734 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
Broadband spectroscopy of quantum noise
Characterizing noise is key to the optimal control of the quantum system it
affects. Using a single-qubit probe and appropriate sequences of and
non- pulses, we show how one can characterize the noise a quantum bath
generates across a wide range of frequencies -- including frequencies below the
limit set by the probe's time. To do so we leverage an exact
expression for the dynamics of the probe in the presence of non- pulses,
and a general inequality between the symmetric (classical) and anti-symmetric
(quantum) components of the noise spectrum generated by a Gaussian bath.
Simulation demonstrates the effectiveness of our method.Comment: 23 pages. Comments welcom
Comparing the Overhead of Topological and Concatenated Quantum Error Correction
This work compares the overhead of quantum error correction with concatenated
and topological quantum error-correcting codes. To perform a numerical
analysis, we use the Quantum Resource Estimator Toolbox (QuRE) that we recently
developed. We use QuRE to estimate the number of qubits, quantum gates, and
amount of time needed to factor a 1024-bit number on several candidate quantum
technologies that differ in their clock speed and reliability. We make several
interesting observations. First, topological quantum error correction requires
fewer resources when physical gate error rates are high, white concatenated
codes have smaller overhead for physical gate error rates below approximately
10E-7. Consequently, we show that different error-correcting codes should be
chosen for two of the studied physical quantum technologies - ion traps and
superconducting qubits. Second, we observe that the composition of the
elementary gate types occurring in a typical logical circuit, a fault-tolerant
circuit protected by the surface code, and a fault-tolerant circuit protected
by a concatenated code all differ. This also suggests that choosing the most
appropriate error correction technique depends on the ability of the future
technology to perform specific gates efficiently
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