# Time-Dependent Gain in Hamiltonian Biases (H-Gain)¶

## Description¶

This feature increases user control of the Hamiltonian that represents the D-Wave system’s quantum anneal by introducing a time-dependent gain on its linear coefficients (biases), $h_i$.

The h_gain_schedule parameter enables users to specify the $g(t)$ function in,

$${\cal H}_{ising} = - \frac{A({s})}{2} \left(\sum_i {\hat\sigma_{x}^{(i)}}\right) + \frac{B({s})}{2} \left(\sum_{i} g(t) h_i {\hat\sigma_{z}^{(i)}} + \sum_{i>j} J_{i,j} {\hat\sigma_{z}^{(i)}} {\hat\sigma_{z}^{(j)}}\right)$$

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

Note

Currently this feature is used experimentally for a form of material simulation described in http://science.sciencemag.org/content/361/6398/162.

## Release Introduced¶

Solver API Release 3.1.9, March 2019

## Properties and Parameters¶

User parameter:

• h_gain_schedule—Sets a time-dependent gain for linear coefficients in the Hamiltonian.

Solver properties (may vary by QPU):

• h_gain_schedule_range—Range of the time-dependent gain applied to qubit biases for this solver.
• max_h_gain_schedule_points—Maximum number of points permitted in a waveform submitted to set a time-dependent gain on linear coefficients