Construction and the ergodicity properties of dual unitary quantum circuits

Borsi, Márton; Pozsgay, Balázs

doi:10.48550/arxiv.2201.07768

Cited by 4 publications

(10 citation statements)

References 56 publications

(152 reference statements)

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“…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: Discussionmentioning

confidence: 99%

“…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 3 or even 5 sites. The integrability properties of these models are not yet understood.…”

Section: Superintegrable Quantum Circuitsmentioning

confidence: 99%

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Integrable deformations of superintegrable quantum circuits

Gombor¹,

Pozsgay²

2022

Preprint

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Superintegrable models are very special dynamical systems: they possess more conservation laws than what is necessary for complete 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.

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Section: Discussionmentioning

confidence: 99%

Section: Superintegrable Quantum Circuitsmentioning

confidence: 99%

Integrable deformations of superintegrable quantum circuits

Gombor¹,

Pozsgay²

2022

Preprint

Self Cite

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“…[8] showed how dynamical correlation functions could be exactly calculated for dual-unitary circuits and classified all such circuits for a local two-dimensional Hilbert space (qubits). No complete characterization of dual-unitary gates exists for arbitrary Hilbert spaces, but various constructions have been proposed leading to rich dynamical behaviours [9][10][11][12][13][14][15]. Subsequent studies led to exact results on scrambling [16,17], computational power [18], solvable initial matrix product states [19], entanglement measures [20] and entanglement barriers [21], the effect of perturbations [22], the evolution of temporal entanglement [23][24][25], and measurement-induced phase transitions [26].…”

Section: Introductionmentioning

confidence: 99%

Emergent quantum state designs and biunitarity in dual-unitary circuit dynamics

Claeys

Lamacraft

2022

Quantum

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Recent works have investigated the emergence of a new kind of random matrix behaviour in unitary dynamics following a quantum quench. Starting from a time-evolved state, an ensemble of pure states supported on a small subsystem can be generated by performing projective measurements on the remainder of the system, leading to a projected ensemble. In chaotic quantum systems it was conjectured that such projected ensembles become indistinguishable from the uniform Haar-random ensemble and lead to a quantum state design. Exact results were recently presented by Ho and Choi [Phys. Rev. Lett. 128, 060601 (2022)] for the kicked Ising model at the self-dual point. We provide an alternative construction that can be extended to general chaotic dual-unitary circuits with solvable initial states and measurements, highlighting the role of the underlying dual-unitarity and further showing how dual-unitary circuit models exhibit both exact solvability and random matrix behaviour. Building on results from biunitary connections, we show how complex Hadamard matrices and unitary error bases both lead to solvable measurement schemes.

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“…qubits [7]. In general, certain non-exhaustive constructions are known [17][18][19][20][21][22], which still contain a plateau of rich behaviour.…”

Section: Introductionmentioning

confidence: 99%

Circuits of space and time quantum channels

Kos¹,

Styliaris²

2022

Preprint

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Exact solutions in interacting many-body systems are scarce and very valuable since they provide crucial insights into the dynamics. This is true for both closed and open quantum systems. Recently introduced dual-unitary models are one example where this is possible. These brick-wall quantum circuits consist of local gates, which are unitary in both time and space directions. In this work we generalise these ideas to obtain exact solutions in open quantum circuits, where each gate is substituted by a local quantum channel. Exact solutions are enabled by demanding additional unitality directions for local quantum channels. That is, local channels preserve the identity operator also in (at least one) space direction. We introduce new families of models, which obey different combinations of unitality conditions, and study their structure. Moreover, we prove that any 4way unital channel can be written as an affine combination of a particular class of dual-unitary gates. Next, we use these families to provide exact solutions of spatio-temporal correlation functions, spatial correlations after a quantum quench, and study their steady states. For solvable quenches, we define initial solvable matrix product density operators (MPDO). In addition, we prove that solvable MPDO in the local purification form are in one-to-one correspondence with quantum channels.

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Construction and the ergodicity properties of dual unitary quantum circuits

Cited by 4 publications

References 56 publications

Integrable deformations of superintegrable quantum circuits

Integrable deformations of superintegrable quantum circuits

Emergent quantum state designs and biunitarity in dual-unitary circuit dynamics

Circuits of space and time quantum channels

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