Estimating Quantum Entropy

Testing identity of collections of quantum states: sample complexity analysis

“…A problem related to testing identity of collections is testing independence of a distribution on × l i=1 [n i ], which was addressed by [Bat+01; LRR13; AD15] and solved in [DK16], which showed a tight sample complexity O(max j ( l i=1 n . This results have be refined in the case the state is known to be close to a state of rank less than k. Quantum entropy estimation has been studied in [Ach+20]. The property testing approach to quantum properties has been reviewed in [MW16], where it is also shown that testing identity to a pure state requires O(1/ǫ 2 ).…”

Quantum algorithms for estimating quantum entropies

“…Various methods [19] have been proposed to estimate quantum entropies in past decades, while a large number of quantum resources are demanded as well. The most straightforward method to estimate quantum entropy is using tomography [20], which figures out the description of the density matrix. In that case, the consumption increases exponentially with the size of the state.…”

“…Regarding quantum computing methods, many proposals based on different models have been proposed [11,20,[22][23][24][25][26]. Specifically speaking, [20] studies the cost of estimating the von Neumann and Rényi entropies in a model where one can get independent copies of the state.…”

Adaptive variational algorithms for quantum Gibbs state preparation

“…However, the von Neumann entropy S(ρ) and its gradients are difficult to measure on real quantum hardware [18,22,23], with the cost scaling exponentially with system size, particularly in the case of Gibbs states, as eigenvalues of the target state ρ G are exponentially suppressed [24,25]. This makes the implementation of variational Gibbs state preparation too demanding for nearterm quantum processors, especially at low temperatures.…”