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.

Technical Terms

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

Table 43 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 \(s\)