11 research outputs found
Optimal verification of entangled states with local measurements
Consider the task of verifying that a given quantum device, designed to
produce a particular entangled state, does indeed produce that state. One
natural approach would be to characterise the output state by quantum state
tomography; or alternatively to perform some kind of Bell test, tailored to the
state of interest. We show here that neither approach is optimal amongst local
verification strategies for two qubit states. We find the optimal strategy in
this case and show that quadratically fewer total measurements are needed to
verify to within a given fidelity than in published results for quantum state
tomography, Bell test, or fidelity estimation protocols. We also give efficient
verification protocols for any stabilizer state. Additionally, we show that
requiring that the strategy be constructed from local, non-adaptive and
non-collective measurements only incurs a constant-factor penalty over a
strategy without these restrictions.Comment: Document includes supplemental material. Main paper: 5 pages, 2 figs;
supplemental material: 16 pages, 2 fig
Quantum algorithms and the finite element method
The finite element method is used to approximately solve boundary value
problems for differential equations. The method discretises the parameter space
and finds an approximate solution by solving a large system of linear
equations. Here we investigate the extent to which the finite element method
can be accelerated using an efficient quantum algorithm for solving linear
equations. We consider the representative general question of approximately
computing a linear functional of the solution to a boundary value problem, and
compare the quantum algorithm's theoretical performance with that of a standard
classical algorithm -- the conjugate gradient method. Prior work had claimed
that the quantum algorithm could be exponentially faster, but did not determine
the overall classical and quantum runtimes required to achieve a predetermined
solution accuracy. Taking this into account, we find that the quantum algorithm
can achieve a polynomial speedup, the extent of which grows with the dimension
of the partial differential equation. In addition, we give evidence that no
improvement of the quantum algorithm could lead to a super-polynomial speedup
when the dimension is fixed and the solution satisfies certain smoothness
properties.Comment: 16 pages, 2 figure
Advances in quantum machine learning
Here we discuss advances in the field of quantum machine learning. The
following document offers a hybrid discussion; both reviewing the field as it
is currently, and suggesting directions for further research. We include both
algorithms and experimental implementations in the discussion. The field's
outlook is generally positive, showing significant promise. However, we believe
there are appreciable hurdles to overcome before one can claim that it is a
primary application of quantum computation.Comment: 38 pages, 17 Figure
The cost of solving linear differential equations on a quantum computer: fast-forwarding to explicit resource counts
How well can quantum computers simulate classical dynamical systems? There is
increasing effort in developing quantum algorithms to efficiently simulate
dynamics beyond Hamiltonian simulation, but so far exact running costs are not
known. In this work, we provide two significant contributions. First, we
provide the first non-asymptotic computation of the cost of encoding the
solution to linear ordinary differential equations into quantum states --
either the solution at a final time, or an encoding of the whole history within
a time interval. Second, we show that the stability properties of a large class
of classical dynamics can allow their fast-forwarding, making their quantum
simulation much more time-efficient. We give a broad framework to include
stability information in the complexity analysis and present examples where
this brings several orders of magnitude improvements in the query counts
compared to state-of-the-art analysis. From this point of view, quantum
Hamiltonian dynamics is a boundary case that does not allow this form of
stability-induced fast-forwarding. To illustrate our results, we find that for
homogeneous systems with negative log-norm, the query counts lie within the
curves and for and error , when outputting a history state.Comment: 8+22 pages, 3 figures. Comments welcome
Pseudoacromegaly
© 2018 Elsevier Inc. Individuals with acromegaloid physical appearance or tall stature may be referred to endocrinologists to exclude growth hormone (GH) excess. While some of these subjects could be healthy individuals with normal variants of growth or physical traits, others will have acromegaly or pituitary gigantism, which are, in general, straightforward diagnoses upon assessment of the GH/IGF-1 axis. However, some patients with physical features resembling acromegaly – usually affecting the face and extremities –, or gigantism – accelerated growth/tall stature – will have no abnormalities in the GH axis. This scenario is termed pseudoacromegaly, and its correct diagnosis can be challenging due to the rarity and variability of these conditions, as well as due to significant overlap in their characteristics. In this review we aim to provide a comprehensive overview of pseudoacromegaly conditions, highlighting their similarities and differences with acromegaly and pituitary gigantism, to aid physicians with the diagnosis of patients with pseudoacromegaly.PM is supported by a clinical fellowship by Barts and the London Charity. Our studies on pituitary adenomas and related conditions received support from the Medical Research Council, Rosetrees Trust and the Wellcome Trust