quantum annealing

This article addresses the question of implementing a maximum flow algorithm on directed graphs in a formulation suitable for a quantum annealing computer. Three distinct approaches are presented. In all three cases, the flow problem is formulated as a quadratic unconstrained binary optimization (QUBO) problem amenable to quantum annealing. The first implementation augments a graph with integral edge capacities into a multigraph with unit-capacity edges and encodes the fundamental objective and constraints of the maximum flow problem using a number of qubits equal to the total capacity of the graph ∑i ci . The second implementation, which encodes flows through edges using a binary representation, reduces the required number of qubits to O(|E|logCmax) , where |E| and Cmax denote the number of edges and maximum edge capacity of the graph, respectively. The third implementation adapts the dual minimum cut formulation and encodes the problem instance using |V| qubits, where |V| is the number of vertices in the graph. Scaling factors for penalty terms and coupling matrix construction times are made explicit in this article.

We introduce the notion of reinforcement quantum annealing (RQA) scheme in which an intelligent agent searches in the space of Hamiltonians and interacts with a quantum annealer that plays the stochastic environment role of learning automata. At each iteration of RQA, after analyzing results (samples) from the previous iteration, the agent adjusts the penalty of unsatisfied constraints and re-casts the given problem to a new Ising Hamiltonian. As a proof-of-concept, we propose a novel approach for casting the problem of Boolean satisfiability (SAT) to Ising Hamiltonians and show how to apply the RQA for increasing the probability of finding the global optimum. Our experimental results on two different benchmark SAT problems (namely factoring pseudo-prime numbers and random SAT with phase transitions), using a D-Wave 2000Q quantum processor, demonstrated that RQA finds notably better solutions with fewer samples, compared to the best-known techniques in the realm of quantum annealing.

Quantum processing units (QPUs) executing annealing algorithms have shown promise in optimization and simulation applications. Hybrid algorithms are a natural bridge to additional applications of larger scale. We present a straightforward and effective method for solving larger-than-QPU lattice-structured Ising optimization problems. Performance is compared against simulated annealing with promising results, and improvement is shown as a function of the generation of D-Wave QPU used.

We investigate the dynamics of quantum correlations between the quantum annealing processor nodes. The quantum annealing processor is simulated by spin-chain model. It is assumed that system started from the thermal state. The Hamiltonian of the system is mathematically designed and analytically solved. The properties of the system are investigated. Negativity is used to investigate the dynamics of quantum correlation between the system nodes. The effect of the system parameters (spin-orbit coupling, coupling constant, and bias parameter) on the dynamics of negativity is explored. Results showed that the coupling constant had a great effect in the dynamics of the quantum correlation.

Quantum annealing algorithms belong to the class of meta-heuristic tools, applicable for solving binary optimization problems. Hardware implementations of quantum annealing, such as the quantum processing units (QPUs) produced by D-Wave Systems [1], have been subject to multiple analyses in research, with the aim of characterizing the technology’s usefulness for optimization and sampling tasks [2–15]. In this paper, we present a real-world application that uses quantum technologies. Specifically, we show how to map certain parts of the realworld traffic flow optimization problem to be suitable for quantum annealing. We show that time-critical optimization tasks, such as continuous redistribution of position data for cars in dense road networks, are suitable candidates for quantum applications. Due to the limited size and connectivity of current-generation D-Wave QPUs, we use a hybrid quantum and classical approach to solve the traffic flow problem. ∗Corresponding author: florian.neu...

The longest path problem on graphs is an NP-hard optimization problem, and as such, it is not known to have an efficient classical solution in the general case. This study develops two quadratic unconstrained binary optimization (QUBO) formulations of this well-known problem. The first formulation is based on an approach outlined by (Bauckhage et al., 2018) for the shortest path problem and follows simply from the principle of assigning positions on the path to vertices; using k|V| binary variables, this formulation will find the longest path that visits exactly k of a graph's |V| vertices, if such a path exists. As a point of theoretical interest, we present a second formulation based on degree constraints that is more complicated, but reduces the dependence of the number of variables on k to logarithmic; specifically, it requires |V| + 2|E|log2 k + 3|E| binary variables to encode the longest path problem. We adapt these basic formulations for several variants of the standard longest path problem. Scaling factors for penalty terms and preprocessing time required to construct the Q matrix representing the problem are made explicit in the paper.

My last article, " Life Through Quantum Annealing " was an exploration of how a broad range of physical phenomena-and possibly the whole universe-can be mapped to a quantum computing process. But the article simply accepts that quantum annealing behaves as it does; it does not attempt to explain why. That answer lies somewhere within a "true" description of quantum mechanics, which is still an outstanding problem. Despite the massive predictive success of quantum mechanics, physicists still can't agree on how its math corresponds to reality. Any such proposal, called an "interpretation" of quantum mechanics, tends to straddle the line between physics and philosophy. There is no shortage of interpretations, and in the words of physicist David Mermin, "New interpretations appear every year. None ever disappear." Am I going to throw one more on that pile? You bet. I'm not going to start from scratch though; I simply propose an ever-so-slight modification to an existing forerunner: the many-worlds interpretation, where other "worlds" or timelines exist in parallel to our own. My modification is this: the only worlds that can exist are those that exist within a causal loop. Stated another way: our universe, or any possible universe, must be a causal loop. I will introduce the relevant concepts and provide an argument for my proposal, but my goal is not to once-and-for-all prove this interpretation as true. Rather, my goal is to explore what happens if we accept the interpretation as true. If we start with the assumption that only causal loop universes can exist, then several interesting things follow-we find parallels to our own universe, and we might even find God.