Quantum computing for finance: Our work is in UDaily.

 Great recent article in UDaily about our joint project with Argonne National Lab, JPMorgan Chase, Fujitsu and Menten AI. We discuss the obstacles and opportunities of quantum computing in finance.

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Optimal Contraction Trees for Tensor Network Quantum Circuit Simulation

We are excited to announce that our paper received the best student paper award at #IEEE High Performance Extreme Computing #HPEC2022! Leading student is Cameron Ibrahim. Congratulations to all!

Cameron Ibrahim, Danylo Lykov, Zichang He, Yuri Alexeev, Ilya Safro "Constructing Optimal Contraction Trees for Tensor Network Quantum Circuit Simulation", 2022, preprint at https://arxiv.org/abs/2209.02895

One of the key problems in tensor network based quantum circuit simulation is the construction of a contraction tree which minimizes the cost of the simulation, where the cost can be expressed in the number of operations as a proxy for the simulation running time. This same problem arises in a variety of application areas, such as combinatorial scientific computing, marginalization in probabilistic graphical models, and solving constraint satisfaction problems. In this paper, we reduce the computationally hard portion of this problem to one of graph linear ordering, and demonstrate how existing approaches in this area can be utilized to achieve results up to several orders of magnitude better than existing state of the art methods for the same running time. To do so, we introduce a novel polynomial time algorithm for constructing an optimal contraction tree from a given order. Furthermore, we introduce a fast and high quality linear ordering solver, and demonstrate its applicability as a heuristic for providing orderings for contraction trees. Finally, we compare our solver with competing methods for constructing contraction trees in quantum circuit simulation on a collection of randomly generated Quantum Approximate Optimization Algorithm Max Cut circuits and show that our method achieves superior results on a majority of tested quantum circuits.

Recently accepted papers in optimization and quantum and quantum inspired computing.

• Xiaoyuan Liu, Hayato Ushijima-Mwesigwa, Indradeep Ghosh, Ilya Safro "Partitioning Dense Graphs with Hardware Accelerators", International Conference on Computational Science (ICCS), 2022, preprint at https://arxiv.org/pdf/2202.09420.pdf
• Ankit Kulshrestha, Ilya Safro "BEINIT: Avoiding Barren Plateaus in Variational Quantum Algorithms", IEEE Quantum Computing and Engineering (QCE), 2022, preprint at https://arxiv.org/abs/2204.13751
• Xiaoyuan Liu, Ruslan Shaydulin, Ilya Safro "Quantum Approximate Optimization Algorithm with Sparsified Phase Operator", IEEE Quantum Computing and Engineering (QCE), 2022, preprint at https://arxiv.org/abs/2205.00118
• Xiaoyuan Liu, Hayato Ushijima-Mwesigwa, Avradip Mandal, Sarvagya Upadhyay, Ilya Safro, Arnab Roy "Leveraging Special-Purpose Hardware for Local Search Heuristics", Computational Optimization and Applications, 2022, preprint at https://arxiv.org/pdf/1911.09810.pdf

Transferring QAOA parameters from small instances to large

The Quantum approximate optimization algorithm (QAOA) is one of the most promising candidates for  achieving quantum advantage through quantum-enhanced combinatorial optimization. However, finding optimal parameters to run QAOA is a hard problem that is usually tackled by variational loop, i.e., the circuit is executed with the current parameters on a quantum device, and then the parameters are updated on a classical device. Such variational loops are extremely time consuming. In our recent paper we find the QAOA parameters for small optimization instances and transfer them to the larger ones accelerating the entire process.

Alexey Galda, Xiaoyuan Liu, Danylo Lykov, Yuri Alexeev, Ilya Safro "Transferability of optimal QAOA parameters between random graphs", IEEE International Conference on Quantum Computing and Engineering (QCE), preprint at https://arxiv.org/pdf/2106.07531.pdf, 2021

In a typical  QAOA setup, a set of quantum circuit parameters is optimized to prepare a quantum state used to find the optimal solution of a combinatorial optimization problem. Several empirical observations about optimal parameter concentration effects for special QAOA MaxCut problem instances have been made in recent literature, however, a rigorous study of the subject is still lacking. We show that convergence of the optimal QAOA parameters around specific values and, consequently, successful transferability of parameters between different QAOA instances can be explained and predicted based on the local properties of the graphs, specifically the types of subgraphs (lightcones) from which the graphs are composed. We apply this approach to random regular and general random graphs. For example, we demonstrate how optimized parameters calculated for a 6-node random graph can be successfully used without modification as nearly optimal parameters for a 64-node random graph, with less than 1% reduction in approximation ratio as a result. This work presents a pathway to identifying classes of combinatorial optimization instances for which such variational quantum algorithms as QAOA can be substantially accelerated.

Tutorial on the quantum approximate optimization algorithm, its applications and simulation

We recorded this tutorial for IEEE International Conference on Quantum Computing and Engineering (QCE) 2020. This tutorial consists of four parts:

1. QAOA theory and quantum computing basics
2. Hands on example of QAOA and MaxCut
3. Introduction to problem decomposition and solving large-scale problems with QAOA
4. Tensor networks and simulation of QAOA with classical computers

Can we outperform Quantum Approximate Optimization Algorithm?

