Concepts#

Find concepts/terminology you are looking for here or under the Generated Ocean Index.

Concepts and Terminology#

access time#

Execution time for a single quantum machine instruction (QMI, or problem).

adiabatic#

An annealing process that experiences no interference from outside energy sources and evolves the Hamiltonian slowly enough is called an adiabatic process.

Learn more: What is Quantum Annealing?.

Advantage#

The Advantage™ quantum computer is the first quantum system designed for business and is the most powerful and connected commercial quantum computer in the world, with more than 5000 qubits and 35,000 couplers. Advantage QPUs are named Advantage_system<x.y>, with x numbering solver (D-Wave system) resources and y possibly incrementing on updates such as newer calibrations; for example, the first online QPU was Advantage_system1.1.

Advantage2#

The Advantage2™ quantum computer is D-Wave’s next-generation QPU, after the Advantage quantum computer.

anneal#

annealing#

See quantum annealing.

anneal offset#

Provide offsets to annealing paths, per qubit.

Learn more:

anneal_offsets for the solver property.
Anneal Offsets for a description.

anneal schedule#

annealing schedule#

A single, global, time-dependent bias controls the changes of energy scales \(A(s)\) and \(B(s)\) during the quantum annealing process.

Learn more:

What is Quantum Annealing? for an introduction.
Standard-Anneal Protocol.
Fast-Anneal Protocol.
Varying the Global Anneal Schedule for pause, quench, and reverse anneal.
Per-QPU Solver Properties and Schedules for the schedules of each QPU, as spreadsheets.

binary quadratic model#

BQM#

A collection of binary-valued variables (variables that can be assigned two values, for example -1, 1) with associated linear and quadratic biases. Sometimes referred to in other tools as a problem.

Learn more: Binary Quadratic Models.

chain#

chains#

One or more nodes or qubits in a target graph that represent a single variable in the source graph. See also embedding.

Learn more:

Minor Embedding for an introduction.
AND Gate: Minor-Embedding for an example.
Minor-Embedding: Best Practices for advanced information.

chain break#

broken chain#

In chains, the qubits that form the nodes of the chain should always end the anneal with the same value; when qubits in a chain take different values, the chain is considered broken.

Learn more

AND Gate: Minor-Embedding explains broken chains.
Using the Problem Inspector uses the problem inspector (the dwave-inspector) for viewing and dealing with broken chains.

chain length#

The number of qubits in a Chain.

Learn more:

Minor Embedding for an introduction.
Minor-Embedding: Best Practices for advanced information.

chain strength#

Magnitude of the negative quadratic bias applied between variables to form a chain.

Learn more:

Minor Embedding for an introduction.
AND Gate: Minor-Embedding for an example.
Minor-Embedding: Best Practices for advanced information.

charge_time#

charge time#

Time charged to your Leap service account.

Learn more: Solver Timing describes the timing for hybrid solvers.

Chimera#

A D-Wave QPU is a lattice of interconnected qubits. While some qubits connect to others via couplers, D-Wave QPUs are not fully connected. For earlier D-Wave 2000Q QPUs, the qubits interconnected in an architecture known as Chimera. See also Pegasus and Zephyr.

Learn more: Topologies.

classical#

classical solver#

An algorithm that runs on any non-quantum computer <https://en.wikipedia.org/wiki/Computer>.

Learn more: Classical Solvers.

clique#

complete graph#

fully connected#

See complete graph on Wikipedia or Clique. A fully connected or complete binary quadratic model is one that has interactions between all of its variables.

combinatorial optimization#

discrete optimization#

The optimization of an objective function defined over a set of discrete values such as Booleans.

composed sampler#

Samplers that apply pre- and/or post-processing to binary quadratic programs without changing the underlying sampler implementation by layering composite patterns on the sampler. For example, a composed sampler might add spin transformations when sampling from a D-Wave quantum computer.

Learn more: Composites.

composite#

A sampler can be composed. The composite pattern allows layers of pre- and post-processing to be applied to binary quadratic programs without needing to change the underlying sampler implementation. We refer to these layers as “composites”. A composed sampler includes at least one sampler and possibly many composites.

Learn more: Composites.

connected graph#

See connected graph on the US NIST site. A connected graph has some path from any vertex to any other. A graph that has at least two vertices without a path between them is disconnected. Any Complete graph is connected (but not all connected graphs are complete).

constrained quadratic model#

CQM#

A collection of variables with associated linear and quadratic biases representing a problem modeled as an objective function and inequality and equality constraints.

Learn more: Constrained Quadratic Model.

constraint#

hard constraint#

soft constraint#

A constraint is a condition of an optimization problem that the solution must satisfy (“hard” constraint) or is preferred to satisfy (“soft” constraint). See Constraint (mathematics).

constraint satisfaction problem#

CSP#

A constraint satisfaction problem (CSP) requires that all the problem’s variables be assigned values, out of a finite domain, that result in the satisfying of all constraints.

