## Intended Audience¶

This document is for users of the D-Wave™ quantum computer system who want to better understand and leverage the physical implementation of the quantum processing unit (QPU) architecture. It assumes that readers have a background in quantum annealing and are familiar with Ising problem formulations.

## Scope¶

This document covers the following topics:

• Background on discrete optimization, quantum annealing, D-Wave QPU operation, and the QPU architecture.
• Integrated control errors (ICE): Dynamic ranges of $h$ and $J$ values and how they may affect results.
• Other factors that affect performance, including temperature, photon flux, readout fidelity, and programming problems.
• Some approaches for maximizing the performance of the QPU.
• Description of the effects of flux noise on the quantum annealing process; includes the procedure that D-Wave uses to correct for drift.

The values discussed in this document are representative properties for a D-Wave QPU. They are not product specifications.

This document does not provide programming instructions. For instructions on programming the system using D-Wave’s open-source Ocean tools, see the Ocean documentation.

## Technical Terms¶

The table below defines some of the technical terms that are used throughout this document.

Table 49 Technical terms.
Term Context Definition
$q_i$ QPU Qubit $i$ for $i \in \{0, \ldots, N-1\}$
$N$ QPU Number of qubits in a QPU
$s_i$ Ising problems Spin state at graph vertex $i$ for $i \in \{1, \ldots, N\}$; $s_i \in \{+1,-1\}$
$\vc s$ Ising problems Vector of spin states $(s_1, \ldots, s_{N})$
$E_{(\vc s)}$ Ising problems Energy at spin configuration $\vc s$
$h_i$ Ising problems Linear coefficient (bias) on qubit $i$
$J_{i,j}$ Ising problems Coupling between spins $s_i$ and $s_j$
$J_{i,j} < 0$ Ising problems Ferromagnetic coupling between spins $s_i$ and $s_j$
$J_{i,j} > 0$ Ising problems Antiferromagnetic coupling between spins $s_i$ and $s_j$
$J_{i,j} = 0$ Ising problems No coupling between spins $s_i$ and $s_j$
$x_i$ QUBO problems Binary state at graph vertex $i$ for $i \in \{1, \ldots, N\}$; $x_i \in \{0,1\}$
$\vc x$ QUBO problems Vector of binary states $(x_1, \ldots, x_{N})$
$\vc Q$ QUBO problems Matrix of interactions between variables
$\vc Q_{i,j}$ QUBO problems Coupling between variables $x_i$ and $x_j$
$t$ Anneal schedule Current time during anneal
$t_f$ Anneal schedule Total time for the anneal
$s$ Anneal schedule Anneal fraction; abstract parameter ranging from 0 to 1. A linear anneal sets $s = t / t_f$.
$A(s)$ Anneal schedule Tunneling energy at anneal fraction $s$
$B(s)$ Anneal schedule Problem Hamiltonian energy at anneal fraction $s$