Quantum annealing in the NISQ era: railway conflict management

Abstract

We are in the Noisy Intermediate-Scale Quantum (NISQ) devices' era, in which quantum hardware has become available for application in real-world problems. However, demonstrating the usefulness of such NISQ devices are still rare. In this work, we consider a practical railway dispatching problem: delay and conflict management on single-track railway lines. We examine the issue of train dispatching consequences caused by the arrival of an already delayed train to the network segment being considered. This problem is computationally hard and needs to be solved almost in real-time. We introduce a quadratic unconstrained binary optimization (QUBO) model of this problem, compatible with the emerging quantum annealing technology. The model's instances can be executed on present-day quantum annealers. As a proof-of-concept, we solve selected real-life problems from the Polish railway network using D-Wave quantum annealers. As a reference, we also provide solutions calculated with classical methods, including those relevant to the community (linear integer programming) and a sophisticated algorithm based on tensor networks for solving Ising instances. Our preliminary results illustrate the degree of difficulty of real-life railway instances for the current quantum annealing technology. Moreover, our analysis shows that the new generation of quantum annealers (the advantage system) perform much worse on those instances than its predecessor.

From quantum speed limits to energy-efficient quantum gates

“…To find the actual solution of the optimal control problem, we now need to determine a function ω(t) such that if each point on the Bloch sphere moves with angular velocity ω from time t = 0 to time τ , then the end result will be a rotation of the Bloch sphere by an angle α about an axis n. Of all such functions, we must find one which minimizes equation ( 20), and then compute the minimal value of the cost. A natural guess, which turns out to be correct, is that the rotation can be implemented with minimal cost by rotating about the axis n at a constant rate 4 . We will now show that the following protocol minimizes the cost, ω(t) = α/τ n. First, it is apparent that this is an allowed protocol since the axis of rotation is n and the sphere rotates by an angle α between time 0 and time τ , so this process results in the correct transformation of each state.…”

Assessing the performance of quantum annealing with nonlinear driving

“…The protocol λ 2 (23b) has the same first derivative at the QCP as the linear protocol, which means that both protocols display the KZM and LZF scales of Eqs. (11) and (12), respectively. On the other hand, λ 2 differs from λ 1 in its first derivatives at the end points, which are null.…”

“…In particular, quantum annealing [6], closely related to adiabatic quantum computing [7], has achieved some prominence [8][9][10][11]. However, from a practical and algorithmic point of view, realizing fault-tolerant adiabatic quantum computing might even be more involved than other computational paradigms.…”

Omnisolver: an extensible interface to Ising spin glass solvers

“…In particular, this will mainly benefit entities that face combinatorial optimization problems in their daily routine, such as railway companies. As an example of such application, we refer an interested reader to the works [9,10].…”