Polynomial scaling of the quantum approximate optimization algorithm for ground-state preparation of the fully connected p -spin ferromagnet in a transverse field

We show that the quantum approximate optimization algorithm (QAOA) can construct, with polynomially scaling resources, the ground state of the fully connected p-spin Ising ferromagnet, a problem that notoriously poses severe difficulties to a vanilla quantum annealing (QA) approach due to the exponentially small gaps encountered at first-order phase transition for p≥3. For a target ground state at arbitrary transverse field, we find that an appropriate QAOA parameter initialization is necessary to achieve good performance of the algorithm when the number of variational parameters 2P is much smaller than the system size N because of the large number of suboptimal local minima. Instead, when P exceeds a critical value PN∗N, the structure of the parameter space simplifies, as all minima become degenerate. This allows achieving the ground state with perfect fidelity with a number of parameters scaling extensively with N and with resources scaling polynomially with N

Reinforcement-learning-assisted quantum optimization

We propose a reinforcement learning (RL) scheme for feedback quantum control within the quantum approximate optimization algorithm (QAOA). We reformulate the QAOA variational minimization as a learning task, where an RL agent chooses the control parameters for the unitaries, given partial information on the system. Such an RL scheme finds a policy converging to the optimal adiabatic solution of the quantum Ising chain that can also be successfully transferred between systems with different sizes, even in the presence of disorder. This allows for immediate experimental verification of our proposal on more complicated models: The RL agent is trained on a small control system, simulated on classical hardware, and then tested on a larger physical sample

Entanglement spectrum degeneracy and the Cardy formula in 1+1 dimensional conformal field theories

We investigate the effect of a global degeneracy in the distribution of the entanglement spectrum in conformal field theories in one spatial dimension. We relate the recently found universal expression for the entanglement Hamiltonian to the distribution of the entanglement spectrum. The main tool to establish this connection is the Cardy formula. It turns out that the Affleck-Ludwig non-integer degeneracy, appearing because of the boundary conditions induced at the entangling surface, can be directly read from the entanglement spectrum distribution. We also clarify the effect of the noninteger degeneracy on the spectrum of the partial transpose, which is the central object for quantifying the entanglement in mixed states. We show that the exact knowledge of the entanglement spectrum in some integrable spinchains provides strong analytical evidences corroborating our results

Quantum information dynamics in multipartite integrable systems

In a non-equilibrium many-body system, the quantum information dynamics between non-complementary regions is a crucial feature to understand the local relaxation towards statistical ensembles. Unfortunately, its characterization is a formidable task, as non-complementary parts are generally in a mixed state. We show that for integrable systems, this quantum information dynamics can be quantitatively understood within the quasiparticle picture for the entanglement spreading. Precisely, we provide an exact prediction for the time evolution of the logarithmic negativity after a quench. In the space-time scaling limit of long times and large subsystems, the negativity becomes proportional to the R\ue9nyi mutual information with R\ue9nyi index . We provide robust numerical evidence for the validity of our results for free-fermion and free-boson models, but our framework applies to any interacting integrable system