Triunitary quantum circuits

@article{Jonay2021TriunitaryQC,
  title={Triunitary quantum circuits},
  author={Cheryne Jonay and Vedika Khemani and Matteo Ippoliti},
  journal={Physical Review Research},
  year={2021}
}
We introduce a novel class of quantum circuits that are unitary along three distinct “arrows of time”. These dynamics share some of the analytical tractability of “dual-unitary” circuits, while exhibiting distinctive and richer phenomenology. We find that two-point correlations in these dynamics are strictly confined to three directions in (1+1)-dimensional spacetime – the two light cone edges, δx = ±vδt, and the static worldline δx = 0. Along these directions, correlation functions are… 

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References

SHOWING 1-10 OF 87 REFERENCES

Exact dynamics in dual-unitary quantum circuits

We consider the class of dual-unitary quantum circuits in 1 + 1 dimensions and introduce a notion of “solvable” matrix product states (MPSs), defined by a specific condition which allows us to tackle

Random Matrix Spectral Form Factor of Dual-Unitary Quantum Circuits

We investigate a class of local quantum circuits on chains of d−level systems (qudits) that share the so-called ‘dual unitarity’ property. In essence, the latter property implies that these systems

Entanglement transitions via space-time rotation of quantum circuits

Time evolution of quantum many-body systems typically leads to a state with maximal entanglement allowed by symmetries. Two distinct routes to impede entanglement growth are inducing localization via

Fractal, Logarithmic, and Volume-Law Entangled Nonthermal Steady States via Spacetime Duality

The extension of many-body quantum dynamics to the non-unitary domain has led to a series of exciting developments, including new out-of-equilibrium entanglement phases and phase transitions. We show

Postselection-Free Entanglement Dynamics via Spacetime Duality.

TLDR
This work proposes a method to sidestep the need to apply postselection on random measurement outcomes in order to repeatedly prepare a given output state in a wide class of nonunitary circuits by taking advantage of spacetime duality.

Correlations in Perturbed Dual-Unitary Circuits: Efficient Path-Integral Formula

Interacting many-body systems with explicitly accessible spatio-temporal correlation functions are extremely rare, especially in the absence of integrability. Recently, we identified a remarkable

Entanglement barriers in dual-unitary circuits

After quantum quenches in many-body systems, finite subsystems evolve non-trivially in time, eventually approaching a stationary state. In typical situations, the reduced density matrix of a given

From dual-unitary to quantum Bernoulli circuits: Role of the entangling power in constructing a quantum ergodic hierarchy

Deterministic classical dynamical systems have an ergodic hierarchy, from ergodic through mixing, to Bernoulli systems that are “as random as a coin-toss”. Dual-unitary circuits have been recently

Maximum velocity quantum circuits

We consider the long-time limit of out-of-time-order correlators (OTOCs) in two classes of quantum lattice models with time evolution governed by local unitary quantum circuits and maximal butterfly

Scrambling speed of random quantum circuits

Random transformations are typically good at “scrambling” information. Specifically, in the quantum setting, scrambling usually refers to the process of mapping most initial pure product states under
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