Noise-Induced Entanglement Transition in One-Dimensional Random Quantum Circuits
Qi Zhang1 and Guang-Ming Zhang1,2*
1State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China 2Frontier Science Center for Quantum Information, Beijing 100084, China
Abstract：A random quantum circuit is a minimally structured model to study entanglement dynamics of many-body quantum systems. We consider a one-dimensional quantum circuit with noisy Haar-random unitary gates using density matrix operator and tensor contraction methods. It is shown that the entanglement evolution of the random quantum circuits is properly characterized by the logarithmic entanglement negativity. By performing exact numerical calculations, we find that, as the physical error rate is decreased below a critical value $p_{\rm c} \approx 0.056$, the logarithmic entanglement negativity changes from the area law to the volume law, giving rise to an entanglement transition. The critical exponent of the correlation length can be determined from the finite-size scaling analysis, revealing the universal dynamic property of the noisy intermediate-scale quantum devices.
Elben A, Kueng R, Huang H Y, van Bijnen R, Kokail C, Dalmonte M, Calabrese P, Kraus B, Preskill J, Zoller P, and Vermersch B 2020 Phys. Rev. Lett.125 200501
2022, Vol. 39 
