From dual-unitary to biunitary: a 2-categorical model for exactly-solvable many-body quantum dynamics

• URL: http://arxiv.org/abs/2302.07280v2
• Date: Tue, 30 May 2023 15:08:26 GMT
• Title: From dual-unitary to biunitary: a 2-categorical model for exactly-solvable many-body quantum dynamics
• Authors: Pieter W. Claeys, Austen Lamacraft, Jamie Vicary
• Abstract summary: Prosen has recently described an alternative model called 'dual-unitary interactions round-a-face' We present a 2-categorical framework that simultaneously generalizes these two existing models.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Dual-unitary brickwork circuits are an exactly-solvable model for many-body chaotic quantum systems, based on 2-site gates which are unitary in both the time and space directions. Prosen has recently described an alternative model called 'dual-unitary interactions round-a-face', which we here call 'clockwork', based on 2-controlled 1-site unitaries composed in a non-brickwork structure, yet with many of the same attractive global properties. We present a 2-categorical framework that simultaneously generalizes these two existing models, and use it to show that brickwork and clockwork circuits can interact richly, yielding new types of generalized heterogeneous circuits. We show that these interactions are governed by quantum combinatorial data, which we precisely characterize. These generalized circuits remain exactly-solvable and we show that they retain the attractive features of the original models such as single-site correlation functions vanishing everywhere except on the causal light-cone. Our presented framework allows us to directly extend the notion of solvable initial states to these biunitary circuits, which are shown to result in maximal entanglement growth and exact thermalization after finitely many time steps under biunitary circuit dynamics.

Related papers

• Fundamental charges for dual-unitary circuits [0.0]
  Dual-unitary quantum circuits have recently attracted attention as an analytically tractable model of many-body quantum dynamics. We show that for 1+1D dual-unitary circuits the set of width-$w$ conserved densities is in one-to-one correspondence with the set of width-$w$ solitons. We also establish a link between fermionic models and dual-unitary circuits, advancing our understanding of what kinds of physics can be explored in this framework.
  arXiv  Detail & Related papers  (2023-12-21T18:59:01Z)
• Solvable entanglement dynamics in quantum circuits with generalized dual unitarity [0.0]
  We study the non-equilibrium dynamics of kicked Ising models in $1+1$ dimensions. These models give rise to time-evolution equivalent to quantum circuits.
  arXiv  Detail & Related papers  (2023-12-19T15:23:55Z)
• Hierarchical generalization of dual unitarity [12.031278034659872]
  Dual-unitary circuits allow for exact answers to interesting physical questions in clean or disordered quantum systems. This family of models shows some non-universal features, like vanishing correlations inside the light-cone and instantaneous thermalization of local observables. We propose a generalization of dual-unitary circuits where the exactly calculable spatial-temporal correlation functions display richer behavior.
  arXiv  Detail & Related papers  (2023-07-06T17:07:05Z)
• Third quantization of open quantum systems: new dissipative symmetries and connections to phase-space and Keldysh field theory formulations [77.34726150561087]
  We reformulate the technique of third quantization in a way that explicitly connects all three methods. We first show that our formulation reveals a fundamental dissipative symmetry present in all quadratic bosonic or fermionic Lindbladians. For bosons, we then show that the Wigner function and the characteristic function can be thought of as ''wavefunctions'' of the density matrix.
  arXiv  Detail & Related papers  (2023-02-27T18:56:40Z)
• Growth of entanglement of generic states under dual-unitary dynamics [77.34726150561087]
  Dual-unitary circuits are a class of locally-interacting quantum many-body systems. In particular, they admit a class of solvable" initial states for which, in the thermodynamic limit, one can access the full non-equilibrium dynamics. We show that in this case the entanglement increment during a time step is sub-maximal for finite times, however, it approaches the maximal value in the infinite-time limit.
  arXiv  Detail & Related papers  (2022-07-29T18:20:09Z)
• Circuits of space and time quantum channels [0.0]
  We show that noise unbiased around the dual-unitary family leads to exactly solvable models, even if dual-unitarity is strongly violated. We prove that any channel unital in both space and time directions can be written as an affine combination of a particular class of dual-unitary gates.
  arXiv  Detail & Related papers  (2022-06-24T08:35:17Z)
• Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains [62.997667081978825]
  Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics. We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
  arXiv  Detail & Related papers  (2022-02-15T19:00:09Z)
• Construction and the ergodicity properties of dual unitary quantum circuits [0.0]
  We consider one dimensional quantum circuits of the type, where the fundamental quantum gate is dual unitary. We review various existing constructions for dual unitary gates and we supplement them with new ideas in a number of cases. A brief mathematical treatment of the recurrence time in such models is presented in the Appendix by Roland Bacher and Denis Serre.
  arXiv  Detail & Related papers  (2022-01-19T18:09:34Z)
• Geometric phase in a dissipative Jaynes-Cummings model: theoretical explanation for resonance robustness [68.8204255655161]
  We compute the geometric phases acquired in both unitary and dissipative Jaynes-Cummings models. In the dissipative model, the non-unitary effects arise from the outflow of photons through the cavity walls. We show the geometric phase is robust, exhibiting a vanishing correction under a non-unitary evolution.
  arXiv  Detail & Related papers  (2021-10-27T15:27:54Z)
• Relevant OTOC operators: footprints of the classical dynamics [68.8204255655161]
  The OTOC-RE theorem relates the OTOCs summed over a complete base of operators to the second Renyi entropy. We show that the sum over a small set of relevant operators, is enough in order to obtain a very good approximation for the entropy. In turn, this provides with an alternative natural indicator of complexity, i.e. the scaling of the number of relevant operators with time.
  arXiv  Detail & Related papers  (2020-07-31T19:23:26Z)
• Models of zero-range interaction for the bosonic trimer at unitarity [91.3755431537592]
  We present the construction of quantum Hamiltonians for a three-body system consisting of identical bosons mutually coupled by a two-body interaction of zero range. For a large part of the presentation, infinite scattering length will be considered.
  arXiv  Detail & Related papers  (2020-06-03T17:54:43Z)

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.