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We present a paradigm for constructing approximate quantum circuits from
reversible classical circuits that operate on many possible encodings of an
input and send almost all encodings of that input to an encoding of the correct
output. We introduce oblivious carry runways, which use piecewise addition
circuits to perform approximate encoded additions and reduce the asymptotic
depth of addition to $O(\lg \lg n)$. We show that the coset representation of

Several experimental and theoretical studies report instances of concerted or
correlated multiple proton tunneling in solid phases of water. Here, we
construct a pseudo-spin model for the quantum motion of protons in a hexameric
H$_2$O ring and extend it to open system dynamics that takes environmental
effects into account in the form of O$-$H stretch vibrations. We approach the
problem of correlations in tunneling using quantum information theory in a
departure from previous studies. Our formalism enables us to quantify the

We study the dynamics of a quantum Brownian particle weakly coupled to a
thermal bath. Working in the Schwinger-Keldysh formalism, we develop an
effective action of the particle up to quartic terms. We demonstrate that this
quartic effective theory is dual to a stochastic dynamics governed by a
non-linear Langevin equation.

Let $\mathcal{M}$ be a ($\sigma$-finite) von Neumann algebra associated with
a normal faithful state $\phi.$ We prove a complex interpolation result for a
couple of two (quasi) Haagerup noncommutative $L_p$-spaces $L_{p_0}
(\mathcal{M}, \phi)$ and $L_{p_1} (\mathcal{M}, \phi), 0< p_0 < p_1\leq
\infty,$ which has further applications to the sandwiched $p$-R\'{e}nyi
divergence.

We map the dynamics of entanglement in random unitary circuits, with finite
on-site Hilbert space dimension $q$, to an effective classical statistical
mechanics, and develop general diagrammatic tools for calculations in random
unitary circuits. We demonstrate explicitly the emergence of a `minimal
membrane' governing entanglement growth, which in 1+1D is a directed random
walk in spacetime (or a variant thereof). Using the replica trick to handle the
logarithm in the definition of the $n$th R\'enyi entropy $S_n$, we map the

We address an experimental scheme to analyze the optical bistability and the
entanglement of two movable mirrors coupled to a two-mode laser inside a doubly
resonant cavity. With this aim we investigate the master equations of the
atom-cavity subsystem in conjunction with the quantum Langevin equations that
describe the interaction of the mirror cavity. The parametric
amplification-type coupling induced by the two-photon coherence on the optical
bistability of the intracavity mean photon numbers is found and investigated.

Angular distribution of photoelectrons released by the ionization of
randomly-oriented molecules with two laser fields of carrier frequencies
$\omega$ and $2\omega$, which are linearly polarized in two mutually-orthogonal
directions, is analyzed in the perturbation limit for the case of one- vs
two-photon ionization process. In particular, we focus on the recently
predicted [Ph.V. Demekhin {\it et al.}, Phys. Rev. Lett. \textbf{121}, 253201
(2018)] forward-backward asymmetry in the photoelectron emission, which is

We present a general variational principle for the dynamics of impurity
particles immersed in a quantum-mechanical medium. By working within the
Heisenberg picture and constructing approximate time-dependent impurity
operators, we can take the medium to be in any mixed state, such as a thermal
state. Our variational method is consistent with all conservation laws and, in
certain cases, it is equivalent to a finite-temperature Green's function
approach. As a demonstration of our method, we consider the dynamics of heavy

Optical dual-pulse pumping actively creates quantum-mechanical superposition
of the electronic and phononic states in a bulk solid. We here made transient
reflectivity measurements in an n-GaAs using a pair of relative-phase-locked
femtosecond pulses and found characteristic interference fringes. This is a
result of quantum-path interference peculiar to the dual-pulse excitation as
indicated by theoretical calculation. Our observation reveals that the pathway

We consider dynamics of a Rydberg impurity in a cloud of ultracold bosonic
atoms in which the Rydberg electron can undergo spin-changing collisions with
surrounding atoms. This system realizes a new type of the quantum impurity
problem that compounds essential features of the Kondo model, the Bose polaron,
and the central spin model. To capture the nontrivial interplay of the
Rydberg-electron spin dynamics and the orbital motion of atoms, we employ a new

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