Construction and the ergodicity properties of dual unitary quantum circuits

Borsi, Márton; Pozsgay, Balázs

doi:10.1103/physrevb.106.014302

Cited by 22 publications

(13 citation statements)

References 54 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We expect that similar calculations are possible for biunitary circuits using the presented graphical calculus, which would establish the connection between biunitary circuits and random matrix theory. Furthermore, while generic parametrizations of dual-unitary gates will generally lead to chaotic quantum dynamics, it is possible to fine-tune the underlying gates such that the full circuit is no longer chaotic and systematic parametrizations of dual-unitary gates remain an active topic of research [9,13,[48][49][50][51][52][53][54]. It is still an open question how parametrizations of these new biunitary connections can influence the level of ergodicity and the corresponding diagnostics of quantum chaos.…”

Section: Discussion and Outlookmentioning

confidence: 99%

See 1 more Smart Citation

Exact dynamics in dual-unitary quantum circuits with projective measurements

Claeys

Marius

Vicary

et al. 2022

Phys. Rev. Research

View full text Add to dashboard Cite

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 rounda-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.

show abstract

Section: Discussion and Outlookmentioning

confidence: 99%

“…However, circuits where wires carry different Hilbert spaces can still be considered, as also argued in Ref. [48] for dual-unitary brickwork circuits.…”

mentioning

confidence: 99%

Exact dynamics in dual-unitary quantum circuits with projective measurements

Claeys

Marius

Vicary

et al. 2022

Phys. Rev. Research

View full text Add to dashboard Cite

show abstract

“…Other examples can be found in the so-called dual unitary circuits [18], where it is known that all conserved charges come from gliders [22]. Non-trivial examples for dual unitary circuits with gliders were found in [24], including models where the shortest glider spans three-or even five-sites. The integrability properties of these models are not yet understood.…”

Section: Superintegrable Quantum Circuitsmentioning

confidence: 99%

“…One of the most interesting questions is, whether these ideas and methods are applicable to other superintegrable models, for example those studied in the recent works [23,24]. Is particle number conservation crucial for our methods to work?…”

Section: The Importance Of Being Oddmentioning

confidence: 99%

Integrable deformations of superintegrable quantum circuits

Gombor,

Pozsgay

2024

SciPost Phys.

Self Cite

View full text Add to dashboard Cite

Superintegrable models are very special dynamical systems: they possess more conservation laws than what is necessary for integrability. This severely constrains their dynamical processes, and it often leads to their exact solvability, even in non-equilibrium situations. In this paper we consider special Hamiltonian deformations of superintegrable quantum circuits. The deformations break superintegrability, but they preserve integrability. We focus on a selection of concrete models and show that for each model there is an (at least) one parameter family of integrable deformations. Our most interesting example is the so-called Rule54 model. We show that the model is compatible with a one parameter family of Yang-Baxter integrable spin chains with six-site interaction. Therefore, the Rule54 model does not have a unique integrability structure, instead it lies at the intersection of a family of quantum integrable models.

show abstract

“…On the other hand, a complete description is available for N = 2 [3], see Section 3. For higher dimensions only isolated constructions are known; an extensive review of known solutions was given in [42]. A numerical method to find new solutions was presented in [43], for an early algebraic investigation see [44].…”

Section: Dual Unitaritymentioning

confidence: 99%

Multi-directional unitarity and maximal entanglement in spatially symmetric quantum states

Mestyán,

Pozsgay,

Wanless

2024

SciPost Phys.

Self Cite

View full text Add to dashboard Cite

We consider dual unitary operators and their multi-leg generalizations that have appeared at various places in the literature. These objects can be related to multi-party quantum states with special entanglement patterns: the sites are arranged in a spatially symmetric pattern and the states have maximal entanglement for all bipartitions that follow from the reflection symmetries of the given geometry. We consider those cases where the state itself is invariant with respect to the geometrical symmetry group. The simplest examples are those dual unitary operators which are also self dual and reflection invariant, but we also consider the generalizations in the hexagonal, cubic, and octahedral geometries. We provide a number of constructions and concrete examples for these objects for various local dimensions. All of our examples can be used to build quantum cellular automata in 1+1 or 2+1 dimensions, with multiple equivalent choices for the “direction of time”.

show abstract

Construction and the ergodicity properties of dual unitary quantum circuits

Cited by 22 publications

References 54 publications

Exact dynamics in dual-unitary quantum circuits with projective measurements

Exact dynamics in dual-unitary quantum circuits with projective measurements

Integrable deformations of superintegrable quantum circuits

Multi-directional unitarity and maximal entanglement in spatially symmetric quantum states

Contact Info

Product

Resources

About