113,942 research outputs found
Robust Ising Gates for Practical Quantum Computation
I describe the use of techniques based on composite rotations to combat
systematic errors in controlled phase gates, which form the basis of two qubit
quantum logic gates. Although developed and described within the context of
Nuclear Magnetic Resonanace (NMR) quantum computing these sequences should be
applicable to any implementation of quantum computation based on Ising
couplings. In combination with existing single qubit gates this provides a
universal set of robust quantum logic gates.Comment: 3 Pages RevTex4 including 2 figures. Will submit to PR
Randomized benchmarking in measurement-based quantum computing
Randomized benchmarking is routinely used as an efficient method for
characterizing the performance of sets of elementary logic gates in small
quantum devices. In the measurement-based model of quantum computation, logic
gates are implemented via single-site measurements on a fixed universal
resource state. Here we adapt the randomized benchmarking protocol for a single
qubit to a linear cluster state computation, which provides partial, yet
efficient characterization of the noise associated with the target gate set.
Applying randomized benchmarking to measurement-based quantum computation
exhibits an interesting interplay between the inherent randomness associated
with logic gates in the measurement-based model and the random gate sequences
used in benchmarking. We consider two different approaches: the first makes use
of the standard single-qubit Clifford group, while the second uses recently
introduced (non-Clifford) measurement-based 2-designs, which harness inherent
randomness to implement gate sequences.Comment: 10 pages, 4 figures, comments welcome; v2 published versio
Bifinite Chu Spaces
This paper studies colimits of sequences of finite Chu spaces and their
ramifications. Besides generic Chu spaces, we consider extensional and
biextensional variants. In the corresponding categories we first characterize
the monics and then the existence (or the lack thereof) of the desired
colimits. In each case, we provide a characterization of the finite objects in
terms of monomorphisms/injections. Bifinite Chu spaces are then expressed with
respect to the monics of generic Chu spaces, and universal, homogeneous Chu
spaces are shown to exist in this category. Unanticipated results driving this
development include the fact that while for generic Chu spaces monics consist
of an injective first and a surjective second component, in the extensional and
biextensional cases the surjectivity requirement can be dropped. Furthermore,
the desired colimits are only guaranteed to exist in the extensional case.
Finally, not all finite Chu spaces (considered set-theoretically) are finite
objects in their categories. This study opens up opportunities for further
investigations into recursively defined Chu spaces, as well as constructive
models of linear logic
What's Decidable About Sequences?
We present a first-order theory of sequences with integer elements,
Presburger arithmetic, and regular constraints, which can model significant
properties of data structures such as arrays and lists. We give a decision
procedure for the quantifier-free fragment, based on an encoding into the
first-order theory of concatenation; the procedure has PSPACE complexity. The
quantifier-free fragment of the theory of sequences can express properties such
as sortedness and injectivity, as well as Boolean combinations of periodic and
arithmetic facts relating the elements of the sequence and their positions
(e.g., "for all even i's, the element at position i has value i+3 or 2i"). The
resulting expressive power is orthogonal to that of the most expressive
decidable logics for arrays. Some examples demonstrate that the fragment is
also suitable to reason about sequence-manipulating programs within the
standard framework of axiomatic semantics.Comment: Fixed a few lapses in the Mergesort exampl
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