Grover Mixers for QAOA: Shifting Complexity from Mixer Design to State Preparation

We propose GM-QAOA, a variation of the Quantum Alternating Operator Ansatz (QAOA) that uses Grover-like selective phase shift mixing operators. GM-QAOA works on any NP optimization problem for which it is possible to efficiently prepare an equal superposition of all feasible solutions; it is designed to perform particularly well for constraint optimization problems, where not all possible variable assignments are feasible solutions. GM-QAOA has the following features: (i) It is not susceptible to Hamiltonian Simulation error (such as Trotterization errors) as its operators can be implemented exactly using standard gate sets and (ii) Solutions with the same objective value are always sampled with the same amplitude. We illustrate the potential of GM-QAOA on several optimization problem classes: for permutation-based optimization problems such as the Traveling Salesperson Problem, we present an efficient algorithm to prepare a superposition of all possible permutations of $n$ numbers, defined on $O(n^2)$ qubits; for the hard constraint $k$-Vertex-Cover problem, and for an application to Discrete Portfolio Rebalancing, we show that GM-QAOA outperforms existing QAOA approaches

A Framework for Incentive Compatible Topology Control in Non-Cooperative Wireless Multi-Hop Networks

In this paper we consider the problem of building and maintaining a network topology with certain desirable features in a wireless multi-hop network where nodes behave like selfish agents. We first provide examples showing that existing topology control approaches are not resilient to strategic node behavior, indicating the need of considering possible selfish node behavior at the design stage. Given this observation, we propose a general framework that can be used as a guideline in the design of incentive compatible topology control protocols. As examples of application of our framework to specific topology control protocols, we present incentive compatible distributed algorithms for building the minimum spanning tree (MST) and the k-closest neighbors graph, which are very well-known topology control approaches. To the best of our knowledge, the ones presented in this paper are the first incentive compatible realizations of topology control presented in the literature

QAOA-based Fair Sampling on NISQ Devices

We study the status of fair sampling on Noisy Intermediate Scale Quantum (NISQ) devices, in particular the IBM Q family of backends. Using the recently introduced Grover Mixer-QAOA algorithm for discrete optimization, we generate fair sampling circuits to solve six problems of varying difficulty, each with several optimal solutions, which we then run on ten different backends available on the IBM Q system. For a given circuit evaluated on a specific set of qubits, we evaluate: how frequently the qubits return an optimal solution to the problem, the fairness with which the qubits sample from all optimal solutions, and the reported hardware error rate of the qubits. To quantify fairness, we define a novel metric based on Pearson's $\chi^2$ test. We find that fairness is relatively high for circuits with small and large error rates, but drops for circuits with medium error rates. This indicates that structured errors dominate in this regime, while unstructured errors, which are random and thus inherently fair, dominate in noisier qubits and longer circuits. Our results provide a simple, intuitive means of quantifying fairness in quantum circuits, and show that reducing structured errors is necessary to improve fair sampling on NISQ hardware

LLVM Static Analysis for Program Characterization and Memory Reuse Profile Estimation

Profiling various application characteristics, including the number of different arithmetic operations performed, memory footprint, etc., dynamically is time- and space-consuming. On the other hand, static analysis methods, although fast, can be less accurate. This paper presents an LLVM-based probabilistic static analysis method that accurately predicts different program characteristics and estimates the reuse distance profile of a program by analyzing the LLVM IR file in constant time, regardless of program input size. We generate the basic-block-level control flow graph of the target application kernel and determine basic-block execution counts by solving the linear balance equation involving the adjacent basic blocks' transition probabilities. Finally, we represent the kernel memory accesses in a bracketed format and employ a recursive algorithm to calculate the reuse distance profile. The results show that our approach can predict application characteristics accurately compared to another LLVM-based dynamic code analysis tool, Byfl.Comment: This paper was accepted at the MEMSYS '23 conference, The International Symposium on Memory Systems, October 02, 2023 - October 05, 2023, Alexandria, V

Predicting Expressibility of Parameterized Quantum Circuits using Graph Neural Network

Parameterized Quantum Circuits (PQCs) are essential to quantum machine learning and optimization algorithms. The expressibility of PQCs, which measures their ability to represent a wide range of quantum states, is a critical factor influencing their efficacy in solving quantum problems. However, the existing technique for computing expressibility relies on statistically estimating it through classical simulations, which requires many samples. In this work, we propose a novel method based on Graph Neural Networks (GNNs) for predicting the expressibility of PQCs. By leveraging the graph-based representation of PQCs, our GNN-based model captures intricate relationships between circuit parameters and their resulting expressibility. We train the GNN model on a comprehensive dataset of PQCs annotated with their expressibility values. Experimental evaluation on a four thousand random PQC dataset and IBM Qiskit's hardware efficient ansatz sets demonstrates the superior performance of our approach, achieving a root mean square error (RMSE) of 0.03 and 0.06, respectively

Online Dominating Set

This paper is devoted to the online dominating set problem and its variants on trees, bipartite, bounded-degree, planar, and general graphs, distinguishing between connected and not necessarily connected graphs. We believe this paper represents the first systematic study of the effect of two limitations of online algorithms: making irrevocable decisions while not knowing the future, and being incremental, i.e., having to maintain solutions to all prefixes of the input. This is quantified through competitive analyses of online algorithms against two optimal algorithms, both knowing the entire input, but only one having to be incremental. We also consider the competitive ratio of the weaker of the two optimal algorithms against the other. In most cases, we obtain tight bounds on the competitive ratios. Our results show that requiring the graphs to be presented in a connected fashion allows the online algorithms to obtain provably better solutions. Furthermore, we get detailed information regarding the significance of the necessary requirement that online algorithms be incremental. In some cases, having to be incremental fully accounts for the online algorithm\u27s disadvantage