Weaving Complex Graph on simple low-dimensional qubit lattices

TL;DR

This paper introduces methods to construct complex quantum networks on simple 2D qubit lattices, enabling advanced quantum simulations despite hardware connectivity limitations.

Contribution

It proposes tunable coupler subsets and dynamic graph engineering techniques to realize complex graphs and quantum walks on low-dimensional qubit arrays.

Findings

Numerical simulations confirm effective quantum walk dynamics.

Implementation of complex graphs like cubes and fullerenes on 2D lattices.

Techniques enable analog quantum simulation on simple superconducting chips.

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.