Check our new paper:

Xiaoyuan Liu, Anthony Angone, Ruslan Shaydulin, Ilya Safro, Yuri Alexeev, Lukasz Cincio "Layer VQE: A Variational Approach for Combinatorial Optimization on Noisy Quantum Computers", preprint at https://arxiv.org/abs/2102.05566, 2021

We propose a hybrid quantum-classical algorithm, Layer Variational Quantum Eigensolver (L-VQE), inspired by the Variational Quantum Eigensolver (VQE). L-VQE is a heuristic approach to solve combinatorial optimization problems on near term intermediate-scale quantum devices. We demonstrate the potential of the proposed approach by applying it to the problem of community detection, a famous problem in network science. Our large-scale numerical simulation study shows that L-VQE has the potential to outperform Quantum Approximate Optimization Algorithm (QAOA), and is more robust to sampling noise as compared with standard VQE approaches.

How to find the best location for wireless charging lanes

Our paper is accepted in Journal of Industrial Management and Optimization 

Ushijima-Mwesigwa, Khan, Chowdhury, Safro "Optimal Installation for Electric Vehicle Wireless Charging Lanes", 2019

The emergence of electric vehicle wireless charging technology, where a whole lane can be turned into a charging infrastructure, leads to new challenges in the design and analysis of road networks. From a network perspective, a major challenge is determining the most important nodes with respect to the placement of the wireless charging lanes. In other words, given a limited budget, cities could face the decision problem of where to place these wireless charging lanes. With a heavy price tag, a placement without a careful study can lead to inefficient use of limited resources. In this work, the placement of wireless charging lanes is modeled as an integer programming problem. The basic formulation is used as a building block for different realistic scenarios. We carry out experiments using real geospatial data and compare our results to different network-based heuristics.

Reproducibility: all datasets, algorithm implementations and mathematical programming formulation presented in this work are available at https://github.com/hmwesigwa/smartcities.git

Hybrid quantum-classical algorithms

Our paper on hybrid quantum-classical algorithms is featured in IEEE Computer, the June's issue on quantum realism.

Ruslan Shaydulin, Hayato Ushijima-Mwesigwa, Christian F.A. Negre, Ilya Safro, Susan M. Mniszewski, Yuri Alexeev "Hybrid Approach for Solving Optimization Problems on Small Quantum Computers", IEEE Computer, vol. 52(6), pp. 18-26, 2019

Solving larger-sized problems is an important area of research in quantum computing. Designing hybrid quantum-classical algorithms is a promising approach to solving this. We discuss decomposition-based hybrid approaches for solving optimization problems and demonstrate them for applications related to community detection.

Solving network community detection problem on quantum computers

Accepted paper in Advanced Quantum Technology journal

Shaydulin, Ushijima-Mwesigwa, Safro, Mniszewski, Alexeev "Network Community Detection On Small Quantum Computers", 2019, preprint at https://arxiv.org/abs/1810.12484

In recent years, a number of quantum computing devices with small numbers of qubits have become available. A hybrid quantum local search (QLS) approach that combines a classical machine and a small quantum device to solve problems of practical size is presented. The proposed approach is applied to the network community detection problem. QLS is hardware‐agnostic and easily extendable to new quantum computing devices as they become available. It is demonstrated to solve the 2‐community detection problem on graphs of sizes of up to 410 vertices using the 16‐qubit IBM quantum computer and D‐Wave 2000Q, and compare their performance with the optimal solutions. The results herein demonstrate that QLS performs similarly in terms of quality of the solution and the number of iterations to convergence on both types of quantum computers and it is capable of achieving results comparable to state‐of‐the‐art solvers in terms of quality of the solution including reaching the optimal solutions.

Finding influential nodes in networks with consumable resources

Accepted paper in Network Science journal 

Ushijima-Mwesigwa, Khan, Chowdhury, Safro, "Centralities for Networks with Consumable Resources", 2019, preprint at https://arxiv.org/abs/1903.00642

Identification of influential nodes is an important step in understanding and controlling the dynamics of information, traffic, and spreading processes in networks. As a result, a number of centrality measures have been proposed and used across different application domains. At the heart of many of these measures lies an assumption describing the manner in which traffic (of information, social actors, particles, etc.) flows through the network. For example, some measures only count shortest paths while others consider random walks. This paper considers a spreading process in which a resource necessary for transit is partially consumed along the way while being refilled at special nodes on the network. Examples include fuel consumption of vehicles together with refueling stations, information loss during dissemination with error-correcting nodes, and consumption of ammunition of military troops while moving. We propose generalizations of the well-known measures of betweenness, random-walk betweenness, and Katz centralities to take such a spreading process with consumable resources into account. In order to validate the results, experiments on real-world networks are carried out by developing simulations based on well-known models such as Susceptible-Infected-Recovered and congestion with respect to particle hopping from vehicular flow theory. The simulation-based models are shown to be highly correlated with the proposed centrality measures.

Does it help to charge the electric cars at intersections?

Accepted paper in Computer-Aided Civil and Infrastructure Engineering 

Khan, Khan Chowdhury, Safro, Ushijima-Mwesigwa "Wireless Charging Utility Maximization and Intersection Control Delay Minimization Framework for Electric Vehicles"

This study presents the Wireless Charging Utility Maximization (WCUM) framework, which aims to maximize the utility of Wireless Charging Units (WCUs) for electric vehicle (EV) charging through the optimal WCU deployment at signalized intersections. Furthermore, the framework aims to minimize the control delay at all signalized intersections of the network. The framework consists of a two‐step optimization formulation, a dynamic traffic assignment model to calculate the user equilibrium, a traffic microsimulator to formulate the objective functions, and a global Mixed Integer Non‐Linear Programming (MINLP) optimization solver. An optimization problem is formulated for each intersection, and another for the entire network. The performance of the WCUM framework is tested using the Sioux Falls network. We perform a comparative study of 12 global MINLP solvers with a case study. Based on solution quality and computation time, we choose the Couenne solver for this framework.

https://onlinelibrary.wiley.com/doi/abs/10.1111/mice.12439