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


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,

\begin{equation} {\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) \end{equation}

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.


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

Release Introduced

Release 3.1.9

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

See Also