Curator's Take
This article tackles a fundamental challenge in quantum computing by developing analytical methods to understand how entanglement spreads through variational quantum circuits, which are the backbone of many near-term quantum algorithms. The researchers provide exact mathematical formulas for tracking quantum correlations as they propagate through circuits with increasing depth, offering crucial insights for optimizing variational quantum eigensolvers and quantum approximate optimization algorithms. Their work bridges theory and practice by demonstrating how circuit parameters directly control the entanglement structure, which could help quantum programmers design more efficient circuits that achieve desired entanglement patterns with minimal depth. The validation through quantum simulations adds practical credibility to these theoretical insights, potentially advancing our ability to harness quantum correlations more strategically in real quantum devices.
— Mark Eatherly
Summary
We study the entanglement distance of variational quantum states for two-qubit and multi-qubit systems. These states are constructed using variational quantum circuits with $R_Y$ rotations and entangling $CZ$ gates.For the two-qubit case, we analytically derive recurrence relations for expectation values of Pauli observables using. This approach allows us to analytically calculate quantum correlators and evaluate the entanglement distance depending on the circuit parameters and depth. The analysis were extended to a closed one-dimensional chain of $N$ qubits. It is shown that with increasing circuit depth, more qubits influence a given qubit, which reflects the spreading of quantum correlations in the system. For a closed one-dimensional chain of $N$ qubits, explicit analytical expressions are derived for the case of two layers. The results are compared with numerical simulations performed using quantum programming tools. The results agree with the theoretical predictions.