Juan Carrasquilla

Quantum computers have long been anticipated to excel in simulating quantum many-body physics. While most previous work has focused on Hermitian physics, we demonstrate the power of variational quantum circuits for resource-efficient simulations of dynamical and equilibrium physics in non-Hermitian systems, revealing new phenomena beyond standard Hermitian quantum machines. Using a variational quantum compilation scheme for fermionic systems, we reduce gate count, save qubits, and eliminate the need for postselection, a major challenge in simulating non-Hermitian dynamics via standard Trotterization. Experimentally, we observed a supersonic mode in the connected density-density correlation function on an $ n = 18 $ fermionic chain after a non-Hermitian, locally interacting quench, which would otherwise be forbidden by the Lieb-Robinson bound in a Hermitian system. Additionally, we investigate sequential quantum circuits generated by tensor networks for ground state preparation, here defined as the eigenstate with the lowest real part eigenvalue, using a variance minimization scheme. Through a trapped-ion implementation on the Quantinuum H1 quantum processor, we accurately capture correlation functions and energies across an exceptional point on a dissipative spin chain up to length $ n = 20 $ using only 3 qubits. Motivated by these advancements, we provide an analytical example demonstrating that simulating single-qubit non-Hermitian dynamics for $Θ(\log(n))$ time from certain initial states is exponentially hard on a quantum computer, offering insights into the opportunities and limitations of using quantum computation for simulating non-Hermitian physics.

Generative models are a promising technology for the enhancement of quantum simulators. These machine learning methods are capable of reconstructing a quantum state from experimental measurements, and can aid in the calculation of physical observables. In this paper, we employ a recurrent neural network (RNN) to reconstruct the ground state of the spin-1/2 XY model, a prototypical Hamiltonian explored in trapped ion simulators. We explore its performance after enforcing a U(1) symmetry, which was recently shown by Hibat-Allah et al. [Phys. Rev. Research 2, 023358 (2020)] to preserve the autoregressive nature of the RNN. By studying the reconstruction of the XY model ground state from projective measurement data, we show that imposing U(1) symmetry on the RNN significantly increases the efficiency of learning, particularly in the early epoch regime. We argue that this performance increase may result from the tendency of the enforced symmetry to alleviate vanishing and exploding gradients, which helps stabilize the training process. Thus, symmetry-enforced RNNs may be particularly useful for applications of quantum simulators where a rapid feedback between optimization and circuit preparation is necessary, such as in hybrid classical-quantum algorithms.