Efficient simulation of rotation-symmetric many-boson open quantum systems via symmetric time-dependent variational ansatz

The efficient simulation of the open-quantum-system dynamics of many interacting bosons is a key requirement for the design of optimal bosonic error-correcting codes and for predicting their performance when subject to noise. In most cases, this however constitutes a daunting computational challenge due to the prohibitively large Hilbert space. Bosonic codes always rely on symmetries and, within typical quantum protocols, their dynamics is constrained onto narrow corners of the full state space.

Here, we present a new paradigm for the simulation of $Z_N$-rotation symmetric many-boson driven-dissipative systems -- i.e. Schrödinger cat codes -- based on a self-consistent multicomponent coherent-state expansion. The method relies on a variational ansatz for the $n$-boson density matrix expressed on a coherent-state subspace, where both the matrix elements and the coherent-state displacement field constitute the time-dependent variational parameters. This method efficiently represents the system dynamics while retaining only the computational complexity of an equivalent $n$-qubit quantum state evolution.

We test our model on several examples, demonstrating its potential application to the predictive simulation of the most advanced bosonic codes.