Related papers: Practical implementation of a quantum backtracking…
We present space efficient Monte Carlo algorithms that solve Subset Sum and Knapsack instances with $n$ items using $O^*(2^{0.86n})$ time and polynomial space, where the $O^*(\cdot)$ notation suppresses factors polynomial in the input size.…
Parameterized complexity enables the practical solution of generally intractable NP-hard problems when certain parameters are small, making it particularly useful in real-world applications. The study of string problems in this framework…
A pivotal task for quantum computing is to speed up solving problems that are both classically intractable and practically valuable. Among these, combinatorial optimization problems have attracted tremendous attention due to their broad…
We survey old and new results about optimal algorithms for summation of finite sequences and for integration of functions from Hoelder or Sobolev spaces. First we discuss optimal deterministic and randomized algorithms. Then we add a new…
We consider worst case time bounds for NP-complete problems including 3-SAT, 3-coloring, 3-edge-coloring, and 3-list-coloring. Our algorithms are based on a constraint satisfaction (CSP) formulation of these problems. 3-SAT is equivalent to…
Current quantum computing devices have different strengths and weaknesses depending on their architectures. This means that flexible approaches to circuit design are necessary. We address this task by introducing a novel space-efficient…
Solving systems of linear equations is a fundamental problem, but it can be computationally intensive for classical algorithms in high dimensions. Existing quantum algorithms can achieve exponential speedups for the quantum linear system…
Following the first paper on quantum algorithms for SDP-solving by Brand\~ao and Svore in 2016, rapid developments has been made on quantum optimization algorithms. Recently Brand\~ao et al. improved the quantum SDP-solver in the so-called…
Quantum computers are expected to have substantial impact on the finance industry, as they will be able to solve certain problems considerably faster than the best known classical algorithms. In this article we describe such potential…
We define and study a statistical mechanics ensemble that characterizes connected solutions in constraint satisfaction problems (CSPs). Built around a well-known local entropy bias, it allows us to better identify hardness transitions in…
This paper studies a fundamental problem in convex optimization, which is to solve semidefinite programming (SDP) with high accuracy. This paper follows from the existing robust SDP-based interior point method analysis due to [Huang, Jiang,…
Quantum state preparation (QSP) is a key component in many quantum algorithms. In particular, the problem of sparse QSP (SQSP) $\unicode{x2013}$ the task of preparing the states with only a small number of non-zero amplitudes…
We introduce two quantum algorithms for solving structured prediction problems. We first show that a stochastic gradient descent that uses the quantum minimum finding algorithm and takes its probabilistic failure into account solves the…
Quantum optimization holds promise for addressing classically intractable combinatorial problems, yet a standardized framework for benchmarking its performance, particularly in terms of solution quality, computational speed, and scalability…
In constrained Markov decision processes (CMDPs) with adversarial rewards and constraints, a well-known impossibility result prevents any algorithm from attaining both sublinear regret and sublinear constraint violation, when competing…
Algorithms based on non-unitary evolution have attracted much interest for ground state preparation on quantum computers. One recently proposed method makes use of ancilla qubits and controlled unitary operators to implement weak…
Multivariate quantum signal processing (M-QSP) has recently been shown to be applicable for non-Hermitian Hamiltonian simulation, opening several problems regarding the optimization landscape, angle-finding, and constant-factor analysis. We…
We study online learning in constrained Markov decision processes (CMDPs) in which rewards and constraints may be either stochastic or adversarial. In such settings, Stradi et al.(2024) proposed the first best-of-both-worlds algorithm able…
This paper summarizes a quantum algorithm of [R.D. Somma, et.al., Phys. Rev. Lett. 101, 130504 (2008)] that simulates a classical annealing process for solving discrete optimization problems. The complexity of the quantum algorithm scales…
We present an exact quantum algorithm for solving the Exact Satisfiability (XSAT) problem, which belongs to the important NP-complete complexity class. The algorithm is based on an intuitive approach that can be divided into two parts:…