Three approaches for representing Lindblad dynamics by a matrix-vector notation

Am-Shallem, Morag; Levy, Amikam; Schaefer, Ido; Kosloff, Ronnie

doi:10.48550/arxiv.1510.08634

Cited by 30 publications

(32 citation statements)

References 17 publications

(24 reference statements)

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“…We can use standard numerical techniques for the exponentiation [109] if we represent ρ and L as a vector and a matrix respectively. To do so, we need to flatten ρ, meaning that we will stack the different rows one after the other.…”

Section: Lindblad Master Equationmentioning

confidence: 99%

Multicore Quantum Computing

Jnane,

Undseth,

Cai

et al. 2022

Preprint

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Any architecture for practical quantum computing must be scalable. An attractive approach is to create multiple cores, computing regions of fixed size that are well-spaced but interlinked with communication channels. This exploded architecture can relax the demands associated with a single monolithic device: the complexity of control, cooling and power infrastructure as well as the difficulties of cross-talk suppression and near-perfect component yield. Here we explore interlinked multicore architectures through analytic and numerical modelling. While elements of our analysis are relevant to diverse platforms, our focus is on semiconductor electron spin systems in which numerous cores may exist on a single chip. We model shuttling and microwave-based interlinks and estimate the achievable fidelities, finding values that are encouraging but markedly inferior to intra-core operations. We therefore introduce optimsed entanglement purification to enable highfidelity communication, finding that 99.5% is a very realistic goal. We then assess the prospects for quantum advantage using such devices in the NISQ-era and beyond: we simulate recently proposed exponentially-powerful error mitigation schemes in the multicore environment and conclude that these techniques impressively suppress imperfections in both the inter-and intra-core operations.

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Section: Lindblad Master Equationmentioning

confidence: 99%

Multicore Quantum Computing

Jnane,

Undseth,

Cai

et al. 2022

Preprint

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“…Suppose that the dimension of the Hilbert space is d. Then, the density operator is a d × d -dimensional matrix, which we tweak into a 1 × d 2 column vector r by stacking the columns of ρ on top of each other. The products between the operators and the density operator then change to matrix vector products [74], which can be solved with conventional numerical methods. For a time independent system the steady state density operator ρss is defined as a state that does not change in time, i.e.…”

Section: Electromagnetic Environment Of the Waveguidementioning

confidence: 99%

Collective bosonic effects in an array of transmon devices

Orell,

Zanner,

Juan

et al. 2021

Preprint

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Multiple emitters coherently interacting with an electromagnetic mode give rise to collective effects such as correlated decay and coherent exchange interaction, depending on the separation of the emitters. By diagonalizing the effective non-Hermitian many-body Hamiltonian we reveal the complex-valued eigenvalue spectrum encoding the decay and interaction characteristics. We show that there are significant differences in the emerging effects for an array of interacting anharmonic oscillators compared to those of two-level systems and harmonic oscillators. The bosonic decay rate of the most superradiant state increases linearly as a function of the filling factor and exceeds that of two-level systems in magnitude. Furthermore, with bosonic systems, dark states are formed at each filling factor. These are in strong contrast with two-level systems, where the maximal superradiance is observed at half filling and with larger filling factors superradiance diminishes and no dark states are formed. As an experimentally relevant setup of bosonic waveguide QED, we focus on arrays of transmon devices embedded inside a rectangular waveguide. Specifically, we study the setup of two transmon pairs realized experimentally in M. Zanner et al., arXiv.2106.05623 (2021, and show that it is necessary to consider transmons as bosonic multilevel emitters to accurately recover correct collective effects for the higher excitation manifolds.

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“…The proof of this property is established in the framework of the Liouville space representation and assumes a system with a closed Lie algebra. Liouville space is a Hilbert space of system operators, embedded with an inner product Â, B ≡ tr Â † B [5,18,19]. In this space, the quantum system is represented in terms of a finite operator basis.…”

Section: A Inertial Solution Of the Free Dynamicsmentioning

confidence: 99%

Fast Route to Thermalization

Dann,

Tobalina,

Kosloff

2019

Preprint

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We present a control scheme for quantum systems coupled to a thermal bath. We demonstrate state-to-state control between two Gibbs states. This scheme can be used to accelerate thermalization and cool the open system. Starting from a microscopic description, we derive the reduced system dynamics, leading to a non-adiabatic master equation. The equation contains non-trivial effects due to the non-adiabatic driving and bath interaction. These special features enable controlling the open system and accelerating the entropy changes. For a two-level system model, we obtain a general solution and introduce a reverse-engineering scheme for control. The control problem is analyzed in the context of the theory of quantum control and the accompanying thermodynamic cost.

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Three approaches for representing Lindblad dynamics by a matrix-vector notation

Cited by 30 publications

References 17 publications

Multicore Quantum Computing

Multicore Quantum Computing

Collective bosonic effects in an array of transmon devices

Fast Route to Thermalization

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