Non-linear quantum-classical scheme to simulate non-equilibrium strongly correlated fermionic many-body dynamics

Kreula, Juha; Clark, Stephen R. L.; Jaksch, Dieter

doi:10.1038/srep32940

Cited by 49 publications

(44 citation statements)

References 38 publications

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“…In our algorithm, parameters are worked out iteratively, therefore the global minimisation is not required. We remark that Trotterisation is used in some hybrid algorithms [10,[12][13][14][15]. In principle our algorithm can be used to replace the Trotterisation method in these instances, to further simplify the task of the quantum computer.…”

Section: Hybrid Quantum Simulation Of Dynamicsmentioning

confidence: 99%

Efficient Variational Quantum Simulator Incorporating Active Error Minimization

2017

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One of the key applications for quantum computers will be the simulation of other quantum systems that arise in chemistry, materials science, etc, in order to accelerate the process of discovery. It is important to ask the following question: Can this simulation be achieved using near future quantum processors, of modest size and under imperfect control, or must it await the more distant era of large-scale fault-tolerant quantum computing? Here we propose a variational method involving closely integrated classical and quantum coprocessors. We presume that all operations in the quantum coprocessor are prone to error. The impact of such errors is minimised by boosting them artificially and then extrapolating to the zero-error case. In comparison to a more conventional optimised Trotterisation technique, we find that our protocol is efficient and appears to be fundamentally more robust against error accumulation.

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Section: Hybrid Quantum Simulation Of Dynamicsmentioning

confidence: 99%

Efficient Variational Quantum Simulator Incorporating Active Error Minimization

2017

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“…VQEs belong to the class of quantum-classical hybrid algorithms where a classical subroutine is enhanced by the computational power of a quantum simulator. Given its potential for near-term use, the VQE approach is increasingly receiving attention in both theoretical [31,40,[51][52][53][54][55][56][57][58][59] and experimental works [30,50,[60][61][62][63][64][65] with a focus on both quantum chemistry as well as fundamental physics and materials science. We now discuss the simulation of quantum chemistry in more detail.…”

Section: Simulating Quantum Chemistrymentioning

confidence: 99%

Quantum Chemistry Calculations on a Trapped-Ion Quantum Simulator

et al. 2018

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Quantum-classical hybrid algorithms are emerging as promising candidates for near-term practical applications of quantum information processors in a wide variety of fields ranging from chemistry to physics and materials science. We report on the experimental implementation of such an algorithm to solve a quantum chemistry problem, using a digital quantum simulator based on trapped ions. Specifically, we implement the variational quantum eigensolver algorithm to calculate the molecular ground state energies of two simple molecules and experimentally demonstrate and compare different encoding methods using up to four qubits. Furthermore, we discuss the impact of measurement noise as well as mitigation strategies and indicate the potential for adaptive implementations focused on reaching chemical accuracy, which may serve as a cross-platform benchmark for multi-qubit quantum simulators.

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“…The Anderson impurity model [1] (AIM), a single spin-degenerate orbital with an intra-orbital Hubbard interaction U coupled to a bath of noninteracting orbitals, is of fundamental importance in its own right as a nontrivial but solvable [2,3] interacting electron model and as an auxiliary problem for dynamical mean-field theory [4,5]. The nonequilibrium properties of this model [6,7] provide an important laboratory for the development of real-time methods [8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Entanglement entropy and computational complexity of the Anderson impurity model out of equilibrium: Quench dynamics

Millis

2017

Phys. Rev. B

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We study the growth of entanglement entropy in density matrix renormalization group calculations of the real-time quench dynamics of the Anderson impurity model. We find that with appropriate choice of basis, the entropy growth is logarithmic in both the interacting and noninteracting singleimpurity models. The logarithmic entropy growth is understood from a noninteracting chain model as a critical behavior separating regimes of linear growth and saturation of entropy, which correspond respectively to an overlapping and gapped energy spectra of the set of bath states. We find that a logarithmic entropy growth is the generic behavior of quenched impurity models when the bath orbitals in the matrix product state are ordered in energy. A noninteracting calculation of the doubleimpurity Anderson model supports the conclusion in the multi-impurity case. The logarithmic growth of entanglement entropy enables studies of quench dynamics to very long times.

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Non-linear quantum-classical scheme to simulate non-equilibrium strongly correlated fermionic many-body dynamics

Cited by 49 publications

References 38 publications

Efficient Variational Quantum Simulator Incorporating Active Error Minimization

Efficient Variational Quantum Simulator Incorporating Active Error Minimization

Quantum Chemistry Calculations on a Trapped-Ion Quantum Simulator

Entanglement entropy and computational complexity of the Anderson impurity model out of equilibrium: Quench dynamics

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