Adam Bouland: Thesis Defense: The space around BQP
Speaker: Adam Bouland
Host: Scott Aaronson
Date: Friday, June 30, 2017
Time: 3:00 PM to 4:30 PM
Refreshments Time: 2:45 PM
Location: G575
Abstract:
This thesis explores the computational power of quantum devices from the perspective of
complexity theory. Quantum computers hold the promise of solving many problems - such as
factoring integers - exponentially faster than classical computers. The computational
power of universal quantum devices is captured by the complexity class BQP, which stands
for “bounded-error quantum polynomial time.” We hope that quantum devices will be capable
of the full power of BQP in the long term. However, quantum computers are very difficult
to build, and therefore the experimental devices of the near future may be incapable of
universal quantum computation. As a result, a number of recent works have studied the
computational power of “weak” models of quantum computers which lie “below BQP.”
The first part of this thesis examines the space "below BQP” and describes a number
of sub-universal models of quantum computation which can nevertheless perform sampling
tasks which are difficult for classical computers. We show that prior models maintain
hardness when their set of quantum operations is restricted, and describe two new models
of “weak” quantum computation which also show advantage over classical devices. A major
theme in this work is that almost any weak device can perform hard sampling tasks. We find
that almost any model which is not universal, but not known to be efficiently classically
simulable, admits a speedup over classical computing for sampling tasks under plausible
assumptions. This work can be seen as progress towards classifying the power of all
restricted quantum gate sets.
On the other hand, recent developments in quantum gravity have opened up the possibility
of modifying quantum mechanics to resolve the black hole information paradox. Inspired by
these debates, the second part of this thesis explores the space “above BQP” - i.e. the
power of quantum computers in the presence of modified theories of quantum mechanics. We
find that almost all modifications allow for drastically more power than BQP, and find
that these speedups may be related to superluminal signaling in these models.
Surprisingly, we find one model which is merely just a bit more powerful than BQP.
Inspired by this model “just above” BQP, we study and resolve an open problem in classical
complexity related to the power of statistical-zero knowledge proof systems.
Members of committee: Scott Aaronson, Aram Harrow, Ryan Williams
Relevant URL:
For more information please contact: Deborah Goodwin, 617.324.7303, <a
href="mailto:dlehto@csail.mit.edu">dlehto@csail.mit.edu</a>
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