Hi everyone,
We will have a special group meeting tomorrow. This will feature Salvatore,
Ryan, and Gian presenting the APS talks they will be giving next week. The
schedule is as follows.
2.30pm - 2.50pm Salvatore
2.50pm - 3.10pm Ryan
3.10pm - 3.30pm Gian Giacomo
Please see below for titles and abstracts of their talks.
Cheers,
Jennifer
---------------------------------------
Annealing of Embedded Spin Glasses
Salvatore Mandra
We discuss recent results on thermal and quantum annealing of random spin
glasses on fully-connected graphs and on fully-connected bipartite graphs.
After the description of the embedding of their classical Hamiltonian onto
Chimera graphs, we discuss what are the optimal embedding parameters, in
relation with the signatures of the quantum phase transitions occurring
during the annealing. Finally, we compare numerical simulations and
analytical expectations for both the embedded spin glass models with
results on the non-embedded models and with runs on D-Wave Machine
installed at NASA Ames.
--------------------------------------------
The Chemical Basis of Trotter Errors in Quantum Simulations of Chemistry
Ryan Babbush
Although the simulation of quantum chemistry is one of the most anticipated
applications of quantum computing, the scaling of known upper bounds on the
complexity of these algorithms is daunting. Prior work has bounded errors
due to Trotterization in terms of the norm of the error operator and
analyzed scaling with respect to the number of spin-orbitals. However, we
find that these error bounds can be loose by up to sixteen orders of
magnitude for some molecules. Furthermore, numerical results for small
systems fail to reveal any clear correlation between ground state error and
number of spin-orbitals. We instead argue that chemical properties, such as
the maximum nuclear charge in a molecule and the filling fraction of
orbitals, can be decisive for determining the cost of a quantum simulation.
Our analysis motivates several strategies to use classical processing to
further reduce the required Trotter step size and to estimate the necessary
number of steps, without requiring additional quantum resources.
------------------------------------------------
Dimensionality reduction for adiabatic quantum optimizer in presence of
local disorder
Gian Guerreschi
Adiabatic quantum optimization (AQO) is a procedure to solve a vast class
of optimization problems by slowly changing the Hamiltonian of a quantum
system. The evolution time necessary for the algorithm to be successful
scales inversely with the minimum energy gap encountered during the
dynamics. Unfortunately, the direct calculation of such gap is strongly
limited by the exponential growth in dimensionality of quantum systems.
Although many special-purpose methods have been devised to reduce the
effective dimensionality of the Hilbert space, they are strongly limited to
particular classes of problems with evident symmetries. Here, we propose
and implement a reduction method that does not rely on any explicit
symmetry and which requires, under certain but quite general conditions,
only a polynomial amount of classical resources. A natural and important
application is the analysis of AQO in presence of local disorder. In this
respect, we show that AQO, even when affected by random noise, can still be
faster than any classical algorithm.
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