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

# All

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