Stability of Local Quantum Dissipative Systems

Cubitt, Toby S.; Lucia, Ángelo; Michalakis, Spyridon; Pérez-Garcı́a, David

doi:10.1007/s00220-015-2355-3

Cited by 64 publications

(90 citation statements)

References 86 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Namely, if the gap is finite (so-called rapidly mixing systems) one can show that this implies a clustering of correlations in the steady state [8,9], meaning that local observables are uncorrelated on a scale larger than ∼ 1/g. Rapid mixing also implies the stability of steady state to local perturbations [10][11][12]. If the gap on the other hand closes in the thermodynamic limit this can lead to a nonequilibrium phase transition [13][14][15][16][17][18] and can result in a non-exponential relaxation [19,20] towards a steady state.…”

Section: Introductionmentioning

confidence: 99%

Relaxation times of dissipative many-body quantum systems

2015

View full text Add to dashboard Cite

We study relaxation times, also called mixing times, of quantum many-body systems described by a Lindblad master equation. We in particular study the scaling of the spectral gap with the system length, the so-called dynamical exponent, identifying a number of transitions in the scaling. For systems with bulk dissipation we generically observe different scaling for small and for strong dissipation strength, with a critical transition strength going to zero in the thermodynamic limit. We also study a related phase transition in the largest decay mode. For systems with only boundary dissipation we show a generic bound that the gap can not be larger than ∼ 1/L. In integrable systems with boundary dissipation one typically observes scaling ∼ 1/L 3 , while in chaotic ones one can have faster relaxation with the gap scaling as ∼ 1/L and thus saturating the generic bound. We also observe transition from exponential to algebraic gap in systems with localized modes.

show abstract

Section: Introductionmentioning

confidence: 99%

Relaxation times of dissipative many-body quantum systems

2015

View full text Add to dashboard Cite

show abstract

“…VI we explore the efficiency of the proposed FTS schemes in both the non-robust and robust settings, by providing, in particular, an upper bound to the circuit complexity of RFTS protocols for QL constraints defined on a lattice. Finally, since FT convergence is a particularly strong form of convergence, it is natural to explore the extent to which it may be related to "rapidly mixing" QL continuous-time dynamics, which is able to efficiently prepare an equilibrium state [59][60][61]. In Sec.…”

Section: Arxiv:170306183v1 [Quant-ph] 17 Mar 2017mentioning

confidence: 99%

Exact stabilization of entangled states in finite time by dissipative quantum circuits

2017

View full text Add to dashboard Cite

Open quantum systems evolving according to discrete-time dynamics are capable, unlike continuous-time counterparts, to converge to a stable equilibrium in finite time with zero error. We consider dissipative quantum circuits consisting of sequences of quantum channels subject to specified quasi-locality constraints, and determine conditions under which stabilization of a pure multipartite entangled state of interest may be exactly achieved in finite time. Special emphasis is devoted to characterizing scenarios where finite-time stabilization may be achieved robustly with respect to the order of the applied quantum maps, as suitable for unsupervised control architectures. We show that if a decomposition of the physical Hilbert space into virtual subsystems is found, which is compatible with the locality constraint and relative to which the target state factorizes, then robust stabilization may be achieved by independently cooling each component. We further show that if the same condition holds for a scalable class of pure states, a continuous-time quasilocal Markov semigroup ensuring rapid mixing can be obtained. Somewhat surprisingly, we find that the commutativity of the canonical parent Hamiltonian one may associate to the target state does not directly relate to its finite-time stabilizability properties, although in all cases where we can guarantee robust stabilization, a (possibly non-canonical) commuting parent Hamiltonian may be found. Beside graph states, quantum states amenable to finite-time robust stabilization include a class of universal resource states displaying two-dimensional symmetry-protected topological order, along with tensor network states obtained by generalizing a construction due to Bravyi and Vyalyi. Extensions to representative classes of mixed graph-product and thermal states are also discussed.

show abstract

“…Therefore, in this situation our semigroups are formed by doubly-stochastic quantum channels (completely positive, unital and trace preserving maps). Since hypercontractivity has been shown to be a very useful tool to find bounds on the convergence time of semigroups of quantum channels [12,18,19], our results could be of interest in quantum information theory. Actually, similar results have been already studied for semigroups consisting of tensor products of q-bits channels, i.e.…”

Section: Introductionmentioning

confidence: 98%