Dynamic linear response quantum algorithm

The dynamic linear response of a quantum system is critical for understanding both the structure and dynamics of strongly interacting quantum systems, including neutron scattering from materials, photon and electron scattering from atomic systems, and electron and neutrino scattering by nuclei. We present a general algorithm for universal quantum computers to calculate the dynamic linear response function with controlled errors and to obtain information about specific final states that can be directly compared to experimental observations.

Figure 1

Approximations of the true response function ${\overline{S}}_O\left(\overline{\omega }\right)$ for the model system described by the Hamiltonian of Eq. (5) for different numbers of the work qubits: $W=6$ (blue line), $W=8$ (red line), and $W=12$ (green line). The exact response is also shown with black dots. The inset shows the maximum error in the sample estimate of $P\left(y\right)$ as a function of the number of samples.

Figure 2

Circuit for measuring the momentum distribution.

Figure 3

Circuit implementation of the $W$ unitary.