Learn more: Constraint Satisfaction Problem.

coupler#

couplers#

Couplers can correlate two qubits such that they tend to end up in the same classical state—both 0 or both 1—or in opposite states. The correlation between coupled qubits is controlled programmatically.

discrete quadratic model#

DQM#

A collection of discrete-valued variables (variables that can be assigned the values specified by a set such as \(\{red, green, blue\}\) or \(\{33, 5.7, 3,14 \}\) ) with associated linear and quadratic biases.

Learn more: Discrete Quadratic Models.

embed#

embedding#

minor embed#

minor-embed#

minor embedding#

minor-embedding#

Nodes and edges on the graph that represents an objective function translate to qubits and couplers in the QPU topology. 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.

Learn more:

Minor Embedding for an introduction.
Minor-Embedding: Best Practices for advanced information.
Topologies on QPU topologies.
NOT Gate: Simple QUBO, AND Gate: Minor-Embedding, and Logic Circuit: Embedding Effects for examples and more information.

excited state#

States of a quantum system that have higher energy than the ground state. Such states represent non-optimal solutions for problems represented by an objective function and infeasible configurations for problems represented by a penalty model.

Learn more: What is Quantum Annealing?.

feasible state#

A state in which the values of variables do not violate any hard constraint.

flux bias#

flux-bias offset#

Flux biases can be used to refine the standard calibration and to bias qubits indirectly when you cannot set a bias on the qubit.

Learn more:

flux_biases for a description of the parameter.
Calibration Refinement fo ran explanation of calibration refinement.
Emulate Linear Biases with Flux-Bias Offsets.

gate model#

circuit model#

Gate-model quantum computing, also known as circuit model, implements compute algorithms with quantum gates, analogously to the use of Boolean gates in classical computers.

Learn more: What is Gate Model?.

graph#

A collection of nodes and edges. A graph can be derived from a model: a node for each variable and an edge for each pair of variables with a non-zero quadratic bias.

ground state#

The lowest-energy state of a quantum-mechanical system and the global minimum of a problem represented by an objective function.

Hamiltonian#

A classical Hamiltonian is a mathematical description of some physical system in terms of its energies. We can input any particular state of the system, and the Hamiltonian returns the energy for that state. For a quantum system, a Hamiltonian is a function that maps certain states, called eigenstates, to energies. Only when the system is in an eigenstate of the Hamiltonian is its energy well defined and called the eigenenergy. When the system is in any other state, its energy is uncertain. For D-Wave quantum computers, the Hamiltonian may be represented as

\begin{equation} {\cal H}_{ising} = \underbrace{\frac{A({s})}{2} \left(\sum_i {\hat\sigma_{x}^{(i)}}\right)}_\text{Initial Hamiltonian} + \underbrace{\frac{B({s})}{2} \left(\sum_{i} h_i {\hat\sigma_{z}^{(i)}} + \sum_{i>j} J_{i,j} {\hat\sigma_{z}^{(i)}} {\hat\sigma_{z}^{(j)}}\right)}_\text{Final Hamiltonian} \end{equation}

where \({\hat\sigma_{x,z}^{(i)}}\) are Pauli matrices operating on a qubit \(q_i\), and \(h_i\) and \(J_{i,j}\) are the qubit biases and coupling strengths.

Learn more:

What is Quantum Annealing? for an introduction.
Annealing Implementation and Controls for advanced information on implementation.

hardware graph#

The hardware graph is the physical lattice of interconnected qubits. See also working graph.

Learn more: Topologies.

hybrid#

Quantum-classical hybrid is the use of both classical and quantum resources to solve problems, exploiting the complementary strengths that each provides.

Learn more:

Hybrid for an introduction.
Sampling with Hybrid Solvers gets you started with hybrid samplers.
Solver Properties & Parameters describes the supported hybrid solvers in the Leap service.
Improving Hybrid Solutions describes best practices.

ICE#

integrated control errors#

The dynamic range of h and J values may be limited by integrated control errors (ICE). The term ICE refers collectively to these sources of infidelity in problem representation.

Learn more: Errors and Error Correction.

infeasible state#

A state in which the values of variables violate a constraint.

Ising#

Traditionally used in statistical mechanics. Variables are “spin up” (\(\uparrow\)) and “spin down” (\(\downarrow\)), states that correspond to \(+1\) and \(-1\) values. Relationships between the spins, represented by couplings, are correlations or anti-correlations. The objective function expressed as an Ising model is as follows:

\begin{equation} \text{E}_{ising}(\pmb{s}) = \sum_{i=1}^N h_i s_i + \sum_{i=1}^N \sum_{j=i+1}^N J_{i,j} s_i s_j \end{equation}

where the linear coefficients corresponding to qubit biases are \(h_i\), and the quadratic coefficients corresponding to coupling strengths are \(J_{i,j}\).

Learn more:

Ising Model on Wikipedia.
Models on supported models.

Leap#

Leap service#

Launched in 2018, the Leap™ quantum cloud service from D-Wave brings quantum computing to the real world by providing real-time cloud access to D-Wave’s systems.

linear program#

linear optimization#

Linear programming (LP) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements and objective are represented by linear relationships. See also nonlinear model.

minimum gap#

The minimum distance between the ground state and the first excited state throughout any point in the anneal.

