24 research outputs found

### Deep reinforcement learning for robust quantum optimization

Machine learning techniques based on artificial neural networks have been
successfully applied to solve many problems in science. One of the most
interesting domains of machine learning, reinforcement learning, has natural
applicability for optimization problems in physics. In this work we use deep
reinforcement learning and Chopped Random Basis optimization, to solve an
optimization problem based on the insertion of an off-center barrier in a
quantum Szilard engine. We show that using designed protocols for the time
dependence of the barrier strength, we can achieve an equal splitting of the
wave function (1/2 probability to find the particle on either side of the
barrier) even for an asymmetric Szilard engine in such a way that no
information is lost when measuring which side the particle is found. This
implies that the asymmetric non-adiabatic Szilard engine can operate with the
same efficiency as the traditional Szilard engine, with adiabatic insertion of
a central barrier. We compare the two optimization methods, and demonstrate the
advantage of reinforcement learning when it comes to constructing robust and
noise-resistant protocols.Comment: 9 pages, 8 figure

### Synchronization in two-level quantum systems

Recently, it was shown that dissipative quantum systems with three or more
levels are able to synchronize to an external signal, but it was stated that it
is not possible for two-level systems as they lack a stable limit cycle in the
unperturbed dynamics. At the same time, several papers, demonstrate, under a
different definition of what is synchronization, that the latter is possible in
qubits, although in different models which also include other elements. We show
how a quantum two-level system can be understood as containing a valid limit
cycle as the starting point of synchronization, and that it can synchronize its
dynamics to an external weak signal. This is demonstrated by analytically
solving the Lindblad equation of a two-level system coupled to an environment,
determining the steady state. This is a mixed state with contributions from
many pure states, each of which provides a valid limit cycle. We show that this
is sufficient to phase-lock the dynamics to a weak external signal, hence
clarifying synchronization in two-level systems. We use the Husimi Q
representation to analyze the synchronization region, defining a
synchronization measure which characterizes the strength of the phase-locking.
Also, we study the stability of the limit cycle and its deformation with the
strength of the signal in terms of the components of the Bloch vector of the
system. Finally, we generalize the model of the three-level system from in
order to illustrate how the stationary fixed point of that model can be changed
into a limit cycle similar to the one that we describe for the two-level
system.Comment: 7 pages, 6 figure

### Spin echo without an external permanent magnetic field

The spin echo techniques aim at the elimination of the effect of a random
magnetic field on the spin evolution. These techniques conventionally utlize
the application of a permanent field which is much stronger than the random
one. The strong field, however, may also modify the magnetic response of the
medium containing the spins, thus altering their ``natural'' dynamics. We
suggest an iterative scheme for generating a sequence of pulses which create an
echo without an external permanent field. The approximation to the ideal echo
improves with the sequence length

### The influence of measurement error on Maxwell's demon

In any general cycle of measurement, feedback and erasure, the measurement
will reduce the entropy of the system when information about the state is
obtained, while erasure, according to Landauer's principle, is accompanied by a
corresponding increase in entropy due to the compression of logical and
physical phase space. The total process can in principle be fully reversible. A
measurement error reduces the information obtained and the entropy decrease in
the system. The erasure still gives the same increase in entropy and the total
process is irreversible. Another consequence of measurement error is that a bad
feedback is applied, which further increases the entropy production if the
proper protocol adapted to the expected error rate is not applied. We consider
the effect of measurement error on a realistic single-electron box Szilard
engine. We find the optimal protocol for the cycle as a function of the desired
power $P$ and error $\epsilon$, as well as the existence of a maximal power
$P^{\max}$.Comment: 5 pages, 4 figure

### Cooling by Heating: Restoration of the Third Law of Thermodynamics

We have made a simple and natural modification of a recent quantum
refrigerator model presented by Cleuren et al. in Phys. Rev, Lett.108, 120603
(2012). The original model consist of two metal leads acting as heat baths, and
a set of quantum dots that allow for electron transport between the baths. It
was shown to violate the dynamic third law of thermodynamics (the
unattainability principle, which states that cooling to absolute zero in finite
time is impossible), but by taking into consideration the finite energy level
spacing in metals we restore the third law, while keeping all of the original
model's thermodynamic properties intact.Comment: 7 pages, 5 figure

### Quantum particle in a split box: Excitations to the ground state

We discuss two different approaches for splitting the wavefunction of a
single-particle-box (SPB) into two equal parts. Adiabatic insertion of a
barrier in the center of a SPB in order to make two compartments which each
have probability 1/2 to find the particle in it is one of the key steps for a
Szilard engine. However, any asymmetry between the volume of the compartments
due to an off-center insertion of the barrier results in a particle that is
fully localized in the larger compartment, in the adiabatic limit. We show that
rather than exactly splitting the eigenfunctions in half by a symmetric
barrier, one can use a non-adiabatic insertion of an asymmetric barrier to
induce excitations to the first excited state of the full box. As the barrier
height goes to infinity the excited state of the full box becomes the ground
state of one of the new boxes. Thus, we can achieve close to exact splitting of
the probability between the two compartments using the more realistic
non-adiabatic, not perfectly centered barrier, rather than the idealized
adiabatic and central barrier normally assumed.Comment: 6 pages, 5 figure

### Bloch-sphere approach to correlated noise in coupled qubits

By use of a generalized Bloch vector construction, we study the decoherence
of a system composed of two interacting qubits in a general noisy environment.
In particular, we investigate the effects of correlations in the noise acting
on distinct qubits. Our treatment of the two-qubit system by use of the
generalized Bloch vector leads to tractable analytic equations for the dynamics
of the 4-level Bloch vector and allows for the application of geometrical
concepts from the well known 2-level Bloch sphere. We find that in the presence
of correlated or anticorrelated noise, the rate of decoherence is very
sensitive to the initial two-qubit state, as well as to the symmetry of the
Hamiltonian. In the absence of symmetry in the Hamiltonian, correlations only
weakly impact the decoherence rate.Comment: 15 pages, 3 figure