The black hole interior from non-isometric codes and complexity

• URL: http://arxiv.org/abs/2207.06536v2
• Date: Tue, 4 Oct 2022 21:43:24 GMT
• Title: The black hole interior from non-isometric codes and complexity
• Authors: Chris Akers, Netta Engelhardt, Daniel Harlow, Geoff Penington, Shreya Vardhan
• Abstract summary: We show how quantum error correction can be used to explain the emergence of the black hole interior. We show that many previous ideas, such as the existence of a large number of "null states", fit naturally into this framework.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum error correction has given us a natural language for the emergence of spacetime, but the black hole interior poses a challenge for this framework: at late times the apparent number of interior degrees of freedom in effective field theory can vastly exceed the true number of fundamental degrees of freedom, so there can be no isometric (i.e. inner-product preserving) encoding of the former into the latter. In this paper we explain how quantum error correction nonetheless can be used to explain the emergence of the black hole interior, via the idea of "non-isometric codes protected by computational complexity". We show that many previous ideas, such as the existence of a large number of "null states", a breakdown of effective field theory for operations of exponential complexity, the quantum extremal surface calculation of the Page curve, post-selection, "state-dependent/state-specific" operator reconstruction, and the "simple entropy" approach to complexity coarse-graining, all fit naturally into this framework, and we illustrate all of these phenomena simultaneously in a soluble model.

Related papers

• Embezzling entanglement from quantum fields [41.94295877935867]
  Embezzlement of entanglement refers to the counterintuitive possibility of extracting entangled quantum states from a reference state of an auxiliary system. We uncover a deep connection between the operational task of embezzling entanglement and the mathematical classification of von Neumann algebras.
  arXiv  Detail & Related papers  (2024-01-14T13:58:32Z)
• Quantum algorithms: A survey of applications and end-to-end complexities [90.05272647148196]
  The anticipated applications of quantum computers span across science and industry. We present a survey of several potential application areas of quantum algorithms. We outline the challenges and opportunities in each area in an "end-to-end" fashion.
  arXiv  Detail & Related papers  (2023-10-04T17:53:55Z)
• Cosmological complexity of the modified dispersion relation [3.0346001106791323]
  The curvature perturbation of the scalar field is identified with the two-mode squeezed state. Our numeric indicates that the complexity of the modified dispersion relation will have a non-linear pattern after the horizon exits. Since the modified dispersion relation can be dubbed as the consequences of various frameworks of quantum gravity, it could be applicable to these frameworks.
  arXiv  Detail & Related papers  (2023-09-04T13:26:20Z)
• Dense outputs from quantum simulations [5.295277584890625]
  The quantum dense output problem is the process of evaluating time-accumulated observables from time-dependent quantum dynamics. This problem arises frequently in applications such as quantum control and spectroscopic computation. We present a range of algorithms designed to operate on both early and fully fault-tolerant quantum platforms.
  arXiv  Detail & Related papers  (2023-07-26T18:16:51Z)
• Overlapping qubits from non-isometric maps and de Sitter tensor networks [41.94295877935867]
  We show that processes in local effective theories can be spoofed with a quantum system with fewer degrees of freedom. We highlight how approximate overlapping qubits are conceptually connected to Hilbert space dimension verification, degree-of-freedom counting in black holes and holography.
  arXiv  Detail & Related papers  (2023-04-05T18:08:30Z)
• Krylov complexity in quantum field theory, and beyond [44.99833362998488]
  We study Krylov complexity in various models of quantum field theory. We find that the exponential growth of Krylov complexity satisfies the conjectural inequality, which generalizes the Maldacena-Shenker-Stanford bound on chaos.
  arXiv  Detail & Related papers  (2022-12-29T19:00:00Z)
• Saturation and recurrence of quantum complexity in random local quantum dynamics [5.803309695504831]
  Quantum complexity is a measure of the minimal number of elementary operations required to prepare a given state or unitary channel. Brown and Susskind conjectured that the complexity of a chaotic quantum system grows linearly in time up to times exponential in the system size, saturating at a maximal value, and remaining maximally complex until undergoing recurrences at doubly-exponential times.
  arXiv  Detail & Related papers  (2022-05-19T17:42:31Z)
• Bounds on quantum evolution complexity via lattice cryptography [0.0]
  We address the difference between integrable and chaotic motion in quantum theory as manifested by the complexity of the corresponding evolution operators. Complexity is understood here as the shortest geodesic distance between the time-dependent evolution operator and the origin within the group of unitaries.
  arXiv  Detail & Related papers  (2022-02-28T16:20:10Z)
• Quantum Computational Complexity -- From Quantum Information to Black Holes and Back [0.0]
  Quantum computational complexity was suggested as a new entry in the holographic dictionary. We show how it can be used to define complexity for generic quantum systems. We highlight the relation between complexity, chaos and scrambling in chaotic systems.
  arXiv  Detail & Related papers  (2021-10-27T18:00:12Z)
• The role of boundary conditions in quantum computations of scattering observables [58.720142291102135]
  Quantum computing may offer the opportunity to simulate strongly-interacting field theories, such as quantum chromodynamics, with physical time evolution. As with present-day calculations, quantum computation strategies still require the restriction to a finite system size. We quantify the volume effects for various $1+1$D Minkowski-signature quantities and show that these can be a significant source of systematic uncertainty.
  arXiv  Detail & Related papers  (2020-07-01T17:43:11Z)
• Multidimensional dark space and its underlying symmetries: towards dissipation-protected qubits [62.997667081978825]
  We show that a controlled interaction with the environment may help to create a state, dubbed as em dark'', which is immune to decoherence. To encode quantum information in the dark states, they need to span a space with a dimensionality larger than one, so different states act as a computational basis. This approach offers new possibilities for storing, protecting and manipulating quantum information in open systems.
  arXiv  Detail & Related papers  (2020-02-01T15:57:37Z)

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.