Operator Entanglement in Local Quantum Circuits I: Chaotic Dual-Unitary  Circuits

The entanglement in operator space is a well established measure for the complexity of quantum many-body dynamics. In particular, that of local operators has recently been proposed as dynamical chaos indicator, i.e. as a quantity able to discriminate between quantum systems with integrable and chaotic dynamics. For chaotic systems the local-operator entanglement is expected to grow linearly in time, while it is expected to grow at most logarithmically in the integrable case. Here we study the dynamics of local-operator entanglement in dual-unitary quantum circuits, a class of "statistically solvable" quantum circuits that we recently introduced. We identify a class of ``completely chaotic" dual-unitary circuits where the local-operator entanglement grows linearly and we provide a conjecture for its asymptotic behaviour which is in excellent agreement with the numerical results. Interestingly, our conjecture also predicts a ``phase transition" in the slope of the local-operator entanglement when varying the parameters of the circuits.

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Operator Entanglement in Local Quantum Circuits II: Solitons in Chains of Qubits

SciPost Physics ◽

10.21468/scipostphys.8.4.068 ◽

2020 ◽

Vol 8 (4) ◽

Cited By ~ 3

Author(s):

Bruno Bertini ◽

Pavel Kos ◽

Tomaz Prosen

Keyword(s):

Closed Form ◽

Quantum Circuits ◽

Local Operator ◽

Closed Form Expression ◽

Exact Results ◽

Two Dimensional ◽

Form Expression ◽

Local Quantum ◽

Local Operators ◽

Operator Entanglement

We provide exact results for the dynamics of local-operator entanglement in quantum circuits with two-dimensional wires featuring ultralocal solitons, i.e. single-site operators which, up to a phase, are simply shifted by the time evolution. We classify all circuits allowing for ultralocal solitons and show that only dual-unitary circuits can feature moving ultralocal solitons. Then, we rigorously prove that if a circuit has an ultralocal soliton moving to the left (right), the entanglement of local operators initially supported on even (odd) sites saturates to a constant value and its dynamics can be computed exactly. Importantly, this does not bound the growth of complexity in chiral circuits, where solitons move only in one direction, say to the left. Indeed, in this case we observe numerically that operators on the odd sublattice have unbounded entanglement. Finally, we present a closed-form expression for the local-operator entanglement entropies in circuits with ultralocal solitons moving in both directions. Our results hold irrespectively of integrability.

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Exponential quantum speed-ups are generic

Quantum Information and Computation ◽

10.26421/qic13.11-12-1 ◽

2013 ◽

Vol 13 (11&12) ◽

pp. 901-924

Author(s):

Fernando G.S.L. Brandao ◽

Michal Horodecki

Keyword(s):

Quantum Circuit ◽

Black Box ◽

Quantum Circuits ◽

Query Complexity ◽

Many Body ◽

Many Body Theory ◽

Exponential Separation ◽

Local Quantum ◽

Bounded Error ◽

Body Theory

A central problem in quantum computation is to understand which quantum circuits are useful for exponential speed-ups over classical computation. We address this question in the setting of query complexity and show that for almost any sufficiently long quantum circuit one can construct a black-box problem which is solved by the circuit with a constant number of quantum queries, but which requires exponentially many classical queries, even if the classical machine has the ability to postselect. We prove the result in two steps. In the first, we show that almost any element of an approximate unitary 3-design is useful to solve a certain black-box problem efficiently. The problem is based on a recent oracle construction of Aaronson and gives an exponential separation between quantum and classical post-selected bounded-error query complexities. In the second step, which may be of independent interest, we prove that linear-sized random quantum circuits give an approximate unitary 3-design. The key ingredient in the proof is a technique from quantum many-body theory to lower bound the spectral gap of local quantum Hamiltonians.

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Many body dynamics

10.1093/oso/9780198708636.003.0018 ◽

2018 ◽

Author(s):

Joseph F. Boudreau ◽

Eric S. Swanson

Keyword(s):

Statistical Mechanics ◽

Body Problem ◽

Many Body ◽

Complex Objects ◽

Constrained Dynamics ◽

Gravitational Systems ◽

Body Dynamics ◽

System Temperature ◽

Speed Up ◽

Gravitating Systems

Specialized techniques for solving the classical many-body problem are explored in the context of simple gases, more complicated gases, and gravitating systems. The chapter starts with a brief review of some important concepts from statistical mechanics and then introduces the classic Verlet method for obtaining the dynamics of many simple particles. The practical problems of setting the system temperature and measuring observables are discussed. The issues associated with simulating systems of complex objects form the next topic. One approach is to implement constrained dynamics, which can be done elegantly with iterative methods. Gravitational systems are introduced next with stress on techniques that are applicable to systems of different scales and to problems with long range forces. A description of the recursive Barnes-Hut algorithm and particle-mesh methods that speed up force calculations close out the chapter.

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Periodically refreshed baths to simulate open quantum many-body dynamics

Physical Review B ◽

10.1103/physrevb.104.045417 ◽

2021 ◽

Vol 104 (4) ◽

Author(s):

Archak Purkayastha ◽

Giacomo Guarnieri ◽

Steve Campbell ◽

Javier Prior ◽

John Goold

Keyword(s):

Many Body ◽

Open Quantum ◽

Body Dynamics

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Ergodic and nonergodic many-body dynamics in strongly nonlinear lattices

Physical Review E ◽

10.1103/physreve.103.052213 ◽

2021 ◽

Vol 103 (5) ◽

Author(s):

Dominik Hahn ◽

Juan-Diego Urbina ◽

Klaus Richter ◽

Rémy Dubertrand ◽

S. L. Sondhi

Keyword(s):

Many Body ◽

Strongly Nonlinear ◽

Nonlinear Lattices ◽

Body Dynamics

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Stacking angle dependent multiple excitonic resonances in bilayer tungsten diselenide

Nanophotonics ◽

10.1515/nanoph-2020-0034 ◽

2020 ◽

Vol 9 (12) ◽

pp. 3881-3887

Author(s):

Ankit Arora ◽

Pramoda K. Nayak ◽

Tejendra Dixit ◽

Kolla Lakshmi Ganapathi ◽

Ananth Krishnan ◽

...

Keyword(s):

Chemical Vapour ◽

Optoelectronic Devices ◽

Interlayer Coupling ◽

Higher Order ◽

Doping Effect ◽

Many Body ◽

Si Substrate ◽

Tungsten Diselenide ◽

Body Dynamics ◽

Insight Into

AbstractWe report on multiple excitonic resonances in bilayer tungsten diselenide (BL-WSe2) stacked at different angles and demonstrate the use of the stacking angle to control the occurrence of these excitations. BL-WSe2 with different stacking angles were fabricated by stacking chemical vapour deposited monolayers and analysed using photoluminescence measurements in the temperature range 300–100 K. At reduced temperatures, several excitonic features were observed and the occurrences of these exitonic resonances were found to be stacking angle dependent. Our results indicate that by controlling the stacking angle, it is possible to excite or quench higher order excitations to tune the excitonic flux in optoelectronic devices. We attribute the presence/absence of multiple higher order excitons to the strength of interlayer coupling and doping effect from SiO2/Si substrate. Understanding interlayer excitations will help in engineering excitonic devices and give an insight into the physics of many-body dynamics.

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