D-Wave QPU Architecture: Chimera

The layout of the D-Wave QPU is critical to translating a QUBO or Ising objective function into a format that a D-Wave system can solve. We know that binary objective functions can be represented as graphs; this chapter explains the mapping between a problem graph and the QPU topology.

Note

Although Ocean software automates this mapping, you should understand it if you are directly programming the QPU because it has implications for the problem-graph size and solution quality. If you are sending your problem to a Leap quantum-classical hybrid solver, the solver handles all interactions with the QPU.

Leap hybrid solvers are described here: Leap’s Hybrid Solvers

The D-Wave QPU is a lattice of interconnected qubits. While some qubits connect to others via couplers, the D-Wave QPU is not fully connected. Instead, the qubits interconnect in an architecture known as Chimera.

Chimera Graph

The Chimera architecture comprises sets of connected unit cells, each with four horizontal qubits connected to four vertical qubits via couplers. Unit cells are tiled vertically and horizontally with adjacent qubits connected, creating a lattice of sparsely connected qubits. See Figure 12.

Chimera graph.  qubits are arranged in unit cells that form bipartite connections.

Fig. 12 A \(3 {\rm x} 3\) Chimera graph, denoted C3. Qubits are arranged in 9 unit cells.

The notation CN refers to a Chimera graph consisting of an \(N {\rm x} N\) grid of unit cells. The D-Wave 2000Q QPU supports a C16 Chimera graph: its 2048 qubits are logically mapped into a \(16 {\rm x} 16\) matrix of unit cells of 8 qubits.

In a D-Wave QPU, the set of qubits and couplers that are available for computation is known as the working graph. The yield of a working graph is typically less than the total number of qubits and couplers that are fabricated and physically present in the QPU.

Connectivity

A unit cell can be rendered as either a cross or a column; see Figure 13.

Logical cross or column layout of qubits in a unit cell

Fig. 13 Cross or column layout of qubits in a unit cell.

In each of these renderings, we can see that there are two sets of four qubits. Each qubit in one set of four is connected to all qubits in the other set, but no qubits connect to the others within its own set of four. Within a unit cell, the qubits have bipartite connectivity.

Chains and Minor Embedding

The nodes and edges on the graph that represents an objective function translate to the qubits and couplers in Chimera. Each logical qubit, in the graph of the objective function, may be represented by one or more physical qubits. The process of mapping the logical qubits to physical qubits is known as minor embedding.

Note

While tools for minor embedding are available in the Ocean SDK, you can also do this manually as explained in the Minor-Embedding a Problem onto the Chimera Graph chapter.