87 research outputs found
An Alphabet of Leakage Measures
We introduce a family of information leakage measures called maximal
-leakage, parameterized by real numbers and . The
measure is formalized via an operational definition involving an adversary
guessing an unknown function of the data given the released data. We obtain a
simple, computable expression for the measure and show that it satisfies
several basic properties such as monotonicity in for a fixed ,
non-negativity, data processing inequalities, and additivity over independent
releases. Finally, we highlight the relevance of this family by showing that it
bridges several known leakage measures, including maximal -leakage
, maximal leakage , local differential
privacy , and local Renyi differential privacy
Quantum Error Correction via Convex Optimization
We show that the problem of designing a quantum information error correcting
procedure can be cast as a bi-convex optimization problem, iterating between
encoding and recovery, each being a semidefinite program. For a given encoding
operator the problem is convex in the recovery operator. For a given method of
recovery, the problem is convex in the encoding scheme. This allows us to
derive new codes that are locally optimal. We present examples of such codes
that can handle errors which are too strong for codes derived by analogy to
classical error correction techniques.Comment: 16 page
Simplified Quantum Process Tomography
We propose and evaluate experimentally an approach to quantum process
tomography that completely removes the scaling problem plaguing the standard
approach. The key to this simplification is the incorporation of prior
knowledge of the class of physical interactions involved in generating the
dynamics, which reduces the problem to one of parameter estimation. This allows
part of the problem to be tackled using efficient convex methods, which, when
coupled with a constraint on some parameters allows globally optimal estimates
for the Kraus operators to be determined from experimental data. Parameterising
the maps provides further advantages: it allows the incorporation of mixed
states of the environment as well as some initial correlation between the
system and environment, both of which are common physical situations following
excitation of the system away from thermal equilibrium. Although the approach
is not universal, in cases where it is valid it returns a complete set of
positive maps for the dynamical evolution of a quantum system at all times.Comment: Added references to interesting related work by Bendersky et a
Compressed sensing quantum process tomography for superconducting quantum gates
We apply the method of compressed sensing (CS) quantum process tomography
(QPT) to characterize quantum gates based on superconducting Xmon and phase
qubits. Using experimental data for a two-qubit controlled-Z gate, we obtain an
estimate for the process matrix with reasonably high fidelity compared
to full QPT, but using a significantly reduced set of initial states and
measurement configurations. We show that the CS method still works when the
amount of used data is so small that the standard QPT would have an
underdetermined system of equations. We also apply the CS method to the
analysis of the three-qubit Toffoli gate with numerically added noise, and
similarly show that the method works well for a substantially reduced set of
data. For the CS calculations we use two different bases in which the process
matrix is approximately sparse, and show that the resulting estimates of
the process matrices match each ther with reasonably high fidelity. For both
two-qubit and three-qubit gates, we characterize the quantum process by not
only its process matrix and fidelity, but also by the corresponding standard
deviation, defined via variation of the state fidelity for different initial
states.Comment: 16 pages, 11 figure
Encoding a qubit into multilevel subspaces
We present a formalism for encoding the logical basis of a qubit into
subspaces of multiple physical levels. The need for this multilevel encoding
arises naturally in situations where the speed of quantum operations exceeds
the limits imposed by the addressability of individual energy levels of the
qubit physical system. A basic feature of the multilevel encoding formalism is
the logical equivalence of different physical states and correspondingly, of
different physical transformations. This logical equivalence is a source of a
significant flexibility in designing logical operations, while the multilevel
structure inherently accommodates fast and intense broadband controls thereby
facilitating faster quantum operations. Another important practical advantage
of multilevel encoding is the ability to maintain full quantum-computational
fidelity in the presence of mixing and decoherence within encoding subspaces.
The formalism is developed in detail for single-qubit operations and
generalized for multiple qubits. As an illustrative example, we perform a
simulation of closed-loop optimal control of single-qubit operations for a
model multilevel system, and subsequently apply these operations at finite
temperatures to investigate the effect of decoherence on operational fidelity.Comment: IOPart LaTeX, 2 figures, 31 pages; addition of a numerical simulatio
Efficient estimation of nearly sparse many-body quantum Hamiltonians
We develop an efficient and robust approach to Hamiltonian identification for
multipartite quantum systems based on the method of compressed sensing. This
work demonstrates that with only O(s log(d)) experimental configurations,
consisting of random local preparations and measurements, one can estimate the
Hamiltonian of a d-dimensional system, provided that the Hamiltonian is nearly
s-sparse in a known basis. We numerically simulate the performance of this
algorithm for three- and four-body interactions in spin-coupled quantum dots
and atoms in optical lattices. Furthermore, we apply the algorithm to
characterize Hamiltonian fine structure and unknown system-bath interactions.Comment: 8 pages, 2 figures. Title is changed. Detailed error analysis is
added. Figures are updated with additional clarifying discussion
Efficient measurement of quantum dynamics via compressive sensing
The resources required to characterise the dynamics of engineered quantum
systems-such as quantum computers and quantum sensors-grow exponentially with
system size. Here we adapt techniques from compressive sensing to exponentially
reduce the experimental configurations required for quantum process tomography.
Our method is applicable to dynamical processes that are known to be
nearly-sparse in a certain basis and it can be implemented using only
single-body preparations and measurements. We perform efficient, high-fidelity
estimation of process matrices on an experiment attempting to implement a
photonic two-qubit logic-gate. The data base is obtained under various
decoherence strengths. We find that our technique is both accurate and noise
robust, thus removing a key roadblock to the development and scaling of quantum
technologies.Comment: New title and authors. A new experimental section. Significant
rewrite of the theor
Entanglement quantification from incomplete measurements: Applications using photon-number-resolving weak homodyne detectors
The certificate of success for a number of important quantum information
processing protocols, such as entanglement distillation, is based on the
difference in the entanglement content of the quantum states before and after
the protocol. In such cases, effective bounds need to be placed on the
entanglement of non-local states consistent with statistics obtained from local
measurements. In this work, we study numerically the ability of a novel type of
homodyne detector which combines phase sensitivity and photon-number resolution
to set accurate bounds on the entanglement content of two-mode quadrature
squeezed states without the need for full state tomography. We show that it is
possible to set tight lower bounds on the entanglement of a family of two-mode
degaussified states using only a few measurements. This presents a significant
improvement over the resource requirements for the experimental demonstration
of continuous-variable entanglement distillation, which traditionally relies on
full quantum state tomography.Comment: 18 pages, 6 figure
Optimal control of quantum gates and suppression of decoherence in a system of interacting two-level particles
Methods of optimal control are applied to a model system of interacting two-level particles (e.g., spin-half atomic nuclei or electrons or two-level atoms) to produce high-fidelity quantum gates while simultaneously negating the detrimental effect of decoherence. One set of particles functions as the quantum information processor, whose evolution is controlled by a time-dependent external field. The other particles are not directly controlled and serve as an effective environment, coupling to which is the source of decoherence. The control objective is to generate target one- and two-qubit unitary gates in the presence of strong environmentally-induced decoherence and under physically motivated restrictions on the control field. The quantum-gate fidelity, expressed in terms of a novel state-independent distance measure, is maximized with respect to the control field using combined genetic and gradient algorithms. The resulting high-fidelity gates demonstrate the feasibility of precisely guiding the quantum evolution via the optimal control, even when the system complexity is exacerbated by environmental coupling. It is found that the gate duration has an important effect on the control mechanism and resulting fidelity. An analysis of the sensitivity of the gate performance to random variations in the system parameters reveals a significant degree of robustness attained by the optimal control solutions
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