48 research outputs found
Time-dependent density functional theory for open spin chains
The application of methods of time-dependent density functional theory
(TDDFT) to systems of qubits provided the interesting possibility of simulating
an assigned Hamiltonian evolution by means of an auxiliary Hamiltonian having
different two-qubit interactions and hence a possibly simpler wave function
evolution. In this note we extend these methods to some instances of Lindblad
evolution of a spin chain.Comment: 11 pages, 6 figure
A quantum-walk-inspired adiabatic algorithm for graph isomorphism
We present a 2-local quantum algorithm for graph isomorphism GI based on an
adiabatic protocol. By exploiting continuous-time quantum-walks, we are able to
avoid a mere diffusion over all possible configurations and to significantly
reduce the dimensionality of the visited space. Within this restricted space,
the graph isomorphism problem can be translated into the search of a satisfying
assignment to a 2-SAT formula without resorting to perturbation gadgets or
projective techniques. We present an analysis of the execution time of the
algorithm on small instances of the graph isomorphism problem and discuss the
issue of an implementation of the proposed adiabatic scheme on current quantum
computing hardware.Comment: 10 pages, 5 figure
Coherent Transport of Quantum States by Deep Reinforcement Learning
Some problems in physics can be handled only after a suitable \textit{ansatz
}solution has been guessed. Such method is therefore resilient to
generalization, resulting of limited scope. The coherent transport by adiabatic
passage of a quantum state through an array of semiconductor quantum dots
provides a par excellence example of such approach, where it is necessary to
introduce its so called counter-intuitive control gate ansatz pulse sequence.
Instead, deep reinforcement learning technique has proven to be able to solve
very complex sequential decision-making problems involving competition between
short-term and long-term rewards, despite a lack of prior knowledge. We show
that in the above problem deep reinforcement learning discovers control
sequences outperforming the \textit{ansatz} counter-intuitive sequence. Even
more interesting, it discovers novel strategies when realistic disturbances
affect the ideal system, with better speed and fidelity when energy detuning
between the ground states of quantum dots or dephasing are added to the master
equation, also mitigating the effects of losses. This method enables online
update of realistic systems as the policy convergence is boosted by exploiting
the prior knowledge when available. Deep reinforcement learning proves
effective to control dynamics of quantum states, and more generally it applies
whenever an ansatz solution is unknown or insufficient to effectively treat the
problem.Comment: 5 figure
Precursors of non-Markovianity
Using the paradigm of information backflow to characterize a non-Markovian
evolution, we introduce so-called precursors of non-Markovianity, i.e.
necessary properties that the system and environment state must exhibit at
earlier times in order for an ensuing dynamics to be non-Markovian. In
particular, we consider a quantitative framework to assess the role that
established system-environment correlations together with changes in
environmental states play in an emerging non-Markovian dynamics. By defining
the relevant contributions in terms of the Bures distance, which is
conveniently expressed by means of the quantum state fidelity, these quantities
are well defined and easily applicable to a wide range of physical settings. We
exemplify this by studying our precursors of non-Markovianity in discrete and
continuous variable non-Markovian collision models.Comment: 9 pages, 4 figures. Close to published versio
Non-perturbative treatment of non-Markovian dynamics of open quantum systems
We identify the conditions that guarantee equivalence of the reduced dynamics
of an open quantum system (OQS) for two different types of environments - one a
continuous bosonic environment leading to a unitary system-environment
evolution and the other a discrete-mode bosonic environment resulting in a
system-mode (non-unitary) Lindbladian evolution. Assuming initial Gaussian
states for the environments, we prove that the two OQS dynamics are equivalent
if both the expectation values and two-time correlation functions of the
environmental interaction operators are the same at all times for the two
configurations. Since the numerical and analytical description of a
discrete-mode environment undergoing a Lindbladian evolution is significantly
more efficient than that of a continuous bosonic environment in a unitary
evolution, our result represents a powerful, non-perturbative tool to describe
complex and possibly highly non-Markovian dynamics. As a special application,
we recover and generalize the well-known pseudomodes approach to open system
dynamics.Comment: 5+4 pages, 2 figures, Close to the version accepted for publication
in Physical Review Letter
Quantum annealing and the Schr\"odinger-Langevin-Kostin equation
We show, in the context of quantum combinatorial optimization, or quantum
annealing, how the nonlinear Schr\"odinger-Langevin-Kostin equation can
dynamically drive the system toward its ground state. We illustrate, moreover,
how a frictional force of Kostin type can prevent the appearance of genuinely
quantum problems such as Bloch oscillations and Anderson localization which
would hinder an exhaustive search.Comment: 5 pages, 4 figures. To appear on Physical Review
Efficient simulation of finite-temperature open quantum systems
Chain-mapping techniques in combination with the time-dependent density
matrix renormalization group are a powerful tool for the simulation of
open-system quantum dynamics. For finite-temperature environments, however,
this approach suffers from an unfavorable algorithmic scaling with increasing
temperature. We prove that the system dynamics under thermal environments can
be non-perturbatively described by temperature-dependent system-environmental
couplings with the initial environment state being in its pure vacuum state,
instead of a mixed thermal state. As a consequence, as long as the initial
system state is pure, the global system-environment state remains pure at all
times. The resulting speedup and relaxed memory requirements of this approach
enable the efficient simulation of open quantum systems interacting with highly
structured environments in any temperature range, with applications extending
from quantum thermodynamics to quantum effects in mesoscopic systems.Comment: 5+5 pages, close to published versio