scholarly journals A Numerically Exact Method for Dissipative Dynamics of Qubits

Proceedings ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 59
Author(s):  
L. M. Cangemi ◽  
G. Passarelli ◽  
V. Cataudella ◽  
P. Lucignano ◽  
G. De Filippis
Keyword(s):  
Weak Coupling ◽  
Numerical Technique ◽  
Lanczos Method ◽  
Reduced Density Matrix ◽  
Intermediate Coupling ◽  
Physical Description ◽  
Adiabatic Quantum Computation ◽  
Truncation Scheme ◽  
Excitation Processes ◽  
Reduced Density

We propose a numerical technique suitable for simulating the dynamics of reduced density matrix of a qubit interacting with its environment. Our approach, based on a combination of short-iterative Lanczos method (SIL) and a flexible truncation scheme, allows to include in the physical description multiple-excitation processes, beyond weak coupling and Markov approximations. We perform numerical simulations of two different model Hamiltonians, that are relevant in the field of adiabatic quantum computation (AQC), and we show that our technique is able to recover the correct thermodynamic behavior of the qubit-bath system, from weak to intermediate coupling regime.

Density matrix and purity evolution in dissipative two-level systems: II. Relaxation

2021 ◽  
Author(s):  
Sambarta Chatterjee ◽  
Nancy Makri
Keyword(s):  
Density Matrix ◽  
Time Evolution ◽  
Reduced Density Matrix ◽  
Level System ◽  
Two Level Systems ◽  
Reduced Density ◽  
Harmonic Bath

We investigate the time evolution of the reduced density matrix (RDM) and its purity in the dynamics of a two-level system coupled to a dissipative harmonic bath, when the system is initially placed in one of its eigenstates.

scholarly journals Entanglement spectrum of geometric states

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Wu-zhong Guo
Keyword(s):  
Entanglement Entropy ◽  
Vacuum State ◽  
Reduced Density Matrix ◽  
Microcanonical Ensemble ◽  
Equality Case ◽  
Entanglement Spectrum ◽  
The Matrix ◽  
Point Correlation ◽  
Single Interval ◽  
Reduced Density

Abstract The reduced density matrix of a given subsystem, denoted by ρA, contains the information on subregion duality in a holographic theory. We may extract the information by using the spectrum (eigenvalue) of the matrix, called entanglement spectrum in this paper. We evaluate the density of eigenstates, one-point and two-point correlation functions in the microcanonical ensemble state ρA,m associated with an eigenvalue λ for some examples, including a single interval and two intervals in vacuum state of 2D CFTs. We find there exists a microcanonical ensemble state with λ0 which can be seen as an approximate state of ρA. The parameter λ0 is obtained in the two examples. For a general geometric state, the approximate microcanonical ensemble state also exists. The parameter λ0 is associated with the entanglement entropy of A and Rényi entropy in the limit n → ∞. As an application of the above conclusion we reform the equality case of the Araki-Lieb inequality of the entanglement entropies of two intervals in vacuum state of 2D CFTs as conditions of Holevo information. We show the constraints on the eigenstates. Finally, we point out some unsolved problems and their significance on understanding the geometric states.

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