A Near-Term Quantum Computing Approach for Hard Computational Problems in Space Exploration

Abstract

The future of Space Exploration is entwined with the future of artificial intelligence (AI) and machine learning. Autonomous rovers, unmanned spacecraft, and remote space habitats must all make intelligent decisions with little or no human guidance. The decision-making required of such NASA assets stretches machine intelligence to its limits. Currently, AI problems are tackled using a variety of heuristic approaches, and practitioners are constantly trying to find new and better techniques. To achieve a radical breakthrough in AI, radical new approaches are needed. Quantum computing is one such approach.Many of the hard combinatorial problems in space exploration are instances of NP-complete or NP-hard problems. Neither traditional computers nor quantum computers are expected to be able to solve all instances of such problems efficiently. Many heuristic algorithms, such as simulated annealing, support vector machines, and SAT solvers, have been developed to solve or approximate solutions to practical instances of these problems. The efficacy of these approaches is generally determined by running them on benchmark sets of problem instances. Such empirical testing for quantum algorithms requires the availability of quantum hardware.Quantum annealing machines, analog quantum computational devices, are designed to solve discrete combinatorial optimization problems using properties of quantum adiabatic evolution. We are now on the cusp of being able to run small-scale examples of these problems on actual quantum annealing hardware which will enable us to test empirically the performance of quantum annealing on these problems. For example, D-Wave builds quantum annealing machines based on superconducting qubits. While at present noise and decoherence in quantum annealing devices cannot be easily controlled or corrected, these devices have been shown to display multi-spin tunneling, a distinct quantum phenomenon at the root of the quantum annealing process. In order to attack an optimization problem on these machines, the problem must be formulated in quadratic unconstrained binary optimization form in which the cost function is strictly quadratic in bit assignments (in physics applications this form is often referred to as an Ising model). The above limitation is not fundamental: all NP-complete problems can be mapped to this form. However, an optimal mapping involving small or no overhead in terms of additional bits is of significant practical interest because of the limited size of early quantum annealing machines.In this article, we discuss a sampling of the hardest artificial intelligence problems in space exploration in the context in which they emerge. We show how to map them onto equivalent Ising models

The quantum adiabatic algorithm applied to random optimization problems: The quantum spin glass perspective

“…Despite its length this review has no pretension of exhaustivity; complementary point of views on the quantum adiabatic algorithm can be found in the reviews [21,22,23,24,50,51,52] and references therein.…”

Multivariable optimization: Quantum annealing and computation

“…The basic point behind the criticisms had been that the incoherent mixture of the tunnelling waves coming from different energy barriers, may lead to localization of the wave functions while penetrating energy barriers, as the phases of the transmitted waves are completely random. However several recent theoretical and experimental studies (see e.g., [9,10,11,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32]) seem to have cleared almost all such doubts. Recently the technological implementation of QA to develop an analog quantum computer has been mastered successfully by the D-wave systems [18].…”

Many-Qudit representation for the Travelling Salesman Problem Optimisation

“…A strategy to solve COP such as TSP in a quantum computer is to map the TSP to a Hamiltonian such that the solution tour can be deduced from the ground state of the corresponding Hamiltonian. Usually, the TSP is cast into a quadratic unconstrained binary optimisation (QUBO) problem, which can be easily mapped to an Ising spin-glass model [17][18][19][20][21][22][23] , taking N 2 qubits to solve the TSP for N cities. This means that the Hilbert space of the corresponding Ising spin-glass model is of size 2 N 2 .…”

“…Conventionally, the TSP can be mapped to a QUBO problem, which is then straight-forwardly mapped to an Ising Hamiltonian [17][18][19][20][21][22][23] . In particular, following the explanation by Smelyanskiy et al 17 , we define a binary variable z iα that is 1 if the i-th city is the α-th location visited in a tour, and is 0 otherwise. The length of the tour is i,j,α d i,j z i,α z j,α+1 , where d i,j is the distance between the i-th an the j-th city.…”