Spatial correlations in the qubit properties of D-Wave 2000Q measured and simulated qubit networks

TL;DR

The paper investigates strong positive spatial correlations in qubits on a D-Wave 2000Q chip, focusing on inter-unit-cell connections. It analyzes LANL QASA data using Geary's $C$ to quantify per-qubit parameter correlations and finds weak global correlations but notable patterns for inter-unit-cell versus intra-unit-cell connections. To explain these effects, it simulates small Chimera-like spin networks with length-dependent couplings, including a dipole-dipole model with $J \\propto \\frac{1}{r^3}$, and shows that connectivity plus distance-dependent weights can produce nontrivial spatial correlations in excitation transfer. The results suggest that architectural features and unprogrammed interactions can drive deviations from idealized identical-qubit models, with implications for embedding strategies and hardware design.

Abstract

We show strong positive spatial correlations in the qubits of a D-Wave 2000Q quantum annealing chip that are connected to qubits outside their own unit cell. By simulating the dynamics of spin networks, we then show that correlation between nodes is affected by a number of factors. The different connectivity of qubits within the network means that information transfer is not straightforward even when all the qubit-qubit couplings have equal weighting. The similarity between connected nodes is further changed when the couplings' strength is scaled according to the physical length of the connections (here to simulate dipole-dipole interactions). This highlights the importance of understanding the architectural features and potentially unprogrammed interactions/connections that can divert the performance of a quantum system away from the idealised model of identical qubits and couplings across the chip.

Figures (5)

• Figure 1: A graph representation of the D-Wave Chimera architecture as present on the 2000Q quantum annealer. The red box shows the 8 qubits that make up a unit cell. (Diagram created using D-Wave NetworkX Python language package D-Wave_Systems2021-bg.)
• Figure 2: Model coded for simulations. The blue connections and the yellow nodes are those used in the simulation. The remaining nodes and connections are shown in black and have been included for completeness.
• Figure 3: System dynamics of the 8 node network.
• Figure 4: Node fidelities at two different times with two different coupling.
• Figure 5: The similarity in the fidelity of connected nodes in the 8 node Chimera architecture. A square at (i,j) is labelled with the relative length of the connection between the nodes i and j and is colourised by the similarity as defined by equation \ref{['sim']}.