Hybrid quantumclassical hierarchy for mitigation of decoherence and determination of excited states
Abstract
Using quantum devices supported by classical computational resources is a promising approach to quantumenabled computation. One powerful example of such a hybrid quantumclassical approach optimized for classically intractable eigenvalue problems is the variational quantum eigensolver, built to utilize quantum resources for the solution of eigenvalue problems and optimizations with minimal coherence time requirements by leveraging classical computational resources. These algorithms have been placed as leaders among the candidates for the first to achieve supremacy over classical computation. Here, we provide evidence for the conjecture that variational approaches can automatically suppress even nonsystematic decoherence errors by introducing an exactly solvable channel model of variational state preparation. Moreover, we develop a more general hierarchy of measurement and classical computation that allows one to obtain increasingly accurate solutions by leveraging additional measurements and classical resources. In conclusion, we demonstrate numerically on a sample electronic system that this method both allows for the accurate determination of excited electronic states as well as reduces the impact of decoherence, without using any additional quantum coherence time or formal errorcorrection codes.
 Authors:
 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division
 Univ. of California, Berkeley, CA (United States). Quantum Nanoelectronics Lab., Dept. of Physics
 Publication Date:
 Research Org.:
 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC21)
 OSTI Identifier:
 1393218
 DOE Contract Number:
 AC0205CH11231
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physical Review A; Journal Volume: 95; Journal Issue: 4
 Country of Publication:
 United States
 Language:
 English
Citation Formats
McClean, Jarrod R., KimchiSchwartz, Mollie E., Carter, Jonathan, and de Jong, Wibe A. Hybrid quantumclassical hierarchy for mitigation of decoherence and determination of excited states. United States: N. p., 2017.
Web. doi:10.1103/PhysRevA.95.042308.
McClean, Jarrod R., KimchiSchwartz, Mollie E., Carter, Jonathan, & de Jong, Wibe A. Hybrid quantumclassical hierarchy for mitigation of decoherence and determination of excited states. United States. doi:10.1103/PhysRevA.95.042308.
McClean, Jarrod R., KimchiSchwartz, Mollie E., Carter, Jonathan, and de Jong, Wibe A. Thu .
"Hybrid quantumclassical hierarchy for mitigation of decoherence and determination of excited states". United States.
doi:10.1103/PhysRevA.95.042308.
@article{osti_1393218,
title = {Hybrid quantumclassical hierarchy for mitigation of decoherence and determination of excited states},
author = {McClean, Jarrod R. and KimchiSchwartz, Mollie E. and Carter, Jonathan and de Jong, Wibe A.},
abstractNote = {Using quantum devices supported by classical computational resources is a promising approach to quantumenabled computation. One powerful example of such a hybrid quantumclassical approach optimized for classically intractable eigenvalue problems is the variational quantum eigensolver, built to utilize quantum resources for the solution of eigenvalue problems and optimizations with minimal coherence time requirements by leveraging classical computational resources. These algorithms have been placed as leaders among the candidates for the first to achieve supremacy over classical computation. Here, we provide evidence for the conjecture that variational approaches can automatically suppress even nonsystematic decoherence errors by introducing an exactly solvable channel model of variational state preparation. Moreover, we develop a more general hierarchy of measurement and classical computation that allows one to obtain increasingly accurate solutions by leveraging additional measurements and classical resources. In conclusion, we demonstrate numerically on a sample electronic system that this method both allows for the accurate determination of excited electronic states as well as reduces the impact of decoherence, without using any additional quantum coherence time or formal errorcorrection codes.},
doi = {10.1103/PhysRevA.95.042308},
journal = {Physical Review A},
number = 4,
volume = 95,
place = {United States},
year = {Thu Apr 06 00:00:00 EDT 2017},
month = {Thu Apr 06 00:00:00 EDT 2017}
}

Meanfield dynamics with stochastic decoherence (MFSD): A new algorithm for nonadiabatic mixed quantum/classical moleculardynamics simulations with nuclearinduced decoherence
The key factors that distinguish algorithms for nonadiabatic mixed quantum/classical (MQC) simulations from each other are how they incorporate quantum decoherencethe fact that classical nuclei must eventually cause a quantum superposition state to collapse into a pure stateand how they model the effects of decoherence on the quantum and classical subsystems. Most algorithms use distinct mechanisms for modeling nonadiabatic transitions between pure quantum basis states ('surface hops') and for calculating the loss of quantummechanical phase information (e.g., the decay of the offdiagonal elements of the density matrix). In our view, however, both processes should be unified in a single descriptionmore » 
Decoherence and energy relaxation in the quantumclassical dynamics for charge transport in organic semiconducting crystals: An instantaneous decoherence correction approach
We explore an instantaneous decoherence correction (IDC) approach for the decoherence and energy relaxation in the quantumclassical dynamics of charge transport in organic semiconducting crystals. These effects, originating from environmental fluctuations, are essential ingredients of the carrier dynamics. The IDC is carried out by measurementlike operations in the adiabatic representation. While decoherence is inherent in the IDC, energy relaxation is taken into account by considering the detailed balance through the introduction of energydependent reweighing factors, which could be either Boltzmann (IDCBM) or MillerAbrahams (IDCMA) type. For a nondiagonal electronphonon coupling model, it is shown that IDC tends to enhance diffusionmore » 
Calculation of absorption spectra involving multiple excited states: Approximate methods based on the mixed quantum classical Liouville equation
We investigate the calculation of absorption spectra based on the mixed quantum classical Liouville equation (MQCL) methods. It has been shown previously that, for a single excited state, the averaged classical dynamics approach to calculate the linear and nonlinear spectroscopy can be derived using the MQCL formalism. This work focuses on problems involving multiple coupled excited state surfaces, such as in molecular aggregates and in the cases of coupled electronic states. A new equation of motion to calculate the dipoledipole correlation functions within the MQCL formalism is first presented. Two approximate methods are then proposed to solve the resulted equationsmore » 
Quantum decoherence and classical correlation in quantum mechanics
We study two conditions for the quantum system to behave classically: decoherence in the quantum interference and the establishment of the classical trajectory in phase space. We show, despite the fact that these two conditions partially conflict with each other, the upsidedown harmonic oscillator with a diffusion term satisfies them simultaneously. The implications for quantum cosmology and the measurement theory of quantum mechanics are given.