Learn more: What is Quantum Annealing?.

model#

A collection of variables with associated biases. Sometimes referred to as a problem.

Learn more: Models

nonlinear model#

A collection of variables with associated biases that constitute an objective function and/or constraints. Sometimes referred to as a problem. See also linear program.

Learn more: Nonlinear Model.

ocean#

Ocean™ software is a suite of tools for using D-Wave Quantum Inc. quantum computers and hybrid solvers.

Learn more: Ocean SDK.

objective function#

objective#

A mathematical expression of the energy of a system as a function of its variables.

Learn more: What is Quantum Annealing?.

one-hot#

For one-hot variables, the only valid values are those in which a single bit is 1 and the others are all zero. See one-hot on Wikipedia for details.

Learn more: Example Constraints: One-Hot, Domain-Wall, n \choose k

Pegasus#

A D-Wave QPU is a lattice of interconnected qubits. While some qubits connect to others via couplers, D-Wave QPUs are not fully connected. For an Advantage QPU, the qubits interconnect in an architecture known as Pegasus. See also Chimera and Zephyr.

Learn more: Topologies.

penalty function#

An algorithm for solving constrained optimization problems. In the context of Ocean tools, penalty functions are typically employed to increase the energy level of a problem’s objective function by penalizing non-valid configurations. See Penalty method on Wikipedia.

Learn more: Penalty Models.

penalty#

penalty model#

An approach to solving constraint satisfaction problems (CSP) using an Ising model or a QUBO by mapping each individual constraint in the CSP to a “small” Ising model or QUBO.

Learn more: Penalty Models.

postprocessing#

Postprocessing in the context of using a solver can refer to additional (classical) computation that improves the results at low cost; for example majority voting on broken chains.

Learn more:

Postprocessing for an introduction.
Postprocessing for results of postprocessing results returned from a quantum computer.

preprocessing#

Preprocessing can refer to some low-cost classical computation applied to a problem before submitting to a solver, or as part of the solver’s work on the problem.

Learn more:

dwave-preprocessing

QMI#

Quantum machine instruction.

QPU#

Quantum processing unit.

Learn more: What is Quantum Annealing?.

qpu_access_time#

QPU time used by a hybrid solver.

Learn more: Solver Timing describes the timing for hybrid solvers.

quadratic model#

A collection of variables with associated linear and quadratic biases. Sometimes referred to as a problem.

Quadratic functions have one or two variables per term. A simple example of a quadratic function is,

\[D = Ax + By + Cxy\]

where \(A\), \(B\), and \(C\) are constants. Single variable terms—\(Ax\) and \(By\) here—are linear with the constant biasing the term’s variable. Two-variable terms—\(Cxy\) here—are quadratic with a relationship between the variables.

Ocean software also provides support for higher order models, which are typically reduced to quadratic for sampling.

Learn more: Quadratic Models.

quantum annealing#

quantum annealer#

Quantum annealers are quantum computers that you initialize in a low-energy state and gradually introduce the parameters of a problem you wish to solve. The slow change makes it likely that the system ends in a low-energy state of the problem, which corresponds to an optimal solution.

Learn more:

What is Quantum Annealing? for an introduction.
Standard-Anneal Protocol.
Fast-Anneal Protocol.
Varying the Global Anneal Schedule for pause, quench, and reverse anneal.

quantum computing#

quantum computer#

A quantum computer is a computer that exploits quantum mechanical phenomena. Today, there are two leading candidate architectures for quantum computers: gate model (also known as circuit model) and quantum annealing.

Learn more: What is Quantum Annealing?

qubit#

qubits#

A qubit, short for quantum bit, is a basic unit of quantum information, a two-state (or two-level) quantum-mechanical system; for example, the spin of the electron in which the two levels can be taken as spin up and spin down. See Qubit on Wikipedia.

QUBO#

Quadratic unconstrained binary optimization. QUBO problems are traditionally used in computer science. Variables are TRUE and FALSE, states that correspond to 1 and 0 values. A QUBO problem is defined using an upper-diagonal matrix \(Q\), which is an \(N\) x \(N\) upper-triangular matrix of real weights, and \(x\), a vector of binary variables, as minimizing the function

\begin{equation} f(x) = \sum_{i} {Q_{i,i}}{x_i} + \sum_{i<j} {Q_{i,j}}{x_i}{x_j} \end{equation}

where the diagonal terms \(Q_{i,i}\) are the linear coefficients and the nonzero off-diagonal terms are the quadratic coefficients \(Q_{i,j}\). This can be expressed more concisely as

\begin{equation} \min_{{x} \in {\{0,1\}^n}} {x}^{T} {Q}{x}. \end{equation}

In scalar notation, the objective function expressed as a QUBO is as follows:

\begin{equation} \text{E}_{qubo}(a_i, b_{i,j}; q_i) = \sum_{i} a_i q_i + \sum_{i<j} b_{i,j} q_i q_j. \end{equation}

Generated Ocean Index#

Search the automatically generated Ocean site index.