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arXiv:2405.16067 · International Conference on Quantum Communications, Networking, and Computing (QCNC)

Weaving Complex Graph on Simple Low-Dimensional Qubit Lattices

Yu–Hang Dang, Shyam Dhamapurkar, Xiao–Long Zhu, Zhengyang Zhou, Hao–Yu Guan, Xiu–Hao Deng

Published Jul 1, 2024• 0 citations
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Abstract

In quantum computing, the connectivity of qubits placed on two-dimensional chips limits the scalability and functionality of solid-state quantum computers. This paper presents two approaches to constructing complex quantum networks from simple qubit arrays, specifically grid lattices. The first approach utilizes a subset of qubits as tunable couplers, effectively yielding a range of non-trivial graph-based Hamiltonians. The second approach employs dynamic graph engineering by periodically activating and deactivating couplers, enabling the creation of effective quantum walks with longer-range couplings. Numerical simulations verify the effective dynamics of these approaches. In terms of these two approaches, we explore implementing various graphs, including cubes and fullerenes, etc, on two-dimensional lattices. These techniques facilitate the realization of analog quantum simulation, particularly continuous-time quantum walks discussed in detail in this manuscript, for different computational tasks on superconducting quantum chips despite their inherent low dimensional simple architecture.

DOI
10.1109/qcnc62729.2024.00027

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In quantum computing, the connectivity of qubits placed on two-dimensional chips limits the scalability and functionality of solid-state quantum computers. This paper presents two approaches to constructing complex quantum networks from simple qubit arrays, specifically grid lattices. The first approach utilizes a subset of qubits as tunable couplers, effectively yielding a range of non-trivial graph-based Hamiltonians. The second approach employs dynamic graph engineering by periodically activating and deactivating couplers, enabling the creation of effective quantum walks with longer-range couplings. Numerical simulations verify the effective dynamics of these approaches. In terms of these two approaches, we explore implementing various graphs, including cubes and fullerenes, etc, on two-dimensional lattices. These techniques facilitate the realization of analog quantum simulation, particularly continuous-time quantum walks discussed in detail in this manuscript, for different computational tasks on superconducting quantum chips despite their inherent low dimensional simple architecture.
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Quantum walks provide a natural framework to approach graph problems with quantum computers, exhibiting speedups over their classical counterparts for tasks such as the search for marked nodes or the prediction of missing links. Continuous-time quantum walk algorithms assume that we can simulate the dynamics of quantum systems where the Hamiltonian is given by the adjacency matrix of the graph. It is known that such can be simulated efficiently if the underlying graph is row-sparse and efficiently row-computable. While this is sufficient for many applications, it limits the applicability for this class of algorithms to study real world complex networks, which, among other properties, are characterized by the existence of a few densely connected nodes, called hubs. In other words, complex networks are typically not row-sparse, even though the average connectivity over all nodes can be very small. In this work, we extend the state-of-the-art results on quantum simulation to graphs that contain a small number of hubs, but that are otherwise sparse. Hopefully, our results may lead to new applications of quantum computing to network science.
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