Related papers: Polynomial-time quantum algorithm for solving the …
I present a single algorithm which solves the clique problems, "What is the largest size clique?", "What are all the maximal cliques?" and the decision problem, "Does a clique of size k exist?" for any given graph in polynomial time. The…
We present a quantum algorithm for solving the hidden subgroup problem in the general linear group over a finite field where the hidden subgroup is promised to be a conjugate of the group of the invertible lower triangular matrices. The…
The problem of efficient multiplication of large numbers has been a long-standing challenge in classical computation and has been extensively studied for centuries. It appears that the existing classical algorithms are close to their…
We describe an algorithm that computes the ground state energy and correlation functions for 2-local Hamiltonians in which interactions between qubits are weak compared to single-qubit terms. The running time of the algorithm is polynomial…
We present the first explicit connection between quantum computation and lattice problems. Namely, we show a solution to the Unique Shortest Vector Problem (SVP) under the assumption that there exists an algorithm that solves the hidden…
A common situation in quantum many-body physics is that the underlying theories are known but too complicated to solve efficiently. In such cases one usually builds simpler effective theories as low-energy or large-scale alternatives to the…
Non-smooth optimization models play a fundamental role in various disciplines, including engineering, science, management, and finance. However, classical algorithms for solving such models often struggle with convergence speed,…
Solving linear systems of equations is a common problem that arises both on its own and as a subroutine in more complex problems: given a matrix A and a vector b, find a vector x such that Ax=b. We consider the case where one doesn't need…
A central problem in quantum computing is to identify computational tasks which can be solved substantially faster on a quantum computer than on any classical computer. By studying the hardest such tasks, known as BQP-complete problems, we…
Quadratic Unconstrained Binary Optimization (QUBO) is a broad class of optimization problems with many practical applications. To solve its hard instances in an exact way, known classical algorithms require exponential time and several…
The application of quantum algorithms to classical problems is generally accompanied by significant bottlenecks when transferring data between quantum and classical states, often negating any intrinsic quantum advantage. Here we address…
There is no known polynomial-time algorithm that can solve an NP problem. Evolutionary search has been shown to be a viable method of finding acceptable solutions within a reasonable time period. Recently quantum computers have surfaced as…
Estimating the eigenvalues of non-normal matrices is a foundational problem with far-reaching implications, from modeling non-Hermitian quantum systems to analyzing complex fluid dynamics. Yet, this task remains beyond the reach of standard…
The optimization of measurements for the state distinction problem has recently been applied to the theory of quantum algorithms with considerable successes, including efficient new quantum algorithms for the non-abelian hidden subgroup…
The Traveling Salesperson Problem (TSP) is a fundamental NP-hard optimisation challenge with widespread applications in logistics, operations research, and network design. While classical algorithms effectively solve small to medium-sized…
The computational complexity of simulating quantum many-body systems generally scales exponentially with the number of particles. This enormous computational cost prohibits first principles simulations of many important problems throughout…
In the circuit model of quantum computing, amplitude amplification techniques can be used to find solutions to NP-hard problems defined on $n$-bits in time $\text{poly}(n) 2^{n/2}$. In this work, we investigate whether such general…
Recently a method for adiabatic quantum computation has been proposed and there has been considerable speculation about its efficiency for NP-complete problems. Heuristic arguments in its favor are based on the unproven assumption of an…
Optimization problems in disciplines such as machine learning are commonly solved with iterative methods. Gradient descent algorithms find local minima by moving along the direction of steepest descent while Newton's method takes into…
The subset sum problem (SSP) can be briefly stated as: given a target integer $E$ and a set $A$ containing $n$ positive integer $a_j$, find a subset of $A$ summing to $E$. The \textit{density} $d$ of an SSP instance is defined by the ratio…