# About this Document¶

## 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.

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 \(s\) |