Entanglement diagnostics for efficient VQA optimization

Abstract

We consider information spreading measures in randomly initialized variational quantum circuits and introduce entanglement diagnostics for efficient variational quantum/classical computations. We establish a robust connection between entanglement measures and optimization accuracy by solving two eigensolver problems for Ising Hamiltonians with nearest-neighbor and long-range spin interactions. As the circuit depth affects the average entanglement of random circuit states, the entanglement diagnostics can identify a high-performing depth range for optimization tasks encoded in local Hamiltonians. We argue, based on an eigensolver problem for the Sachdev–Ye–Kitaev model, that entanglement alone is insufficient as a diagnostic to the approximation of volume-law entangled target states and that a large number of circuit parameters is needed for such an optimization task.

Barren plateaus in quantum tensor network optimization

“…Focusing on local observables the analysis in [29] suggests that the onset of barren plateaus is related to the entanglement in the causal cone of the observable 2 . This is analysed in detail in [36] where the authors show that sufficiently large amounts of entanglement in the quantum circuit are necessary for the emergence of unitary 2-designs and claim that entanglement-induced barren plateaus [33,34,77] and barren plateaus for local cost functions are equivalent.…”

“…The severity of the barren plateau problem depends on the cost function [29] and the PQC architecture [28,30,31]. A plethora of proposals exist to avoid barren plateaus in certain cases [29,[31][32][33][34][35][36][37][38][39][40][41].…”

Quantum chaos and circuit parameter optimization

“…We begin with specifying the circuit architecture used in this paper and briefly review the relation between the entanglement made by random circuit unitaries and the optimization efficiency of VQAs [4][5][6][7][8]10].…”

“…Generic quantum gates create an entanglement between qubits. Entanglement is a valuable resource for achieving quantum advantage, but it also becomes a hurdle for successful optimization of circuit control parameters at the same time, specifically when random circuit states are much more highly entangled than the ground state of the Hamiltonian encoding the task [4][5][6][7][8]. Quantum information in such highly entangled states is scrambled, and a successful adjustment of circuit parameters via local gradient search typically requires over-parametrization [7,[9][10][11].…”

Efficient estimation of trainability for variational quantum circuits

“…Numerous investigations have proposed strategies to address the barren-plateau issue. In the context of entanglement-induced barren plateaus, most strategies rely on limiting the amount of entanglement [16][17][18][19][20].…”