259 research outputs found
Ground State Spin Logic
Designing and optimizing cost functions and energy landscapes is a problem
encountered in many fields of science and engineering. These landscapes and
cost functions can be embedded and annealed in experimentally controllable spin
Hamiltonians. Using an approach based on group theory and symmetries, we
examine the embedding of Boolean logic gates into the ground state subspace of
such spin systems. We describe parameterized families of diagonal Hamiltonians
and symmetry operations which preserve the ground state subspace encoding the
truth tables of Boolean formulas. The ground state embeddings of adder circuits
are used to illustrate how gates are combined and simplified using symmetry.
Our work is relevant for experimental demonstrations of ground state embeddings
found in both classical optimization as well as adiabatic quantum optimization.Comment: 6 pages + 3 pages appendix, 7 figures, 1 tabl
Realizable Hamiltonians for Universal Adiabatic Quantum Computers
It has been established that local lattice spin Hamiltonians can be used for
universal adiabatic quantum computation. However, the 2-local model
Hamiltonians used in these proofs are general and hence do not limit the types
of interactions required between spins. To address this concern, the present
paper provides two simple model Hamiltonians that are of practical interest to
experimentalists working towards the realization of a universal adiabatic
quantum computer. The model Hamiltonians presented are the simplest known
QMA-complete 2-local Hamiltonians. The 2-local Ising model with 1-local
transverse field which has been realized using an array of technologies, is
perhaps the simplest quantum spin model but is unlikely to be universal for
adiabatic quantum computation. We demonstrate that this model can be rendered
universal and QMA-complete by adding a tunable 2-local transverse XX coupling.
We also show the universality and QMA-completeness of spin models with only
1-local Z and X fields and 2-local ZX interactions.Comment: Paper revised and extended to improve clarity; to appear in Physical
Review
The Computational Power of Minkowski Spacetime
The Lorentzian length of a timelike curve connecting both endpoints of a
classical computation is a function of the path taken through Minkowski
spacetime. The associated runtime difference is due to time-dilation: the
phenomenon whereby an observer finds that another's physically identical ideal
clock has ticked at a different rate than their own clock. Using ideas
appearing in the framework of computational complexity theory, time-dilation is
quantified as an algorithmic resource by relating relativistic energy to an
th order polynomial time reduction at the completion of an observer's
journey. These results enable a comparison between the optimal quadratic
\emph{Grover speedup} from quantum computing and an speedup using
classical computers and relativistic effects. The goal is not to propose a
practical model of computation, but to probe the ultimate limits physics places
on computation.Comment: 6 pages, LaTeX, feedback welcom
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