8 research outputs found
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
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
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
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
Permutationally invariant state reconstruction
Feasible tomography schemes for large particle numbers must possess, besides
an appropriate data acquisition protocol, also an efficient way to reconstruct
the density operator from the observed finite data set. Since state
reconstruction typically requires the solution of a non-linear large-scale
optimization problem, this is a major challenge in the design of scalable
tomography schemes. Here we present an efficient state reconstruction scheme
for permutationally invariant quantum state tomography. It works for all common
state-of-the-art reconstruction principles, including, in particular, maximum
likelihood and least squares methods, which are the preferred choices in
today's experiments. This high efficiency is achieved by greatly reducing the
dimensionality of the problem employing a particular representation of
permutationally invariant states known from spin coupling combined with convex
optimization, which has clear advantages regarding speed, control and accuracy
in comparison to commonly employed numerical routines. First prototype
implementations easily allow reconstruction of a state of 20 qubits in a few
minutes on a standard computer.Comment: 25 pages, 4 figues, 2 table