The simulation of the non-Markovian behaviour of a two-level system

Semina, I.; Petruccione, Francesco

doi:10.1016/j.physa.2016.01.042

Cited by 5 publications

(3 citation statements)

References 9 publications

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“…Density matrix methods are a natural choice for modeling open quantum systems and there have been a plethora of methods to capture Markovian and non-Markovian dynamics, from perturbative to numerical techniques [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][49][50][51][52][53]. However, in the non-Markovian regime many of these methods struggle from the same challenges such as maintaining the positivity, and therefore physical nature, of the system density matrix.…”

mentioning

confidence: 99%

Capturing Non-Markovian Dynamics on Near-Term Quantum Computers

Head-Marsden,

Krastanov,

Mazziotti

et al. 2020

Preprint

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With the rapid progress in quantum hardware, there has been an increased interest in new quantum algorithms to describe complex many-body systems searching for the still-elusive goal of 'useful quantum advantage'. Surprisingly, quantum algorithms for the treatment of open quantum systems (OQSs) have remained underexplored, in part due to the inherent challenges of mapping non-unitary evolution into the framework of unitary gates. Evolving an open system unitarily necessitates dilation into a new effective system to incorporate critical environmental degrees of freedom. In this context, we present and validate a new quantum algorithm to treat non-Markovian dynamics in OQSs built on the Ensemble of Lindblad's Trajectories approach, invoking the Sz.-Nagy dilation theorem. Here we demonstrate our algorithm on the Jaynes-Cummings model in the strong coupling and detuned regimes, relevant in quantum optics and driven quantum systems studies. This algorithm, a key step towards generalized modeling of non-Markovian dynamics on a noisy-quantum device, captures a broad class of dynamics and opens up a new direction in OQS problems.

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mentioning

confidence: 99%

Capturing Non-Markovian Dynamics on Near-Term Quantum Computers

Head-Marsden,

Krastanov,

Mazziotti

et al. 2020

Preprint

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“…14,15 Many methods approximate the kernel through perturbative techniques, and while they are effective for small perturbations about the Markovian limit, they can in general limit or destroy the positivity of the density matrix. 16 Other methods have been developed to treat non-Markovian dynamics with built-in positivity in specific systems, [17][18][19][20][21][22][23][24][25][26][27][28][29] but the development of a general, practical framework for non-Markovian approximations that maintains the positive semidefiniteness of the density matrix remains a significant problem. 19 Recent work has produced an exact, closed form master equation which allows the treatment of non-Markovian dynamics for Gaussian environments.…”

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confidence: 99%

Ensemble of Lindblad's trajectories for non-Markovian dynamics

Head-Marsden

Mazziotti

2019

Phys. Rev. A

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Although, Lindblad developed a general Markovian theory for open-system dynamics while maintaining the positivity of the density matrix, a practical non-Markovian analogue remains a significant problem. Here, we present an extension of Lindblad's theory through an ensemble of Lindbladian trajectories originating from different times in the system's history. This approach provides an account of the system's memory while preserving the positivity of the density matrix. We apply the theory to the Jaynes-Cummings model to capture non-Markovian dynamics in the weak and strong coupling regimes.

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“…On the contrary, the non-Markovian evolution depends on the history of the system, and it is more challenging to treat both analytically and numerically [19]. In this sense, despite some recent results [20][21][22][23][24][25][26][27][28][29][30], including a work on the sufficient conditions for a completely positive and trace preserving (CPTP) non-Markovian dynamics [31], a general non-Markovian quantum simulator has not been fully devel-oped yet. A paradigmatic feature of non-Markovian dynamics is the existence of quantum memory effects as an extension of the classical history-dependent dynamics to the quantum domain.…”

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confidence: 99%

Algorithmic quantum simulation of memory effects

et al. 2017

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We propose a method for the algorithmic quantum simulation of memory effects described by integrodifferential evolution equations. It consists in the systematic use of perturbation theory techniques and a Markovian quantum simulator. Our method aims to efficiently simulate both completely positive and nonpositive dynamics without the requirement of engineering non-Markovian environments. Finally, we find that small error bounds can be reached with polynomially scaling resources, evaluated as the time required for the simulation

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The simulation of the non-Markovian behaviour of a two-level system

Cited by 5 publications

References 9 publications

Capturing Non-Markovian Dynamics on Near-Term Quantum Computers

Capturing Non-Markovian Dynamics on Near-Term Quantum Computers

Ensemble of Lindblad's trajectories for non-Markovian dynamics

Algorithmic quantum simulation of memory effects

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