Simulating Open Quantum System Dynamics on NISQ Computers with Generalized Quantum Master Equations

Abstract

We present a quantum algorithm based on the generalized quantum master equation (GQME) approach to simulate open quantum system dynamics on noisy intermediate-scale quantum (NISQ) computers. This approach overcomes the limitations of the Lindblad equation, which assumes weak system–bath coupling and Markovity, by providing a rigorous derivation of the equations of motion for any subset of elements of the reduced density matrix. The memory kernel resulting from the effect of the remaining degrees of freedom is used as input to calculate the corresponding non-unitary propagator. We demonstrate how the Sz.-Nagy dilation theorem can be employed to transform the non-unitary propagator into a unitary one in a higher-dimensional Hilbert space, which can then be implemented on quantum circuits of NISQ computers. We validate our quantum algorithm as applied to the spin-boson benchmark model by analyzing the impact of the quantum circuit depth on the accuracy of the results when the subset is limited to the diagonal elements of the reduced density matrix. Our findings demonstrate that our approach yields reliable results on NISQ IBM computers.

Quantum simulation of bosons with the contracted quantum eigensolver

“…Among them, the simulation of fermions is specifically interesting because electrons are fermions and hence, their simulation is directly related to molecular behavior. In this paper, however, we focus on many-boson systems [20][21][22][23][24][25][26][27] that are equally important in nature.…”

Mapping Molecular Hamiltonians into Hamiltonians of Modular cQED Processors

“…The development of quantum computing simulations for modeling chemical systems is a subject of immense interest. Recent studies have already explored the potential of quantum computing as applied to electronic structure calculations, − quantum dynamics simulations, − and simulations of molecular spectroscopy. − Currently quantum computing facilities are often called noisy intermediate-scale quantum (NISQ) computers, due to their intrinsic limitations, including architectures based on superconducting circuits, trapped ions, , and nuclear magnetic resonance. , To achieve moderate accuracy and reliability in spite of noise and decoherence, simulations of chemical systems have relied on hybrid quantum-classical algorithms, including the variational quantum eigensolver (VQE) method ,, and quantum machine learning methods , where only part of the computation is performed on the quantum computer, sometimes applied with the aid of error mitigation techniques, while the rest of the calculation is run on a conventional computer.…”

“…With σ̂(0) initialized according to different electronic distributions, and with their corresponding σ̂( t ) propagated with TT-TFD, we obtain the Liouville space superoperator scriptP . For more details about the generation of the P pop false( t false) matrix we refer to ref . Next we show how to reduce the dimensionality of the nonunitary time evolution superoperator of the spin-boson model to obtain the population-only superoperator as in eq . We note that for the full time evolution operator, σ j j f u l l false( t false) = ∑ l , m = 1 N e scriptG j j , l m normalf normalu normall normall false( t false) σ l m f u l l false( 0 false) When the initial state is diagonal (i.e., σ jk (0) = 0 for k ≠ j ), eq can be simplified as follows: σ j j f u l l false( t false) = ∑ l = 1 N e scriptG …”

“…With σ̂(0) initialized according to different electronic distributions, and with their corresponding σ̂( t ) propagated with TT-TFD, we obtain the Liouville space superoperator scriptP . For more details about the generation of the P pop false( t false) matrix we refer to ref .…”

Editorial: Quantum Computing for Chemistry

“…The selection of papers reflects the abundance of open problems in quantum computing simulations for chemistry. Most of these papers report new quantum algorithms for predicting the electronic structure of molecules − and simulating chemical dynamics. , For example, ref presents a new quantum algorithm that produces wave functions for quantum chemistry problems that are systematically improvable. Reference introduces low-cost wave functions based on coupled-cluster with paired double excitations, which are optimal wave function ansätze for variational quantum algorithms.…”