Integrable nonunitary open quantum circuits
- URL: http://arxiv.org/abs/2011.06565v2
- Date: Fri, 19 Mar 2021 17:00:13 GMT
- Title: Integrable nonunitary open quantum circuits
- Authors: Lucas S\'a, Pedro Ribeiro, and Toma\v{z} Prosen
- Abstract summary: We explicitly construct an integrable and strongly interacting dissipative quantum circuit via a trotterization of the Hubbard model with imaginary interaction strength.
The construction allows us to explicitly build circuits belonging to different non-Hermitian symmetry classes.
- Score: 0.9290757451344674
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We explicitly construct an integrable and strongly interacting dissipative
quantum circuit via a trotterization of the Hubbard model with imaginary
interaction strength. To prove integrability, we build an inhomogeneous
transfer matrix, from which conserved superoperator charges can be derived, in
particular, the circuit's dynamical generator. After showing the trace
preservation and complete positivity of local maps, we reinterpret them as the
Kraus representation of the local dynamics of free fermions with single-site
dephasing. The integrability of the map is broken by adding interactions to the
local coherent dynamics or by removing the dephasing. In particular, even
circuits built from convex combinations of local free-fermion unitaries are
nonintegrable. Moreover, the construction allows us to explicitly build
circuits belonging to different non-Hermitian symmetry classes, which are
characterized by the behavior under transposition instead of complex
conjugation. We confirm all our analytical results by using complex spacing
ratios to examine the spectral statistics of the dissipative circuits.
Related papers
- Strong zero modes in integrable quantum circuits [0.0]
We show that an exact SZM operator can be constructed for certain integrable quantum circuits.
Our predictions are corroborated by numerical simulations of infinite-temperature autocorrelation functions.
arXiv Detail & Related papers (2024-01-22T19:02:33Z) - Toolbox for nonreciprocal dispersive models in circuit QED [44.99833362998488]
We provide a systematic method for constructing effective dispersive Lindblad master equations to describe weakly-anharmonic superconducting circuits.
Results can be used for the design of complex superconducting quantum processors with non-trivial routing of quantum information.
arXiv Detail & Related papers (2023-12-13T18:44:55Z) - Integrability as an attractor of adiabatic flows [0.0]
We consider two generic models of spin chains that are parameterized by two independent couplings.
In one, the integrability breaking is global while, in the other, integrability is broken only at the boundary.
These regions act as attractors of adiabatic flows similar to river basins in nature.
arXiv Detail & Related papers (2023-08-18T18:00:03Z) - Krylov complexity and Trotter transitions in unitary circuit dynamics [0.0]
Floquet circuits arising as the Trotter decomposition of Hamiltonian dynamics are studied.
We find that local maximally ergodic operators appear at a critical Trotter step.
arXiv Detail & Related papers (2023-08-07T18:01:29Z) - Entanglement and localization in long-range quadratic Lindbladians [49.1574468325115]
Signatures of localization have been observed in condensed matter and cold atomic systems.
We propose a model of one-dimensional chain of non-interacting, spinless fermions coupled to a local ensemble of baths.
We show that the steady state of the system undergoes a localization entanglement phase transition by tuning $p$ which remains stable in the presence of coherent hopping.
arXiv Detail & Related papers (2023-03-13T12:45:25Z) - 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) - Exact solutions of interacting dissipative systems via weak symmetries [77.34726150561087]
We analytically diagonalize the Liouvillian of a class Markovian dissipative systems with arbitrary strong interactions or nonlinearity.
This enables an exact description of the full dynamics and dissipative spectrum.
Our method is applicable to a variety of other systems, and could provide a powerful new tool for the study of complex driven-dissipative quantum systems.
arXiv Detail & Related papers (2021-09-27T17:45:42Z) - Entanglement and charge-sharpening transitions in U(1) symmetric
monitored quantum circuits [1.1968749490556412]
We study how entanglement dynamics in non-unitary quantum circuits can be enriched in the presence of charge conservation.
We uncover a charge-sharpening transition that separates different scrambling phases with volume-law scaling of entanglement.
We find that while R'enyi entropies grow sub-ballistically as $sqrttt$ in the absence of measurement, for even an infinitesimal rate of measurements, all average R'enyi entropies grow ballistically with time.
arXiv Detail & Related papers (2021-07-21T18:00:13Z) - Signatures of Self-Trapping in the Driven-Dissipative Bose-Hubbard Dimer [0.0]
We investigate signatures of a self-trapping transition in the driven-dissipative Bose Hubbard dimer.
We find clear signatures of a localization-delocalization crossover as a function of hopping to interaction ratio.
A finite a pump-loss asymmetry restores a delocalization crossover in the steady-state imbalance and leads to a finite intra-dimer dissipation.
arXiv Detail & Related papers (2021-02-08T09:29:09Z) - Probing eigenstate thermalization in quantum simulators via
fluctuation-dissipation relations [77.34726150561087]
The eigenstate thermalization hypothesis (ETH) offers a universal mechanism for the approach to equilibrium of closed quantum many-body systems.
Here, we propose a theory-independent route to probe the full ETH in quantum simulators by observing the emergence of fluctuation-dissipation relations.
Our work presents a theory-independent way to characterize thermalization in quantum simulators and paves the way to quantum simulate condensed matter pump-probe experiments.
arXiv Detail & Related papers (2020-07-20T18:00:02Z) - 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.