Emulation of large-scale qubit registers with a phase-space approach

A phase-space approach is used and benchmarked for the simulation of the continuous-time evolution of large registers of qubits. It is based on a statistical ensemble of independent mean-field trajectories, where mean field is introduced at the level of the qubits, substituting quantum fluctuations/correlations with classical ones. The approach only involves at worse a quadratic cost in the system size, allowing to simulate up to several thousands of qubits on a classical computer. It provides qualitatively accurate description of one-qubit observables’ evolutions, making it a useful reference in comparison to techniques limited to small qubit numbers. The predictive power is, however, less robust for multiqubit observables. We benchmark the method on the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mi>k</a:mi> </a:math> -local transverse-field Ising model, considering a large variety of systems ranging from local to all-to-all interactions, and from weak to strong coupling regimes, with up to 2000 qubits. To showcase the versatility of the approach, simulations on two-dimensional and three-dimensional Ising models are also made.