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.
| 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 \(s\) |