# Flux-Bias Offsets¶

## Description¶

In an optimal QPU calibration, annealing an unbiased chain produces spin-state statistics that are equally split between spin-up and spin-down. When plotted against the $h$ values, this even distribution results in a sigmoid curve that passes through the point of origin (0,0); see Figure 90. However, qubits in a chain with strong negative $J$ values experience a $J$-induced bias—an offset magnetic field that is potentially $s$-dependent. This field shifts the sigmoid curve of plotted $h$ values from its ideal path. To compensate, chains using strong negative $J$ couplings must be recalibrated to remove the bias from the chain and reduce the incidence of analog errors that may be associated with minor-embedding.

Recalibration involves applying per-qubit flux-bias offsets to nudge the plotted $h$ sigmoid to its ideal position. The optimal offset value for a chain depends on the qubits and couplers involved and on the chain coupling strength.

 [1] For information on the measured performance improvements resulting from this feature, see Virtual Graphs for High-Performance Embedded Topologies, D-Wave White Paper Series, no. 14-1020A, 2017. This and other white papers are available from https://www.dwavesys.com/resources/publications.

## Release Introduced¶

Solver API Release 3.0, January 2018

## Properties and Parameters¶

User parameter:

• flux_biases—Parameter that takes a list of flux-bias offset values with which to calibrate a chain.

Solver properties:

• extended_j_range—Property that shows the extended range of values possible for the coupling strengths (quadratic coefficients), $J$, for the solver.
• per_qubit_coupling_range—Property that identifies the limits on the total coupling strength possible for a qubit.