An operator growth hypothesis for open quantum systems

• URL: http://arxiv.org/abs/2212.06180v1
• Date: Mon, 12 Dec 2022 19:00:12 GMT
• Title: An operator growth hypothesis for open quantum systems
• Authors: Budhaditya Bhattacharjee, Xiangyu Cao, Pratik Nandy, Tanay Pathak
• Abstract summary: We study the dissipative $q$-body Sachdev-Ye-Kitaev (SYK$_q$) model. We conjecture to be generic for any dissipative (open) quantum systems.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Extending the formalism of Phys. Rev. X 9, 041017, we aim to provide an operator growth hypothesis in certain open quantum systems. Our results are based on the study of the dissipative $q$-body Sachdev-Ye-Kitaev (SYK$_q$) model, governed by the Markovian dynamics. We introduce a notion of ''operator size concentration'' which allows a diagrammatic and combinatorial proof of the asymptotic linear behavior of the two sets of Lanczos coefficients ($a_n$ and $b_n$) in the large $q$ limit. Our results corroborate with the semi-analytics in finite $q$ in the large $N$ limit, and the numerical Arnoldi iteration in finite $q$ and finite $N$ limit. As a result, Krylov complexity exhibits exponential growth following a saturation at a time that grows logarithmically with the inverse dissipation strength. The growth of complexity is suppressed compared to the closed system results, yet it upper bounds the growth of the normalized out-of-time-ordered correlator (OTOC). We conjecture this to be generic for any dissipative (open) quantum systems and may generalize the chaos bound in such cases. We also provide a plausible explanation of the results from the dual gravitational side.

Related papers

• KPZ scaling from the Krylov space [83.88591755871734]
  Recently, a superdiffusion exhibiting the Kardar-Parisi-Zhang scaling in late-time correlators and autocorrelators has been reported. Inspired by these results, we explore the KPZ scaling in correlation functions using their realization in the Krylov operator basis.
  arXiv  Detail & Related papers  (2024-06-04T20:57:59Z)
• Towards large-scale quantum optimization solvers with few qubits [59.63282173947468]
  We introduce a variational quantum solver for optimizations over $m=mathcalO(nk)$ binary variables using only $n$ qubits, with tunable $k>1$. We analytically prove that the specific qubit-efficient encoding brings in a super-polynomial mitigation of barren plateaus as a built-in feature.
  arXiv  Detail & Related papers  (2024-01-17T18:59:38Z)
• Operator dynamics in Lindbladian SYK: a Krylov complexity perspective [0.0]
  We analytically establish the linear growth of two sets of coefficients for any generic jump operators. We find that the Krylov complexity saturates inversely with the dissipation strength, while the dissipative timescale grows logarithmically.
  arXiv  Detail & Related papers  (2023-11-01T18:00:06Z)
• The Franke-Gorini-Kossakowski-Lindblad-Sudarshan (FGKLS) Equation for Two-Dimensional Systems [62.997667081978825]
  Open quantum systems can obey the Franke-Gorini-Kossakowski-Lindblad-Sudarshan (FGKLS) equation. We exhaustively study the case of a Hilbert space dimension of $2$.
  arXiv  Detail & Related papers  (2022-04-16T07:03:54Z)
• A lower bound on the space overhead of fault-tolerant quantum computation [51.723084600243716]
  The threshold theorem is a fundamental result in the theory of fault-tolerant quantum computation. We prove an exponential upper bound on the maximal length of fault-tolerant quantum computation with amplitude noise.
  arXiv  Detail & Related papers  (2022-01-31T22:19:49Z)
• Rise and fall, and slow rise again, of operator entanglement under dephasing [0.0]
  We study the operator space entanglement entropy (OE) of 1D many-body models undergoing dissipative evolution. Under dephasing, after the initial 'rise and fall' the OE can rise again, increasing logarithmically at long times. We trace this behavior back to anomalous classical diffusion processes.
  arXiv  Detail & Related papers  (2022-01-13T17:41:13Z)
• Optimal convergence rate in the quantum Zeno effect for open quantum systems in infinite dimensions [1.5229257192293197]
  In open quantum systems, the quantum Zeno effect consists in frequent applications of a given quantum operation. We prove the optimal convergence rate of order $tfrac1n$ of the Zeno sequence by proving explicit error bounds. We generalize the convergence result for the Zeno effect in two directions.
  arXiv  Detail & Related papers  (2021-11-27T14:41:10Z)
• Annihilating Entanglement Between Cones [77.34726150561087]
  We show that Lorentz cones are the only cones with a symmetric base for which a certain stronger version of the resilience property is satisfied. Our proof exploits the symmetries of the Lorentz cones and applies two constructions resembling protocols for entanglement distillation.
  arXiv  Detail & Related papers  (2021-10-22T15:02:39Z)
• Large Learning Rate Tames Homogeneity: Convergence and Balancing Effect [43.00475513526005]
  We consider using Gradient Descent (GD) with a large learning rate on a homogeneous matrix factorization problem. We prove a convergence theory for constant large learning rates well beyond $2/L$. We rigorously establish an implicit bias of GD induced by such a large learning rate, termed 'balancing'
  arXiv  Detail & Related papers  (2021-10-07T17:58:21Z)
• Bounding the finite-size error of quantum many-body dynamics simulations [6.657101721138396]
  We derive rigorous upper bounds on the Finite-size error (FSE) of local observables in real time quantum dynamics simulations from a product state. Our bounds are practically useful in determining the validity of finite-size results, as we demonstrate in simulations of the one-dimensional (1D) quantum Ising and Fermi-Hubbard models.
  arXiv  Detail & Related papers  (2020-09-25T04:30:25Z)
• Quantum aspects of chaos and complexity from bouncing cosmology: A study with two-mode single field squeezed state formalism [0.0]
  This paper is devoted to the study of out-of-equilibrium aspects and quantum chaos appearing in the universe. We use the $Out-of-Time Ordered correlation (OTOC)$ functions for probing the random behaviour of the universe both at early and the late times.
  arXiv  Detail & Related papers  (2020-09-08T16:10:52Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.