相关论文: Solving the Market Split Problem with Lattice Enum…

The past decade has witnessed a dramatic acceleration of lattice quantum chromodynamics calculations in nuclear and particle physics. This has been due to both significant progress in accelerating the iterative linear solvers using…

The discrete logarithm problem (DLP) is the basis for several cryptographic primitives. Since Shor's work, it has been known that the DLP can be solved by combining a polynomial-size quantum circuit and a polynomial-time classical…

Combinatorial optimization is considered a promising class of problems in which quantum computers can show significant advantages. However, problems of practical relevance typically have more variables than current or foreseeable quantum…

Quadratic Unconstrained Binary Optimization (QUBO) problems are prevalent in real-world applications, such as portfolio optimization, but pose significant computational challenges for large-scale instances. We propose a hybrid…

Modern graphics hardware is designed for highly parallel numerical tasks and promises significant cost and performance benefits for many scientific applications. One such application is lattice quantum chromodyamics (lattice QCD), where the…

Quantum algorithms have shown promise in solving Quadratic Unconstrained Binary Optimization (QUBO) problems, benefiting from their connection to the transverse field Ising model. Various Ising solvers, both classical and quantum, have…

Lattice reduction is a NP-hard problem well known in computer science and cryptography. The Lenstra-Lenstra-Lovasz (LLL) algorithm based on the calculation of orthogonal Gram-Schmidt (GS) bases is efficient and gives a good solution in…

This paper is devoted to the analysis of a numerical scheme based on the Finite Element Method for approximating the solution of Koiter's model for a linearly elastic elliptic membrane shell subjected to remaining confined in a prescribed…

Emerging quantum processors provide an opportunity to explore new approaches for solving traditional problems in the post Moore's law supercomputing era. However, the limited number of qubits makes it infeasible to tackle massive real-world…

Quantum circuits are typically represented by a (ordered) sequence of gates over a set of virtual qubits. During compilation, the virtual qubits of the gates are assigned to the physical qubits of the underlying quantum hardware, a step…

Constraint satisfiability problems, crucial to several applications, are solved on a quantum computer using Grover's search algorithm, leading to a quadratic improvement over the classical case. The solutions are obtained with high…

We present a quantum algorithm for implementing $\phi^4$ lattice scalar field theory on qubit computers. The field is represented in the discretized field amplitude basis. The number of qubits and elementary gates required by the…

We present a new algorithm for computing a truncated Markov basis of a lattice. In general, this new algorithm is faster than existing methods. We then extend this new algorithm so that it solves the linear integer feasibility problem with…

We present a method that integrates any quantum algorithm capable of finding solutions to integer linear programs into the Branch-and-Price algorithm, which is regularly used to solve large-scale integer linear programs with a specific…

Recent progress in LLMs, such as reasoning models, has demonstrated strong abilities to solve complex competitive programming problems, often rivaling top human competitors. However, it remains underexplored whether these abilities…

We formulate a path-integral Monte Carlo algorithm for simulating lattice systems consisting of fictitious particles governed by a generalized exchange statistics. This method, initially proposed for continuum systems, introduces a…

The difficulty of factoring large integers into primes is the basis for cryptosystems such as RSA. Due to the widespread popularity of RSA, there have been many proposed attacks on the factorization problem such as side-channel attacks…

We give a quantum algorithm for solving the Bounded Distance Decoding (BDD) problem with a subexponential approximation factor on a class of integer lattices. The quantum algorithm uses a well-known but challenging-to-use quantum state on…

Topological quantum computing is an alternative framework for avoiding the quantum decoherence problem in quantum computation. The problem of executing a gate in this framework can be posed as the problem of braiding quasiparticles. Because…

This chapter presents the Bilevel Optimization LIBrary of the test problems (BOLIB for short), which contains a collection of test problems, with continuous variables, to help support the development of numerical solvers for bilevel…