QPU Hamiltonian

In all cases we will refer to $H$ as being of the form

$$H = -\sum_j\Delta_jn_j \ + \ \sum_j\Omega_j\sigma^x_j \ + \ H_{i}$$

where $H_i$ is the interaction term in the Hamiltonian. Values of $\Omega_j$ and $\Delta_j$ respectively represent the amplitude and the detuning of the driving field applied to the qubit $j$. Avoiding technical details we will refer to eigenstates of $H$ (and in particular to the ground state) as equilibrium states.

Although the QPU currently only supports a Rydberg interaction, emu-mps supports both the Rydberg interaction term and the XY interaction.

The Rydberg interaction reads

$$H_{rr} = \sum_{i>j} U_{ij} n_{i}n_{j}$$

where

$$U_{ij} = \frac{C_{6}}{r_{ij}^{6}},$$

and the XY interaction reads

$$H_{xy} = \sum_{i>j} U_{ij} (\sigma^+_{i}\sigma^-_{j} + h.c.)$$

where

$$U_{ij} = \frac{C_{3}(1-3 \cos^2(\theta_{ij}))}{r_{ij}^{3}},$$

In these formulas, $r_{ij}$ represents the distance between qubits $i$ and $j$, and $\theta_{ij}$ represents a configurable angle (see here (external)). Currently, Pasqal quantum devices only support Rydberg interactions, and different devices have different $C_6$ coefficients and support for different maximum driving amplitudes $\Omega$. Intuitively, under stronger interactions (rydberg-rydberg and laser-rydberg), bond dimension will grow more quickly (see here), thus affecting performance of our tensor network based emulator. For a list of the available devices and their specifications, please refer to the Pulser documentation (see here (external)).