum algorithm which solves collision problem in an expected polynomial time. Especially, when the function is two-to-one, we present a quantum algorithm which can find a collision with certainty in a worst-case…
From the 1970s up to now, Mastermind, a classic two-player game, has attracted plenty of attention, not only from the public as a popular game, but also from the academic community as a scientific issue. Mastermind with n positions and k…
Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time…
We study the power of classical and quantum algorithms equipped with nonuniform advice, in the form of a coin whose bias encodes useful information. This question takes on particular importance in the quantum case, due to a surprising…
We investigate algorithmic control of a large swarm of mobile particles (such as robots, sensors, or building material) that move in a 2D workspace using a global input signal (such as gravity or a magnetic field). We show that a maze of…
We consider the quantum complexity of computing Schatten $p$-norms and related quantities, and find that the problem of estimating these quantities is closely related to the one clean qubit model of computation. We show that the problem of…
The Binary Space Partitioning-Tree~(BSP-Tree) process was recently proposed as an efficient strategy for space partitioning tasks. Because it uses more than one dimension to partition the space, the BSP-Tree Process is more efficient and…
Partial differential equations (PDEs) play a crucial role in financial mathematics, particularly in portfolio optimization, and solving them using classical numerical or neural network methods has always posed significant challenges. Here,…