Detecting and quantifying entanglement on near-term quantum devices

Abstract

Quantum entanglement is a key resource in quantum technology, and its quantification is a vital task in the current Noisy Intermediate-Scale Quantum (NISQ) era. This paper combines hybrid quantum-classical computation and quasi-probability decomposition to propose two variational quantum algorithms, called Variational Entanglement Detection (VED) and Variational Logarithmic Negativity Estimation (VLNE), for detecting and quantifying entanglement on near-term quantum devices, respectively. VED makes use of the positive map criterion and works as follows. Firstly, it decomposes a positive map into a combination of quantum operations implementable on near-term quantum devices. It then variationally estimates the minimal eigenvalue of the final state, obtained by executing these implementable operations on the target state and averaging the output states. Deterministic and probabilistic methods are proposed to compute the average. At last, it asserts that the target state is entangled if the optimized minimal eigenvalue is negative. VLNE builds upon a linear decomposition of the transpose map into Pauli terms and the recently proposed trace distance estimation algorithm. It variationally estimates the well-known logarithmic negativity entanglement measure and could be applied to quantify entanglement on near-term quantum devices. Experimental and numerical results on the Bell state, isotropic states, and Breuer states show the validity of the proposed entanglement detection and quantification methods.

Noisy intermediate-scale quantum algorithms

“…Thus, those algorithms that tackle the SVD problem can also be used to extract entanglement properties (Bravo-Prieto et al, 2020). In (Wang et al, 2020a), authors propose a NISQ algorithm for the separability problem by providing a variational approach to employ the positive map criterion. This criterion establishes that the quantum state ρ AB is separable if and only if for arbitrary quantum system R and arbitrary positive map N B→R from B to R, we have N B→R (ρ AB ) ≥ 0.…”

Noise-Induced Entanglement Transition in One-Dimensional Random Quantum Circuits

“…[47] More recently, quantum algorithms are proposed to measure the entanglement negativity in noisy intermediate-scale quantum devices. [48] In summary, we have simulated noisy random quantum circuits with density matrix operators and tensor contractions, and characterized the mixed state entanglement through the logarithmic entanglement negativity. With the decreasing gate error rate, we have found that the scaling law of the maximal logarithmic negativity changes from the area law to the volume law.…”

Noisy induced entanglement transition in one-dimensional random quantum circuits

“…To measure the mixed state entanglement, we have used the logarithmic entanglement negativity, which can be measured experimentally through the PT moments [47]. More recently quantum algorithms are proposed to measure the entanglement negativity in noisy intermediate-scale quantum devices [48].…”