Related papers: A Factorisation Algorithm in Adiabatic Quantum Com…
Binary quadratic programming problems have attracted much attention in the last few decades due to their potential applications. This type of problems are NP-hard in general, and still considered a challenge in the design of efficient…
Distribution networks with periodically repeating events often hold great promise to exploit economies of scale. Joint replenishment problems are a fundamental model in inventory management, manufacturing, and logistics that capture these…
By introducing a quadratic perturbation to the canonical dual of the maxcut problem, we transform the integer programming problem into a concave maximization problem over a convex positive domain under some circumstances, which can be…
We extend the work of Hen for the Bernstein-Vazirani problem and Simon's problem on an adiabatic quantum computer. Our results are based on the Ising objective function for quantum annealing. For each problem we determine its objective…
At present, several models for quantum computation have been proposed. Adiabatic quantum computation scheme particularly offers this possibility and is based on a slow enough time evolution of the system, where no transitions take place. In…
This paper presents a new method to reduce the optimization of a pseudo-Boolean function to QUBO problem which can be solved by quantum annealer. The new method has two aspects, one is coefficient optimization and the other is variable…
Solving the floating-point equation $x \otimes y = z$, where $x$, $y$ and $z$ belong to floating-point intervals, is a common task in automated reasoning for which no efficient algorithm is known in general. We show that it can be solved by…
The problem of decomposing a given covariance matrix as the sum of a positive semi-definite matrix of given rank and a positive semi-definite diagonal matrix, is considered. We present a projection-type algorithm to address this problem.…
We introduce a new deterministic factoring algorithm, which could be described in the cryptographically fashionable term of "factoring with hints": we show that, given the knowledge of the factorisations of $O(N^{1/3+\epsilon})$ terms…
In adiabatic quantum computing the aim is to track an eigenstate as the Hamiltonian changes. In the usual setup this is achieved using the natural time-dependent Hamiltonian evolution of the system and the main technical tool is the…
Quantum computing offers significant potential for solving NP-hard combinatorial (optimization) problems that are beyond the reach of classical computers. One way to tap into this potential is by reformulating combinatorial problems as a…
Advances in quantum algorithms suggest a tentative scaling advantage on certain combinatorial optimization problems. Recent work, however, has also reinforced the idea that barren plateaus render variational algorithms ineffective on large…
For two relatively prime positive integers $a, b\in \mathbb{N}$, it is known that exactly one of the two Diophantine equations $$ax + by \ =\ \frac{(a-1)(b-1)}{2}\ \mbox{ and }\ 1 + ax + by \ =\ \frac{(a-1)(b-1)}{2}$$ has a nonnegative…
In quantum adiabatic evolution algorithms, the quantum computer follows the ground state of a slowly varying Hamiltonian. The ground state of the initial Hamiltonian is easy to construct; the ground state of the final Hamiltonian encodes…
This paper presents the concept of digit polynomials, which leads to a deterministic and unconditional integer factorization algorithm with the runtime complexity $\mathcal{O}(N^{1/4+\epsilon})$. Strassen's well known factoring approach is…
Quantum adiabatic algorithm is of vital importance in quantum computation field. It offers us an alternative approach to manipulate the system instead of quantum gate model. Recently, an interesting work arXiv:1805.10549 indicated that we…
Quantum information processing is likely to have far-reaching impact in the field of artificial intelligence. While the race to build an error-corrected quantum computer is ongoing, noisy, intermediate-scale quantum (NISQ) devices provide…
We investigate prime factorization from two perspectives: quantum annealing and computational algebraic geometry, specifically Gr\"obner bases. We present a novel scalable algorithm which combines the two approaches and leads to the…
We consider digitized-counterdiabatic quantum computing as an advanced paradigm to approach quantum advantage for industrial applications in the NISQ era. We apply this concept to investigate a discrete mean-variance portfolio optimization…
The discrete formulation of adiabatic quantum computing is compared with other search methods, classical and quantum, for random satisfiability (SAT) problems. With the number of steps growing only as the cube of the number of variables,…