261 research outputs found
A General Transfer-Function Approach to Noise Filtering in Open-Loop Quantum Control
We present a general transfer-function approach to noise filtering in
open-loop Hamiltonian engineering protocols for open quantum systems. We show
how to identify a computationally tractable set of fundamental filter
functions, out of which arbitrary transfer filter functions may be assembled up
to arbitrary high order in principle. Besides avoiding the infinite recursive
hierarchy of filter functions that arises in general control scenarios, this
fundamental filter-functions set suffices to characterize the error suppression
capabilities of the control protocol in both the time and frequency domain. We
prove that the resulting notion of filtering order reveals conceptually
distinct, albeit complementary, features of the controlled dynamics as compared
to the order of error cancellation, traditionally defined in the Magnus sense.
Examples and implications are discussed.Comment: Paper plus supplementary material. 10 pages, 1 figure. Unnumbered
equation between 2 and 3 corrected. Results are unchange
Total correlations as fully additive entanglement monotones
We generalize the strategy presented in Refs. [1, 2], and propose general
conditions for a measure of total correlations to be an entanglement monotone
using its pure (and mixed) convex-roof extension. In so doing, we derive
crucial theorems and propose a concrete candidate for a total correlations
measure which is a fully additive entanglement monotone.Comment: 8 pages, 3 figures. Title changed, new result
On the dynamics of initially correlated open quantum systems: theory and applications
We show that the dynamics of any open quantum system that is initially
correlated with its environment can be described by a set of (or less)
completely positive maps, where d is the dimension of the system. Only one such
map is required for the special case of no initial correlations. The same maps
describe the dynamics of any system-environment state obtained from the initial
state by a local operation on the system. The reduction of the system dynamics
to a set of completely positive maps allows known numerical and analytic tools
for uncorrelated initial states to be applied to the general case of initially
correlated states, which we exemplify by solving the qubit dephasing model for
such states, and provides a natural approach to quantum Markovianity for this
case. We show that this set of completely positive maps can be experimentally
characterised using only local operations on the system, via a generalisation
of noise spectroscopy protocols. As further applications, we first consider the
problem of retrodicting the dynamics of an open quantum system which is in an
arbitrary state when it becomes accessible to the experimenter, and explore the
conditions under which retrodiction is possible. We also introduce a related
one-sided or limited-access tomography protocol for determining an arbitrary
bipartite state, evolving under a sufficiently rich Hamiltonian, via local
operations and measurements on just one component. We simulate this protocol
for a physical model of particular relevance to nitrogen-vacancy centres, and
in particular show how to reconstruct the density matrix of a set of three
qubits, interacting via dipolar coupling and in the presence of local magnetic
fields, by measuring and controlling only one of them.Comment: 19 pages. Comments welcom
Noise Detection with Spectator Qubits and Quantum Feature Engineering
Designing optimal control pulses that drive a noisy qubit to a target state
is a challenging and crucial task for quantum engineering. In a situation where
the properties of the quantum noise affecting the system are dynamic, a
periodic characterization procedure is essential to ensure the models are
updated. As a result, the operation of the qubit is disrupted frequently. In
this paper, we propose a protocol that addresses this challenge by making use
of a spectator qubit to monitor the noise in real-time. We develop a quantum
machine-learning-based quantum feature engineering approach for designing the
protocol. The complexity of the protocol is front-loaded in a characterization
phase, which allow real-time execution during the quantum computations. We
present the results of numerical simulations that showcase the favorable
performance of the protocol.Comment: The source code, datasets, and trained models that were used to
generate the results in this paper are publicly available at
https://github.com/akramyoussry/QFEN
Resource-efficient digital characterization and control of classical non-Gaussian noise
We show the usefulness of frame-based characterization and control [PRX
Quantum 2, 030315 (2021)] for non-Markovian open quantum systems subject to
classical non-Gaussian dephasing. By focusing on the paradigmatic case of
random telegraph noise and working in a digital window frame, we demonstrate
how to achieve higher-order control-adapted spectral estimation for
noise-optimized dynamical decoupling design. We find that, depending on the
operating parameter regime, control that is optimized based on non-Gaussian
noise spectroscopy can substantially outperform standard Walsh decoupling
sequences as well as sequences that are optimized based solely on Gaussian
noise spectroscopy. This approach is also intrinsically more resource-efficient
than frequency-domain comb-based methods
Zeno effect for quantum computation and control
It is well known that the quantum Zeno effect can protect specific quantum
states from decoherence by using projective measurements. Here we combine the
theory of weak measurements with stabilizer quantum error correction and
detection codes. We derive rigorous performance bounds which demonstrate that
the Zeno effect can be used to protect appropriately encoded arbitrary states
to arbitrary accuracy, while at the same time allowing for universal quantum
computation or quantum control.Comment: Significant modifications, including a new author. To appear in PR
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