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We uncover a topological classification applicable to open fermionic systems
governed by a general class of Lindblad master equations. These `quadratic
Lindbladians' can be captured by a non-Hermitian single-particle matrix which
describes internal dynamics as well as system-environment coupling. We show
that this matrix must belong to one of ten non-Hermitian Bernard-LeClair
symmetry classes which reduce to the Altland-Zirnbauer classes in the closed

Quantum algorithm design usually assumes access to a perfect quantum computer
with ideal properties like full connectivity, noise-freedom and arbitrarily
long coherence time. In Noisy Intermediate-Scale Quantum (NISQ) devices,
however, the number of qubits is highly limited and quantum operation error and
qubit coherence are not negligible. Besides, the connectivity of physical
qubits in a quantum processing unit (QPU) is also strictly constrained.
Thereby, additional operations like SWAP gates have to be inserted to satisfy

In this paper, we eliminate the classical outer learning loop of the Quantum
Approximate Optimization Algorithm (QAOA) and present a strategy to find good
parameters for QAOA based on topological arguments of the problem graph and
tensor network techniques. Starting from the observation of the concentration
of control parameters of QAOA, we find a way to classically infer parameters
which scales polynomially in the number of qubits and exponentially with the

Recent progress in observing and manipulating mechanical oscillators at
quantum regime provides new opportunities of studying fundamental physics, for
example, to search for low energy signatures of quantum gravity. For example,
it was recently proposed that such devices can be used to test quantum gravity
effects, by detecting the change in the [x,p] commutation relation that could
result from quantum gravity corrections. We show that such a correction results

Private quantum money allows a bank to mint quantum money states that it can
later verify, but that no one else can forge. In classically verifiable quantum
money - introduced by Gavinsky [Gav12] - the verification is done via an
interactive protocol between the bank and the user, where the communication is
classical, and the computational resources required of the bank are classical.
In this work, we consider stateless interactive protocols in which the minting

Quantum many-body systems (QMBs) are some of the most challenging physical
systems to simulate numerically. Methods involving tensor networks (TNs) have
proven to be viable alternatives to algorithms such as quantum Monte Carlo or
simulated annealing, but have been applicable only for systems of either small
size or simple geometry due to the NP-hardness of TN contraction. In this
paper, we present a heuristic improvement of TN contraction that reduces the
computing time, the amount of memory, and the communication time. We

Quantum technologies exploit entanglement to enhance various tasks beyond
their classical limits including computation, communication and measurements.
Quantum metrology aims to increase the precision of a measured quantity that is
estimated in the presence of statistical errors using entangled quantum states.
We present a novel approach for finding (near) optimal states for metrology in
the prescence of noise, using variational techniques as a tool for efficiently

Even though foundations of the eigenstate thermalization hypothesis (ETH) are
based on random matrix theory, physical Hamiltonians and observables
substantially differ from random operators. One of the major challenges is to
embed local integrals of motion (LIOMs) within the ETH. Here we focus on their
impact on fluctuations and structure of the diagonal matrix elements of local
observables. We first show that nonvanishing fluctuations entail the presence
of LIOMs. Then we introduce a generic protocol to construct observables,

Predicting features of complex, large-scale quantum systems is essential to
the characterization and engineering of quantum architectures. We present an
efficient approach for predicting a large number of linear features using
classical shadows obtained from very few quantum measurements. This approach is
guaranteed to accurately predict $M$ linear functions with bounded
Hilbert-Schmidt norm from only $\log (M)$ measurement repetitions. This
sampling rate is completely independent of the system size and saturates

Fundamental modifications of the standard Schr\"odinger equation by
additional nonlinear terms have been considered for various purposes over the
recent decades. It came as a surprise when, inverting Abner Shimony's
observation of "peaceful coexistence" between standard quantum mechanics and
relativity, N. Gisin proved in 1990 that any (deterministic) nonlinear
Schr\"odinger equation would allow for superluminal communication. This is by
now the most spectacular and best known anomaly. We discuss further anomalies,

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