Stability of logarithmic Sobolev inequalities under a noncommutative change of measure

Junge, Marius; LaRacuente, Nicholas; Rouzé, Cambyse

doi:10.48550/arxiv.1911.08533

Cited by 6 publications

(9 citation statements)

References 22 publications

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“…The above results can be extended to Lindbladians L satisfying GNS-symmetry of states via the noncommutative change of measure in [JLR19]. Very recently this result has been independently obtained in [GR21] using very different techniques.…”

Section: Introductionmentioning

confidence: 72%

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Geometric Approach Towards Complete Logarithmic Sobolev Inequalities

Gao,

Junge,

2021

Preprint

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In this paper, we use the Carnot-Caratheodory distance from sub-Riemanian geometry to prove entropy decay estimates for all finite dimensional symmetric quantum Markov semigroups. This estimate is independent of the environment size and hence stable under tensorization. Our approach relies on the transference principle, the existence of t-designs, and the sub-Riemannian diameter of compact Lie groups and implies estimates for the spectral gap.

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Section: Introductionmentioning

confidence: 72%

“…Using the noncommutative change of measure in [JLR19, Theorem 4.1], we obtain the existence of CLSI constant for all finite dimensional quantum Markov semigroup satisfies detailed balance condition (see e.g. [JLR19] for detailed defintion. ).…”

Section: Lemma 33 ([Gjl20]mentioning

confidence: 99%

Geometric Approach Towards Complete Logarithmic Sobolev Inequalities

Gao,

Junge,

2021

Preprint

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“…Furthermore, our particular form has a unique and usually full rank fixed point state as long as depolarizing strength is non-zero, a useful property in theoretical analysis and in estimating rates of decay to equilibrium [91,92]. While the D 4 form contains some unitary rotation, because this rotation commutes with the restriction to the fixed point algebra, one may still apply recent results showing exponential decay of relative entropy to the fixed point [93][94][95].…”

Section: Modeling Qubit Movements Via Physically Inferred Channelsmentioning

confidence: 99%

Modeling Short-Range Microwave Networks to Scale Superconducting Quantum Computation

LaRacuente¹,

Smith²,

Imany³

et al. 2022

Preprint

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A core challenge for superconducting quantum computers is to scale up the number of qubits in each processor without increasing noise or cross-talk. Distributing a quantum computer across nearby small qubit arrays, known as chiplets, could solve many problems associated with size. We propose a chiplet architecture over microwave links with potential to exceed monolithic performance on near-term hardware. We model and evaluate the chiplet architecture in a way that bridges the physical and network layers. We find concrete evidence that distributed quantum computing may accelerate the path toward useful and ultimately scalable quantum computers. In the long-term, short-range networks may underlie quantum computers just as local area networks underlie classical datacenters and supercomputers today.

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“…where the infimum is always attained by σ = E N (ρ). Indeed, for any σ satisfying E N (σ) = σ, we have the following chain rule (see [37,Lemma 3.4])…”

Section: Transportation Cost From Local Indistinguishabilitymentioning

confidence: 99%

Quantum concentration inequalities

De Palma,

Rouzé

2021

Preprint

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We establish transportation cost inequalities (TCI) with respect to the quantum Wasserstein distance by introducing quantum extensions of well-known classical methods: first, using a non-commutative version of Ollivier's coarse Ricci curvature, we prove that high temperature Gibbs states of commuting Hamiltonians on arbitrary hypergraphs H = (V, E) satisfy a TCI with constant scaling as O(|V |). Second, we argue that the temperature range for which the TCI holds can be enlarged by relating it to recently established modified logarithmic Sobolev inequalities. Third, we prove that the inequality still holds for fixed points of arbitrary reversible local quantum Markov semigroups on regular lattices, albeit with slightly worsened constants, under a seemingly weaker condition of local indistinguishability of the fixed points. Finally, we use our framework to prove Gaussian concentration bounds for the distribution of eigenvalues of quasi-local observables and argue the usefulness of the TCI in proving the equivalence of the canonical and microcanonical ensembles and an exponential improvement over the weak Eigenstate Thermalization Hypothesis.

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Stability of logarithmic Sobolev inequalities under a noncommutative change of measure

Cited by 6 publications

References 22 publications

Geometric Approach Towards Complete Logarithmic Sobolev Inequalities

Geometric Approach Towards Complete Logarithmic Sobolev Inequalities

Modeling Short-Range Microwave Networks to Scale Superconducting Quantum Computation

Quantum concentration inequalities

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